Observing the effect of interprocess communication in auto controlled ant colony optimization-based...

CONCURRENCY AND COMPUTATION PRACTICE AND EXPERIENCEConcurrency Computat Pract Exper 2014 26241ndash270Published online 2 January 2013 in Wiley Online Library (wileyonlinelibrarycom) DOI 101002cpe2977

Observing the effect of interprocess communication in auto controlledant colony optimization-based scheduling on computational grid

Pawan Kumar Tiwari and Deo Prakash Vidyarthidagger

School of Computer and Systems Sciences Jawaharlal Nehru University New Delhi India

SUMMARY

Computational grids allow the sharing of geographically distributed computational resources in an efficientreliable and secure manner Grid is still in its infancy and there are many problems associated with the com-putational grid namely job scheduling resource management information service information securityrouting fault tolerance and many more Scheduling of jobs on grid nodes is an NP-class problem warrantingfor heuristic and meta-heuristic solution approach In the proposed work a meta-heuristic technique autocontrolled ant colony optimization has been applied to solve this problem The work observes the effectof interprocess communication in process to optimize turnaround time of the job The proposed modelhas been simulated in Matlab For the different scenarios in computational grid results have been analyzedResult of the proposed model is compared with another meta-heuristic technique genetic algorithm that hasbeen applied for the same purpose It is found that auto controlled ant colony optimization not only givesbetter solution in comparison to genetic algorithm but also converges faster because initial solution itselfis good because of constructive and decision-based policy adapted by the former Concurrency and Compu-tation Practice and Experience 2012copy 2012 Wiley Periodicals Inc

Received 27 April 2012 Revised 8 November 2012 Accepted 9 November 2012

KEY WORDS scheduling ant colony optimization arrival rate processing rate interprocesscommunication turnaround time

1 INTRODUCTION

A computational grid deals primarily with the computational requirement of the jobs [1] It is definedas a hardware and software infrastructure that provides dependable consistent pervasive andinexpensive access to high-end computational capabilities despite the geographical distribution ofboth resources and the users At one end of the grid are the end users or the participants of the gridand at the other end lies the grid infrastructure These users may demand the execution of jobs using anintelligent interface The grid middleware searches for the appropriate resources from the pool ofregistered resources of the grid Depending on the execution policies of the grid and the requirements ofthe job the job will be eventually scheduled on one of the suitable resources Thus the grid usersvisualize the grid as an enormous source of computational power that may execute the job efficiently

Scheduling over the grid is entirely different from the scheduling of uniprocessor system that has asingle objective of utilizing CPU maximally by keeping it busy all through [2 3 27 28] Often in gridsystem two types of scheduler exist local and global scheduler The latter one tries to meet therequirement of the different users by sending the jobs to different clusters of the grid keeping inmind the load balancing factor [4 5] The local scheduler allocates the jobstasks on differentprocessors by adopting some scheduling policy considering the local factors at any instance

Correspondence to Deo Prakash Vidyarthi School of Computer and Systems Sciences Jawaharlal Nehru UniversityNew Delhi India

daggerE-mail dpvjnuacin

Copyright copy 2012 John Wiley amp Sons Ltd

242 P K TIWARI AND D P VIDYARTHI

Grid scheduling is a well-known NP-class problem having a very large search space of possiblesolutions [6] To find the near optimal solution many soft computing techniques have been appliedas discussed in literature [20 22 29 30] Ant colony optimization (ACO) is one such technique Inthe ant algorithm category it is the latest successful algorithm [24 25] ACO can provide a betteroptimal solution for all combinatorial optimization problems but the mapping of the parameters ofthis technique with the tuned constraint of the problem is a tough task [7ndash11]

Many models that use ACO for solving grid scheduling problem are focused on the minimizationof turnaround time (TAT) Task scheduling for minimization of TAT in computational grid is afundamental issue for fetching high-end capacity to achieve better performance It is discussed in[12ndash15] The optimal usage of large number of resources is the main objectives of these scheduling policies

Interprocess communication (IPC) plays an important role in scheduling the jobs over the grid IPCaffects the time taken in job execution and thus warrants a proper grid scheduling Very few studieshave been made to study the effect of IPC in scheduling Communication contention in task schedulinghas been discussed by Sinnen and Sousa [23] In [22] effect of IPC has been observed using anothersoft computing techniques genetic algorithm (GA) We have proposed a grid scheduler using a variantof ACO and observed the effect of IPC on the performance of grid scheduling

The outline of the paper is as follows After the introduction in Section 1 the problem is stated andelaborated in Section 2 Auto controlled ACO-based scheduling model is presented in Section 3whereas experimental evaluation and observation is described in Section 4 Conclusion of the workis drawn in Section 5

2 THE PROBLEM

Scheduling of the tasks is an integrated part of any computing systems An intensive research has beencarried out in this area and the results have been widely publicized With the emergence of Open GridService Architecture (OGSA) in computational grid newer scheduling models and algorithms are indemand for addressing new concerns in the grid environment The complexity of schedulingincreases with the size of the grid that makes it highly infeasible

Three phases of scheduling are involved in grid Phase one discovers the set of different resourcesaccording to the specialty of the jobtask Phase two collects the information of queuing lengthreliability and the speed of the node to match it with the application In the third phase allocationand execution takes place [12]

A global grid scheduler often called resource broker acts as an interface between the user and thedistributed resources and hide the complexities of computational grid It performs all the three phasesof scheduling in grid environment Besides it is also responsible for monitoring and tracking theprogress of application execution along with adapting to the changes in the run time environment ofthe grid variation in resource share availability and failures Grid environment is composed bydifferent types of processing nodes storage units scientific instrumentation and informationbelonging to different research organizations and so forth Each time a virtual organization usersubmits a job in the grid it has to make a reference with resource broker There is also a localscheduler on each site of the nodes that takes care of the scheduling inside the node In our problemwe have assumed that local scheduler works in first come first serve manner [1ndash4 16 17] althoughit may adopt in any other local policy

The scheduling parameters might be throughput system utilization TAT waiting time responsetime fairness level of security availability and so forth [12] The factors that may affect thescheduling decisions are as follows

Speed of the node Speed of the node plays an important role in optimizing most of the aforemen-tioned discussed parameters

Number of the nodes It is expected that as the number of node increases grid will becomemore powerful for doing different type of jobs in a faster way There is a tradeoff in costmanagement and execution time

Copyright copy 2012 John Wiley amp Sons Ltd Concurrency Computat Pract Exper 2014 26241ndash270DOI 101002cpe

OBSERVING THE EFFECT OF IPC IN AUTO CONTROLLED ACO-BASED SCHEDULINGON COMPUTATIONAL GRID

243

Number of processors Obviously the more the number of processors in a node the more will be thestrength of execution

Exiting workload It is the second most important parameter that is useful in deciding the allocationof a task on a particular machinenode The more the pre-assigned workload the higher will bethe TAT of the current job

Local scheduling policy of the node Global grid scheduler allocates the job on appropriate nodeshowever there is a local scheduler to all the nodes that affects the local scheduling decision Itmay be first come first serve round-robin scheduling rank-based scheduling and so forth

Degree of interaction in the job

There are two important scenarios in this situation

(1) How many modulessubjobs of the job need interaction(2) What is the amount of interaction among the different modules of the job

It is noteworthy that TAT increases as (1) or (2) increases

Load on the network In OGSA load of the network is time-dependent Effect of the load of thenetwork can be seen on TAT especially in the case of IPC The higher the load of the networkat any instance of time the higher will be the TAT

As mentioned earlier performance of the scheduling algorithm is affected by all of theaforementioned parameters but it will be more interesting to observe how the degree of interactionamong the jobs may affect the performance of the scheduling algorithm We have studied the effectof IPC in the proposed scheduling algorithm for the computational grid Auto controlled ACO(AACO) has been utilized for this purpose

3 THE PROPOSED MODEL

The proposed model considers optimization of the TAT (total processing time) of the job submitted tocomputational grid for execution to observe the effect of IPC

31 Turnaround time

Turnaround time is the time when a job is submitted for the execution in the grid and finally completesthe execution Scheduler allocates the job consisting of taskssubjobs onto the computing nodes of thegrid and optimizes the TAT It has been quantified in the following subsection

32 Fitness function

In OGSA different users submit their jobs unaware of others So there may be a queue on each site or on thenodes of the computational grid According to the queuing theory [18 19] in general scheduling problem incomputational grid will fall under MMk system Arrival of jobtask on node i follow a poison distributionwith arrival rate li their execution process follows an exponential distribution with service rate mi

Let l and m be the average arrival and service rate of an individual site at any given timerespectively then average waiting time is given by l

m mleth THORN and average waiting time plus service

time is given by lm mleth THORN thorn 1

m that after simplification gives 1mleth THORN known as littlersquos theorem

Let us assume that a user submits a job that has l tasks on a computational grid having m nodesArrival and service rates of the ith node is li and mi respectively Average waiting time includingservice time of the ith node may be given by

Ti frac14Xljfrac141

limi mi lieth THORN thorn

1mi

Njwji (1)



where wji is equal to 1 if jth task is allocated on ith machine and 0 otherwiseNj is the number of instructionsin jth task So finishing time T of the whole job according to this allocation will be as in Equation (2)

T frac14 maxmifrac141 Tieth THORN (2)

Here m is the total number of nodes involved in the computationSubstituting the value of Ti from Equation (1) into Equation (2) we obtain the following Equation (3)

T frac14 maxmifrac141Xljfrac141


1mi

Njwji

(3)

Because our objective is to minimize finishing time so the objective function in our case will be

F frac14 Min Teth THORN (4)

Value of T will be obtained from Equation (3) and minimum is taken over all possible schedules oftasks that is all possible values of allocation of tasks j with machine i Fitness function formaximization can be written as follows

L frac14 1T

(5)

According to Equation (5) L will be the maximum for the schedule that has minimumcorresponding value of T

The aforementioned derived fitness function does not consider the IPC overhead [20] This functionis modified by adding IPC in this For this we consider an extra input in the form of the complete list ofmodules that requires communication with each other Also the amount of communication that ishow many bit of communication is required between them

Let lki and mki be the arrival rate and service rate of the network between the link of kth node and ithnode of the grid then the average waiting time on this link for communication would be

lkimki mki lkieth THORN where lki frac14 lik mki frac14 mik (6)

So if rth task is allocated on kth node and sth task is allocated on ith node then total communicationtime on the link will be

lkimki mki lkieth THORN thorn

1mki

Crs (7)

where Crs is the bit of communication between rth and sth task obtained from the communication costmatrix C 1le r sle l 1le i klem and Cii= 0

Total communication elapsed for all possible tasks between link of ith and kth node can be obtained as

Xlrfrac141

Xlsfrac14rthorn1

Crswkrwislki

mki mki lkieth THORN thorn1mki

(8)

where wkr assigns a value of 1 if rth task is assigned on machine k and 0 otherwise and l is the total numberof moduletasks in the job submitted by the user Thus total time Ω taken by the computational grid forcommunication between the modules will be as follows

Ω frac14 Max1lei klemi lt k

Xlrfrac141

Xlsfrac14rthorn1

lkimki mki lkieth THORNthorn 1mki

0BB

1CCACrswkrwis

2664

3775 (9)

where m is the total number of machines in the given computational grid and l is the total number of tasksin the submitted job



245

Let us consider that each node is not directly linked with the other Further let h(ki) be the set thatconsist of the node (necessary for establishing communication between node k and i) in an increasingorder starting from node k and ending with node i in such a way that each predecessor in the setsequence is directly connected with its successor and let hd(ki) be the hamming distance betweenkth and ith node It can be written mathematically as h(ki) = h0(ki) h1(ki) hc(ki) where c isthe hamming distance between node k and i that is c= hd(ki) h0(ki) = k hc(ki) = i

In this case Ω may be modified as follows


Xlrfrac141

Xlsfrac14rthorn1

Xhd kieth THORN1

tfrac140f l meth THORN

( )Crswkrwis

(10)

where f l meth THORN frac14 lht kieth THORNhtthorn1 kieth THORN

mht kieth THORNhtthorn1 kieth THORN mht kieth THORNhtthorn1 kieth THORNlht kieth THORNhtthorn1 kieth THORN thorn 1

mht kieth THORNhtthorn1 kieth THORN

Our objective function will be modified as follows

F frac14 Min1lei klemi lt k

T thorn Ωfrac12 (11)

Standard fitness function according to Equation (10) for our problem will be

L frac14 1T thorn Ω

(12)

According to Equation (12) L will be the maximum for the schedule that has the minimumexecution plus communication time

33 The model

The proposed model minimizes the time of the job submitted for the execution It uses AACO for thispurpose The various modules of the AACO specific to this problem are as follows [12]

The computational grid consists of n nodesmachines These machines are distributed globally andsituated at large distances A user has submitted a job that consists of l parallel tasks and wants to finishthe job as quickly as possible Because in computational grid there are many jobs running on themachines we consider arrival rate of the tasks on each machine to follow poison distribution andtheir execution to follow exponential distribution According to arrival and service rate on eachmachine there will be a queue of certain length on each node So in the first part of the model wewill allocate the tasks on different machines by applying AACO method and improve it iteratively

To simplify the model some assumptions have been laid down as follows

bull Each node has a single processorbull Arrival of jobtask on each node follow a poison distribution with arrival rate li their executionfollow a exponential distribution with service rate mi and the task process in each individualmachine is an MM1 queuing system

bull All the tasks in the submitted job are parallel in naturebull We have not considered the setup time that will take place just before the scheduling processbull Arrival rate of process on each individual machine may vary with respect to the time Howeverservice rate of each node is same with respect to time

bull Assigning a task to a particular machine will be seen as one step move of the antbull Path of a single ant will be completed when it will assign all the tasks to the machinesbull Whenever the ant will allocate a task it will fall under allocated task and next task will be chosenfrom nonallocated task



The various steps of AACO for this purpose are as follows

1 Construct the representation graph of the problem in the following notation G= ((T N) L)where T consists of the set of subjobtasks that is T= T1 T2 Tl and N will consist ofset of machinesnodes that is N = 1 2 n L= T11 T12 T1n T21 T21 T2n Tl1 Tl2 Tln Here L denotes the set of all possible moves by the ant that is Tln will denotethat task l is assigned on machine n

2 Initially ant may take any task Ti from the set T randomly and allocate it on a machine m accord-ing to the state transition rule After allocation of the first task on machine any other task k willupdate the corresponding kj value in the heuristic matrix through the memory of ant s that onetask is already allocated and decrease the desirability up to the considerable remark

3 Initial pheromone value tij= t0 8 i j where t0 frac14 min1leileleth TiXl

ifrac141Ti THORN

4 Value of q0 is auto controlled in the interval (085 095) in each iteration according to the fitnessof earlier iteration where q0 is the state selection threshold point of AACO algorithm Thisinterval provides useful information about exploration and exploitation ratio Empirically wefound that this range of interval offers good results

5 Initially heuristic information value ij of allocating the task i to the machine j will be equal toij frac14 1

etmeth THORNij 8i 2 T j 2 N where (etm)ij is the execution time of task i on machine j6 Each individual ant will reach to their destination that is will construct the whole path and it can

be seen as allocation of all the tasks to some machines So there will be exactly l steps incompleting the whole tour where l is the cardinality (T)

7 Each ant have l temporary memory locations corresponding to each machine j for storing thebusy time period denoted as (btp)j (j = 1 2 n) of each machine separately at each step ofthe ant Busy time period (btp)j of each machine will be updated at each constructive step ofthe ant For convenience at each constructive step of the ant busy time period of jth machinehas been denoted by (btp)j(step(h)) (h = 0 1 2 l 1) It will be the cumulative sum of theoverall time consumed by the machine j for this constructed particular schedule up to this stepFor example suppose there are four machines in a grid and there are 10 tasks in the job thenthere will be 10 steps (including zeroth step of the ant) in constructed tour of the ant Againsuppose up to fifth step constructed schedule by a particular ant is (221132 ) and allocated taskson these machines up to this step are (791324) then

btpeth THORN2 step 0eth THORNeth THORN frac14 0btpeth THORN2 step 1eth THORNeth THORN frac14 etm 7 2eth THORNbtpeth THORN2 step 2eth THORNeth THORN frac14 etm 7 2eth THORN thorn etm 9 2eth THORNbtpeth THORN2 step 3eth THORNeth THORN frac14 etm 7 2eth THORN thorn etm 9 2eth THORNbtpeth THORN2 step 4eth THORNeth THORN frac14 etm 7 2eth THORN thorn etm 9 2eth THORNbtpeth THORN2 step 5eth THORNeth THORN frac14 etm 7 2eth THORN thorn etm 9 2eth THORN andbtpeth THORN2 step 6eth THORNeth THORN frac14 etm 7 2eth THORN thorn etm 9 2eth THORN thorn etm 4 2eth THORN

but because machine 4 is yet not participated in the constructed schedule up to this step so (btp)4(step(6)) = 0 and for machine 3 (btp)3(step(4)) = 0 But (btp)3(step(5)) = etm(23) which will alwaysmemorize the ant that machine 4 is not used up to the fifth step Still at next step the selection ofmachine is only determined by the selection rule given at point no-9 But the desirability ofmachine participated in earlier steps decreases with a considerable amount according to the heuristicfunction given at point no-8 which plays a major role in selecting the machine as given at pointno-9 One point should be noted here is that although li arrival rate on machine i is variable withrespect to time and is different for eachmachine in a very small interval of time (let us say comparablewith the time taken in constructing a whole tour of ant) it can be assumed to be fixed to li Forsimplicity we have updated this waiting time in etm matrix that is updated with respect to time



247

8 Heuristic information value will be calculated in the next step according to the following formulaij step heth THORNeth THORN frac14 1

btpeth THORNj step h1eth THORNeth THORNthorn etmeth THORNij (h = 1 2 n 1) where (btp)j(step(h 1)) is the busy time

period of machine j up to step (h 1) Here we see that the changes will be reflected in only nvalues of

ij out of (l n) entries ij(step(0)) will be taken from initial heuristic matrix given atpoint no 5 We would like to elaborate the use of heuristic information with the same example thatis given at point no-7 Value of ij will be stored in a heuristic information matrix of size l n

12 step 1eth THORNeth THORN frac14 1btpeth THORN2 step 0eth THORNeth THORN thorn etmeth THORN12

frac14 1etmeth THORN12


frac14 1etmeth THORN72 thorn etmeth THORN12

From the aforementioned calculation it is clear that the value of the heuristic information functionfor allocating the task 1 at step 1 was high in comparison with step 2 because in step 1 task 7 isallocated on the machine 2 It should be noted here that ij is calculated before allocation of the taskat each step although (btp)j is calculated after allocation of the task in each step

9 Each machine has a busy time period array In each move of the ant out of n options only one(btp)j of the corresponding machine will be updated that has been selected according to ACOchoice rule (as explained at point no-7)

SJi frac14 argmax i=2tabuketh THORN tijijn o

if qleq0RWS otherwise

(

where RWS is the roulette wheel scheme ith task of the corresponding ant will be allocated to thejth machine and corresponding j will be selected according to the aforementioned formula Forelaborating this formula we again take the same example that is given at point no-7 Up to fifthstep tabuk of that particular ant will consist of 7 9 1 3 2 4 so in sixth step value of i will beselected only from the set 5 6 8 10 although value of j will be selected from all four machinesthat is from the set 1 2 3 4 So out of all 16 values one will be selected according to theaforementioned formula and the value of the corresponding i and j will be updated (let us say task8 is selected and allocated on the machine 3) Then current schedule of that particular ant up tothis step will be (2211323 ) and value of tabuk that will be used at seventh step will be(7913248) Hence at seventh step value of i will be selected only from the set 5 6 10 Butagain value of j will be selected from all four machines that is from the set 1 2 3 4 accordingto the aforementioned formula and so on till the ant completed their whole tour

10 After each iteration calculate the fitness function for each complete tour constructed by thedifferent ants Update the value of pheromones that are responsible for the best tour by theamount 1

T iteminto the edges belonging to the best schedule in each iteration from the following equation

tij 1 geth THORNtij thorn g 1

T itemin

0legle1

Where Tmin is the turn around time of best schedule at previous iteration

11 In case of IPC although the initial allocation of task on nodes has been carried out in the way asdescribed earlier but the evaluation of the fitness of the schedule generated by different ants istested by new modified fitness function In this scenario schedule of an ant that is better forwithout communication (WC) case may not be better for IPC case For each scheduleminimum expensive route of IPC for different module of the task has been obtained byDijkstrarsquos shortest path algorithm

We illustrate this step for Variable Network Constant Message (VNCM) case through an example(other cases have also similar approach) Suppose for simplicity there are only 12 nodes in a gridsystem and there are seven tasks in a submitted job at any instance Suppose we are releasing six



ants at a particular iteration The corresponding schedule of all six different ants and theircorresponding TAT for WC case and VNCM case is given in Table I First entry of each bracketof the schedule is denoting the task number and second entry of each bracket is denoting thecorresponding node on which this particular task is scheduledAlthough ant number 6 is providingbetter solution for WC case (261220) but the solution obtained by this ant in VNCM case is1220429 whereas ant number 2 that was not good for WC case is providing better solution inVNCM case (1218214) So in VNCM case the following seven entries (which is offeredby ant number 2) out of (7 12) entries of pheromone matrix will be updated at this iterationt (7 2) t (4 5) t (5 12) t (3 8) t (2 11) t (1 2) and t (6 6) instead of the following entriest (4 2) t (5 5) t (6 12) t (7 8) t (2 11) t (1 6) and t (3 2) which is provided by ant number 6

and is updated in case of WC The updating amount of step 10 for VNCM case is 1T itemin

= (11218214) instead of 1T itemin

= (1261220) as in the case of WC The busy time period of

machine (btp)j and heuristic information ij will be calculated in a similar fashion asexplained in the previous steps for the WC case (See Appendix B for details)

12 In each iteration value of evaporation coefficient g is auto controlled in the interval (01 04)dynamically in accordance to the performance of ants as a group in previous iteration

Table I Description of schedule

Schedule generated by ants WC (TAT) VNCM (TAT)

Ant 1 (12) (45) (312) (68) (711) (26) (53) 341286 1300494Ant 2 (72) (45) (512) (38) (211) (12) (66) 290364 1218214Ant 3 (72) (25) (612) (18) (511) (46) (33) 292921 1252129Ant 4 (22) (35) (512) (48) (111) (76) (63) 290364 1249573Ant 5 (22) (45) (612) (38) (111) (76) (52) 299548 1227397Ant 6 (42) (55) (612) (78) (211) (16) (32) 261220 1220429

WC without communication TAT turnaround time VNCM Variable Network Constant Message

4 EXPERIMENTAL EVALUATION

This section evaluates the performance of the proposed model Different values of the input parameters aregenerated randomly between a certain feasible limit Summary of all the observations and effect of varyingthe range of one parameter while keeping the other constant have been studied Five different networkenvironments as given in the succeeding text have been considered broadly for various experiments

Case 1 In this case scheduling of only parallel independent tasks has been considered For evaluating thequality of solution of different schedules generated by different ants fitness function (5) has beenused The graph for this without communication case is depicted in blue line and is abbreviated asWC in all figures

Case 2 This case considers dependent parallel tasks of the job submitted by the users Thuscommunication between different tasks of the job is effective There are four differenttypes of instances in this category

Case 21 Variable range of IPC over constant load of network link It is represented in yellowline and abbreviated as CNVM (Constant Network Variable Message) in all thefigures

Case 22Constant range of IPC over constant load of network link It is represented in black lineand abbreviated as CNCM (Constant Network Constant Message) in all the figures

Case 23 Variable range of IPC over variable load of network link It is represented in red lineand abbreviated as VNVM (Variable Network Variable Message) in all the figures

Case 24Constant range of IPC over variable load of network link It is represented in green lineand abbreviated as VNCM in all the figures

Effect of IPC is also dependent on the connection links between different nodes For this we havecreated a link of the graph For a given number of nodes m the number of network links is 2m After



249

the construction of the graph we have distributed the network load and bandwidth randomly in theprescribed range Hamming distance is calculated within the program Hamming distance hd istotally dependent on the constructed graph so we have not mentioned the range of the hammingdistance in any of the experiment Normally we have observed that hamming distance varies up to10 for 100 numbers of nodes In the following three figures the number of node has been fixed to10 but the network connections in all three figures are different and hence their hamming distancevaries accordingly For a given set of experiment graph is assumed to be fixed (Figure 1)

Fitness function (12) is used for evaluating the different solutions generated by ants for theaforementioned four environments (case 21 to 24) Description of different variables their notationmeaning and the prescribed range have been listed in Table II The experiments with the giveninput data have been conducted for 20 to 200 numbers of nodes in the grid We have shown thegraph for the experiment only with 20 30 50 and 70 nodes Range of the data has been presentedin the form of a table

41 Effect of increase of range of IPC at a particular instance on turnaround time

In this experiment we have fixed all other variable input of the grid Only the range of IPC has beenchanged Two observation graphs have been shown for TAT in Figures 2 and 3 for all fiveenvironments respectively Various inputs are as follows

Table II Description of the input

Variable Meaning Range

m Number of nodes in the grid 10 to 200l Number of tasks in the job 20 to 1000Ant Number of artificial ants 2 to 10Itn Number of iteration 20 to 200mi[] Speed of processors in(MIPS) (101ndash300)li[] Load of processors in (MIPS) (1ndash100)lrs[] Network load in (MBPS) 60ndash90mrs[] network bandwidth (in MBPS) 100ndash120Task[]size Task size (MIs) 2000ndash50000Crs[] Message size (in Mega Bits) 0ndash200g Pheromone decay parameter 01ndash04q0 State selection threshold point 085 to 095hd Hamming distance Dependent on the graph

Figure 1 Variation of hamming distance for 10 numbers of nodes in different network setup


Figure 2 Observation graph of message communication range 0ndash30Mb on turnaround time


Number of machines = 50 number of tasks = 50 range of ant = 2ndash5 range of arrival rate = 1ndash100MIPSrange of processing speed = 200ndash300MIPS range of task size = 2000ndash30000Million Instructions rangeof network load= 60ndash90Mbps range of bandwidth= 100ndash120Mbps

1 From Figures 2 and 3 it is observed that as the size of message of IPC increases the TAT withcommunication (all four different cases) is elevated with a considerable amount

2 It is also observed that differences in the graph of all the four instances that consider IPC dependon the range of message size For example for message communication range 0ndash200Mb amutual difference in all the four instances of the graph was more visible rather than that whichconsiders 0ndash30Mb IPC

3 It is clear from the aforementioned two figures that for the same data set there is no effect on WCcase for increasing the amount of IPC Although solution may converge at different iteration indifferent run because of stochastic nature of algorithm

4 Mutual differences in all the four cases that consider IPC also depend on the range of networkload and range of network bandwidth

5 Turnaround time of case 22 is more than the TAT of case 21 that is black lines will never liebelow the yellow line in all the conditions

6 Turnaround time of case 24 is more than the TAT of case 22 that is green line will never liebelow the red line in all the conditions

7 There is no comparison between case 21 with that of case 23 and case 24 Similarly there is nocomparison between case 24 with that of case 21 and 22 that is sometimes we see that lowerlimit line of case 2 (for all four cases) is yellow line but in some other experiment lower limitline of case 2 (for all four cases) is red lines Similarly upper limit line of case 2 (for all fourcases) is exchanged by green and black lines In many experiments we observe only two lines




251

of case 2 (for all four cases) in place of four lines because some lines coincides with the otherline but the condition of case 1 and case 2 (for all four cases) is always true

42 Effect of range of task size on turnaround time

This experiment considers number of machines in grid and number of tasks to be fixed Twoobservation graphs have been shown for the TAT respectively in Figures 4 and 5 with all fivepossibilities as mentioned in Section 4 for different size of task range Various inputs are as follows

Number of machines = 20 number of tasks = 50 range of ant = 2ndash5 range of arrival rate = 1ndash100MIPSrange of processing speed= 200ndash300MIPS range of load of network= 60ndash90Mbps range of load ofbandwidth= 100ndash120Mbps range of IPC=0ndash200Mb

It is observed from the Figures 4 and 5 two graphs that when the range of task size was 2000ndash8000the TAT varies in the range of 1171231 to 1027453 unit of time when the IPC is effective whereasTAT varied from 869456 to 765421 unit of time without IPC When the range of task size is increasedfrom 2000 to 50000 we observe that the TAT varies in the range of 5373659 to 4301430 unit of timewith IPC and varying from 4608038 to 3535809 unit of time without IPC

In addition the following observation has been made

1 Turnaround time of case 22 is more than the TAT of case 21 that is black line will never liebelow the yellow line in all the condition

2 Turnaround time of case 24 is more than the TAT of case 22 that is green line will never liebelow the red line in all the condition

3 It is also observed that differences in the graph of all the four instances that consider IPC depends onthe range of task size and range of IPC For example for message communication range 0ndash200Mbmutual differences in all the four instances of the graph that consider task size of range2000ndash8000Mb is more visible rather than that of Figure 2 that consider range of task size2000ndash50000

Figure 4 Turnaround time observation for certain task size range

Figure 5 Turnaround time observation for different task size range



4 From Figures 4 and 5 it is clear that as the size of task is generated in higher range TAT of allfive instances increases

43 Effect of increased number of tasks on turnaround time

This experiment considers number of machines in the grid to be fixed and number of tasks varyingInputs are as follows

Number of machines = 30 range of ant = 2ndash6 range of arrival rate = 1ndash100MIPS range ofprocessing speed = 200ndash300MIPS range of task size = 2000ndash50000Million Instructions rangeof load of network = 60ndash90Mbps range of load of bandwidth = 100ndash120Mbps range ofIPC = 0ndash100Mb

Observation has been taken for the TAT with all five possibilities mentioned in Section 4 (Figure 6)The experiment is conducted again on same input (30 machines) with 120 tasks and 200 tasks as

shown in Figures 7 and 8 respectively (Figures 7 amp 8)

431 Effect of task size Next set of experiment is performed on the same number of machines butthe size of task is generated in slightly lower range (2000ndash30000) in comparison with the earlier oneRest of the data set is same except the range of the size of task and number of task There are three suchdata sets In the first data set the number of tasks is 10 in the second data set the number of tasks is 20and in last data set the number of tasks is 50 For clarity only three possibilities that is WC (case 21

Figure 6 Turnaround time observation on 30 machines with 60 tasks





253

blue line) VNCM (case 24 green line) CNCM (case 24 black line) out of five possibilities havebeen depicted in Figure 9 given as follows (Figure 9)

The following observations are derived from the graphs

1 Most of the solutions converge by 100 generations2 From Figure 6 7 and 8 it is conspicuous that when the number of tasks increases TAT also

increases that is in the case of WC for 60 tasks the makespan is 3219217 that becomes5475750 for 120 tasks and further 9355631 for 200 tasks Similar is the case with constantcommunication and with variable communication

3 Similar observation is derived from Figure 9 also4 It is observed that the TAT with constant communication on constant load and link bandwidth is

more than that which considers variable communication5 Also observed is that the TAT with constant communication on variable load and link bandwidth

is also more than that which considers variable communication

44 Effect of increased number of machines on turnaround time

This experiment considers varying number of machines in the grid and fixed number of task Variousinputs are as follows

Numbers of machines are 20 30 50 and 70 respectively Number of tasks = 50 range of ant = 2ndash5range of arrival rate = 1ndash100MIPS range of processing speed = 200ndash300MIPS range of tasksize = 2000ndash30000Million Instructions range of load of network = 60ndash90Mbps range of load ofbandwidth = 100ndash120Mbps Observation of TAT is depicted in Figures 10ndash13 for 20 30 50 and 70machine respectively

Observations taken for the TAT with five possibilities are as followsFirst one considers no communication between the modules and in second constant

communication of 200Mb with variable load and bandwidth of link is considered The third oneconsiders constant load and bandwidth of link network with variable communication of 200MbThe fourth one considers variable load and bandwidth of network link with variable communication

Figure 9 Turnaround time observation on 30 machines with variable task in (2000ndash30000) interval







of 200Mb The fifth one considers constant load and bandwidth of network link with constantcommunication of 200Mb

In the next experiment all the data set is again generated in the same range as given in Section 431for initial 30 machines but after that we run the experiment three times and incremented 10 machinesin the next two experiment Processing speed of incremented machine is generated in the range130ndash190MIPS whereas the arrival speeds are generated in the range of 30ndash100MIPS For clarity inFigure 14 we have depicted third experiment (ie 30+ 20) separately just below the compared figure(Figure 14)

1 Turnaround time for initial 30 machines on the same data set of 50 tasks was 1634275 unit oftime

2 Turnaround time after incrementing 10 machines (in initial 30 machines) in specified rangereduces to 1575461 unit of time

3 Turnaround time after incrementing 20 machines (in initial 30 machines) in specified rangereduces to 1524352unit of time

The following observations are derived from the aforementioned graphs

1 Most of the solution converges by 100 generations


(a)

(b)

Figure 14 (a) Turnaround time observation with 30 tasks and varying number of machines (processingspeed lower) (b) turnaround time observation with 30 tasks and varying number of machines (processing

speed lower)


255

Co

2 From Figures 10ndash13 it is observed that TAT for all five instances on same set of submitted taskin the grid decreases as the number of machines increases in the grid

3 From Figure 14 it is clear that rate of decrease of TAT becomes very slow with the number ofmachines in the grid after a certain threshold value of machines provided that the arrival rateand processing speed of the machines are generated in the predefined fixed range

441 Effect of increase of arrival rates (l) at any instance on turnaround time In this experiment wehad fixed all the inputs except the range of arrival rate (l) of machines Various inputs are as follows

Number of machines = 20 number of tasks = 50 range of ant = 2ndash5 range of processingspeed = 200ndash300MIPS range of task size = 2000ndash30000Million Instructions range of load ofnetwork = 60ndash90Mbps range of load of bandwidth 100ndash120Mbps Observation of TAT is depictedin Figure 15

Range of arrival rate (l1) = 1ndash100 (denoted as lamda1 in Figure 15)Range of arrival rate (l2) = 30ndash100 (denoted as lamda2 in Figure 15)It is observed from the aforementioned figure that if we perform the experiment exactly on the same

set of data but the arrival rate of different machines are generated in higher range of interval TAT forall five instances increases

442 Effect of increase of m at any instance on turnaround time In this experiment we have fixed allthe inputs except the range of processing rate (m) of machines Various inputs are as follows

Number of machines = 20 number of tasks = 50 range of ant = 2ndash5 MIPS range of processingspeed = 200ndash300MIPS range of task size = 2000ndash30000Million Instructions range of load ofnetwork = 60ndash90Mbps range of load of bandwidth = 100ndash120Mbps (Figure 16)

Range of processing speed (m1) = 200ndash300 (denoted as mu1 in Figure 16)Range of processing speed (m2) = 230ndash330 (denoted as mu2 in Figure 16)It is observed that if we perform the experiment exactly on the same set of data but the processing

speed of different machines are generated in higher range of interval TAT for all five instancesdecreases

pyright copy 2012 John Wiley amp Sons Ltd Concurrency Computat Pract Exper 2014 26241ndash270DOI 101002cpe

Figure 16 Observation of effect of processing speed on turnaround time

Figure 15 Observation of effect of arrival rate on turnaround time


45 Effect of IPC on turnaround time with variation of network congestiontraffic load and theirvariable speed

In this section we see the effect of IPC at a particular instance of time with high network traffic Wewill also see that if a particular traffic route is found almost busy for a long period then what will be theeffect if we increase the bandwidth of that particular route

451 Effect of increase of network load at a particular instance of time on turnaround time In thisexperiment we had fixed all the input except the range of network load (lrs[]) of machines Variousinputs are as follows

Number of machines = 30 number of tasks = 90 range of ant = 2ndash5 MIPS range of arrivalrate = 1ndash100MIPS range of processing speed=200ndash300MIPS range of task size = 2000ndash10000MillionInstructions range of IPC=0ndash200Mb range of load of bandwidth = 100ndash120Mbps Observation ofTAT for this data set is depicted in Figure 17

Range of network load (lrs[]) = 60ndash90 (denoted as Nlamda1 in Figure 17)Range of network load (lrs[]) = 75ndash90 (denoted as Nlamda2 in Figure 17)It is observed that if we perform the experiment exactly on the same set of data but the load of the

network in the grid are generated in higher range of interval TAT for all four instances with IPCincreases except one that do not consider communication

452 Effect of increase of network bandwidth at any instance on turnaround time In thisexperiment we had fixed all the inputs except the range of network load (lrs[]) of machinesVarious inputs are as follows

Number of machines = 30 number of tasks = 90 range of ant = 2ndash5 MIPS range of arrivalrate 1ndash100MIPS range of processing speed = 200ndash300MIPS range of task size = 2000ndash10000MillionInstructions range of IPC=0ndash200Mb range of network load= 60ndash90Mbps Observation of TAT forthis data set is depicted in Figure 18

Range of network bandwidth (mrs[]) = 100ndash120 (denoted as Nmu1 in Figure 18)Range of network bandwidth (mrs[]) = 110ndash120 (denoted as Nmu2 in Figure 18)


Figure 17 Observation of effect of network load on turnaround time



257

It is observed from the experiment that if we perform the experiment on exactly the same setof input data but the bandwidth of the network in the grid are generated in higher range ofinterval TAT for all four instances with IPC decreases except one that consider nocommunication

5 COMPARISON WITH GENETIC ALGORITHM-BASED MODEL

We have compared the proposed AACO-based model with GA-based [21] model for the same objectiveof scheduling the parallel tasks The comparison is made for the same grid and task environment In thementioned paper [21] initial population is generated randomly that is a random sequence of machine isgenerated for all available tasks to constitute a chromosome Population is a collection of such differentchromosomes After this the best half population is selected on the basis of their fitness values Uniformcrossover with some specified uniform crossover probability is applied [35] along with some simplemutation process New population of full size is generated in the next iteration This process isrepeated until the stopping criteria are achieved

In [22] scheduling of parallel task had been studied on three instances first instance was paralleltask without any IPC the second instance considers the variable range of IPC over the constant loadof link network whereas the third instance considers the constant range of IPC over the constantload of link network In this paper we have performed the experiment with all three instances aswas performed in [22] In addition experiment is conducted on two more instances one thatconsiders variable range of IPC over the variable load of link network and the other one considersconstant range of IPC over the variable load of link network



51 Effect of number of tasks

Our model is compared with GA-based model on all five instances as mentioned earlier Schematicdiagram of Virtual Grid of 50 nodes on which the performance evaluation of the proposedalgorithm has been carried out is shown in Appendix A

511 Case 1 50 machines 50 tasks Number of machines = 50 number of tasks = 50 arrivalspeed = 1ndash100MIPS processing speed = 101ndash200 range of tasks = 2000ndash4000MI range of load ofnetwork = 1ndash10 Mbps network bandwidth = 15ndash20Mbps range of ant = 2ndash5 messagecommunication range = 0ndash2Mb Observation of TAT for this data set is depicted in Figures 19 and 20for auto controlled ACO and GA respectively

We observe that although proposed algorithm provides a slight improvement in TAT (WC case) butin all other four instances which consider IPC a major improvement is seen

512 Case 2 50 machines 100 tasks Number of machines = 50 number of tasks = 100 arrivalspeed = 1ndash100MIPS processing speed = 101ndash200 range of task = 2000ndash4000 range of load ofnetwork = 1ndash10Mbps network bandwidth = 15ndash20Mbps range of ant = 2ndash6 messagecommunication range =0ndash2Mb Observation of TAT for this data set is depicted in Figures 21 and 22for auto controlled ACO and GA respectively

It is observed that the proposed algorithm provides a significant improvement in TAT in comparisonto GA in all the cases that consider IPC

513 Case 3 50 machines 150 tasks Number of machines = 50 number of tasks = 150 arrivalspeed = 1ndash100MIPS processing speed= 101ndash200 range of task= 2000ndash4000 range of load of

Figure 19 Turnaround time comparison graph of all the five instances with auto controlled ant colonyoptimization

Figure 20 Turnaround time observation for the same data set on all five instances by GA



259

network= 1ndash10Mbps network bandwidth= 15ndash20Mbps range of ant = 2ndash6 message communicationrange = 0ndash2Mb Observation of TAT for this data set is depicted in Figures 23 and 24 for autocontrolled ACO and GA respectively

In this case also we observe that proposed algorithm provide a significant improvement in TAT incomparison to GA in all the cases that consider IPC

We observe fromFigures 19ndash24 that as theworkload increases on a given grid system the solution given bythe proposed algorithm is much better than what is proposed by GA-based model [22]


Figure 22 Turnaround time observation for all five instances on the same data set by GA





52 Effect of variable interprocess communication

Comparison of scalability of AACO with GA is carried out when size of IPC increases Performanceevaluation of the proposed algorithm is carried out on the same virtual grid which is discussed inSection 5 and is shown in Appendix A

521 Case 1 range of interprocess communication 0ndash2Mb Number of machines = 50 number oftasks = 50 arrival speed = 1ndash100MIPS processing speed = 101ndash200 range of task = 2000ndash4000MIrange of load of network = 1ndash10Mbps network bandwidth = 15ndash20Mbps range of ant = 2ndash5message communication range = 0ndash2Mb Observation of TAT for this data set is depicted in Figures25 and 26 for auto controlled ACO and GA respectively

522 Case 2 range of interprocess communication 0ndash12Mb Number of machines = 50 number oftasks = 50 arrival speed = 1ndash100MIPS processing speed = 101ndash200 range of task = 2000ndash4000MIrange of load of network = 1ndash10Mbps network bandwidth = 15ndash20Mbps range of ant = 2ndash5message communication range = 0ndash12Mb Observation of TAT for this data set is depicted inFigures 27 and 28 for auto controlled ACO and GA respectively


We observe that the scalability of the proposed model for all four instances that consider IPCbecomes more effective as the size of IPC increases in comparison with the GA-based model [22]

53 Comparison with other models

We have compared the proposed auto controlled ACO (AACO) model with other grid schedulingmodels for example Min-Min Minimum Execution Time (MET) Minimum Completion Time(MCT) Heterogeneous Earliest Finish Time (HEFT) on all five different instances for differentinputs [22 26 31ndash34]

531 Number of machines (M) = 5 number of larger tasks (N1) = 5 number of smaller tasks (N2) = 25arrival speed = 1ndash100MIPS processing speed = 101ndash200 range of larger task = 2000ndash4000MI rangeof smaller task = 100ndash300MI range of IPC = 0ndash40Mb range of network load = 1ndash10MIPS range ofnetwork bandwidth = 12ndash20MIPS (Figure 31)

532 Number of machines (M) = 5 number of larger tasks (N1) = 15 number of smaller tasks(N2) = 3 arrival speed= 1ndash100MIPS processing speed= 101ndash200 range of larger task = 2000ndash4000MIrange of smaller task= 100ndash300MI range of IPC=0ndash6Mb range of network load = 02ndash045MIPSrange of network bandwidth = 06ndash15MIPS (Figure 32)






261

533 Number of machines (M) = 5 number of larger tasks (N1) = 6 number of smaller tasks(N2) =40 arrival speed=1ndash100MIPS processing speed=101ndash200 range of larger task =2000ndash4000MIrange of smaller task= 100ndash300MI range of IPC=0ndash6Mb range of network load=02ndash045MIPSrange of network bandwidth= 06ndash15MIPS (Figure 33)







535 Number of machines (M)= 5 number of larger tasks (N1) = 50 number of smaller tasks(N2) = 0arrival speed = 1ndash100MIPS processing speed = 101ndash200 range of larger task= 2000ndash4000MI range ofsmaller task= 100ndash300MI range of IPC=0ndash2Mb range of network load = 02ndash045MIPS range ofnetwork bandwidth= 06ndash15MIPS (Figure 35)

536 Number of machines (M) = 30 number of larger tasks (N1) = 50 number of smaller tasks(N2) = 0 arrival speed = 1ndash100MIPS processing speed= 101ndash200 range of larger task= 2000ndash4000MIrange of smaller task = 200ndash300MI range of IPC=0ndash100Mb range of network load= 1ndash10MIPSrange of network bandwidth = 14ndash20MIPS (Figure 36)


Figure 32 Comparison of turnaround time observation of AACO with four different algorithms




263

537 Number of machines (M) = 30 number of larger tasks (N1) = 50 number of smaller tasks(N2) = 0 arrival speed= 1ndash100MIPS processing speed=101ndash200 range of larger task = 2000ndash4000MIrange of smaller task= 100ndash150MI range of IPC=0ndash10Mb range of network load= 02ndash045MIPSrange of network bandwidth = 05ndash095MIPS (Figure 37)

In the following subsections we have compared the dynamic AACO with Static algorithms such asHEFT Min-Min and MCT in the same range of data as carried out in Sections 5 and 513 for 50machines We have not included MET as it is not effective (evident from Figures 31-37) for allrealistic applications

538 Number of machines = 50 number of larger tasks = 50 number of smaller tasks = 0 arrivalspeed = 1ndash100MIPS processing speed = 101ndash200 range of larger task = 2000ndash4000MI range of






load of network = 1ndash10Mbps network bandwidth = 15ndash20Mbps range of ant = 2ndash5 messagecommunication range = 0ndash2Mb (Figure 38)

539 Number of machines = 50 number of tasks = 100 arrival speed= 1ndash100MIPS processingspeed= 101ndash200 range of task = 2000ndash4000 range of load of network= 1ndash10Mbps networkbandwidth = 15ndash20Mbps range of ant = 2ndash6 message communication range= 0ndash2Mb (Figure 39)




Figure 38 Comparison of AACO with three different techniques



265

5311 Number of machines = 50 number of tasks = 50 arrival speed = 1ndash100MIPS processingspeed= 101ndash200 range of task = 2000ndash4000MI range of load of network= 1ndash10Mbps networkbandwidth =15ndash20Mbps range of ant = 2ndash5 message communication range=0ndash12Mb (Figure 41)







From the aforementioned experiments we observe that higher range of network bandwidth does not

always guarantee the minimum TAT it is the ratio lki

mki mkilkieth THORN that affects the TAT in the case of IPC

We find from the aforementioned experiments that although the proposed algorithm is providingbetter solution in all these cases but in the case of WC solution provided by HEFT is alsocomparable with that of AACO (especially when either all the tasks are of larger size or when all ofthem are smaller size) but in mixed case the difference of TAT is more visible in WC case alsoThe effect of IPC in all other four instances increases in the following cases

1 As the ratio lki

mki mkilkieth THORN increases for the network on the same grid for same IPC

2 As the range of IPC increase for the same network construction3 Both the ratio given in (1) and range of IPC given in (2) increases



267

But if the ratio given in case (1) is increasing and range of IPC given in case (2) is decreasing or viceversa then effect of IPC on TAT depends on the fact that from what amount parameters in cases (1)and (2) are deviating

We also observe from the aforementioned experiments that MET is not effective in all these fiveinstances It is because it does not consider the machinersquos ready time that is the waiting time of themachine at the time of allocation It allocates the task on the machine that gives minimum executiontime that result in most of the tasks allocation on the same machine IPC is not effective if the tasksare allocated on the same machine so times taken in all five instances are almost same for METalgorithm From the aforementioned comparison we found that HEFT is also a good algorithm forthe WC case because the complexity of the algorithm is very less than that of AACO Only thingthat we need before the processing of task is the rank for each task for the order of their scheduling[34] A similar type of thing has been carried out with the help of pheromone matrix in the case ofAACO dynamically rather than the HEFT that adapted the static approach for ranking

Although the proposed model have been developed for effective grid scheduling that gives emphasisto IPC we observe that it gives good result in comparison with other famous grid schedulingalgorithms for example Min-Min MCT MET HEFT and GA for TAT also

6 CONCLUSION

In this work the benefit of using an AACO technique for the performance improvement of scheduling inthe computational grid is elaborated It is observed through regress experimentation that how the proposedmethod performs under given IPC Experimental study indicates that the proposed model can allocate thejob to the appropriate nodes of the computational grid effectively and efficiently

There are many characteristic quality of service parameters expected to be improved by schedulingof the jobs over the grid Proposed work considers TAT and derives the objective function for testingthe quality of each solution for the five different scenarios It also observes the effect of IPC on TATACO-based model provides not only better solution for the scheduling problem in comparison with theother soft computing technique such as GA but also converges quickly

REFERENCES

1 Foster I Kesselman C The Grid 2 Blueprint for a New Computing Infrastructure Morgan Kaufmann An Imprint ofElsevier San Francisco CA 2004

2 Buyya R Abramson D Giddy J An architecture for resource management and scheduling system in global compu-tational grid High Performance Computing Asia China IEEE CS Press USA vol 1 2000 283ndash289

3 Shi Z Dongarra J Scheduling workflow applications on processors with different capabilities Future GenerationComputer Systems 2006 22665ndash675

4 Yu J Buyya R Tham CK Cost-based scheduling of scientific workflow applications on utility grids In Proc of theFirst Int Conf on e-Science and Grid Computing 2005 IEEE

5 Yuan Y Li X Wang Q Timendashcost trade-off dynamic scheduling algorithm for workflow in grids In Proc 10th IntConf Comput Supported Coop Work Des Nanjing China May 2006

6 Gareym M Johnson D Computers and Intractability A Guide to the Theory of NP-Completeness New YorkFreeman 1979

7 Dorigo M StUumltzle T Ant colony optimization PHI 20068 Zhao N Wu Z Zhao Y Quan T Ant colony optimization algorithms with mutation mechanism and its applications

Expert System with Applications 2010 374805ndash48109 Ghafurian S Javadian N An ant colony algorithm for solving fixed destination multi-depot travelling salesman

problems Applied Soft Computing 2011 11(1)1256ndash126210 Dorigo M Gamberdella LM Ant colony system a cooperative learning approach to the travelling salesman problem

IEEE Transaction on Evolutionary Computation 1997 153ndash6611 Dorigo M Manieezoo V Colorni A The ant system an autocatalytic optimizing process Technical Report 91ndash016

Departimento di Elettronica Politecnico di Milano Milan 199112 Tiwari PK Optimizing QoS parameters in computational grid using ACO MTech Dissertation JNU New Delhi

India 201013 Xu Z Hou X Sun J Ant algorithm-based task scheduling in grid computing IEEE CCECE 2003 1107ndash111014 Chen W Zhang J An ant colony optimization approach to a grid workflow scheduling problem with various QoS

requirements IEEE Transaction on System Man and Cybernetics Part C 2009 39(1)29ndash43



15 Fidanova S Durchova M Ant algorithm for grid scheduling problem Large Scale Computing Lecture Notes inComputer Science No 3743 Springer Germany 2006 405ndash412

16 Li K Job scheduling for grid computing on meta-computers Proceedings of the IEEE IPDPS 200517 Abawajy JH Automatic job scheduling policy for grid computing LNCS Springer-Verlag Berlin Heidelberg 2005

3516101ndash10418 Cooper RB Introduction to Queuing Theory Second Edition North Holland Publications New York 198119 Hock C Queuing Modeling Fundamentals John Wiley amp Sons Ltd New York 199620 Tripathi AK Sarker BK Kumar N Vidyarthi DP A GA based multiple task allocation load consideration Interna-

tional Journal of Information and Computing Science 2000 336ndash4421 Goldberg DE Genetic algorithms in search optimization and machine learning Pearson 200522 Prakash S Vidyarthi DP Observations on effect of IPC in GA based scheduling on computational grid International

Journal of Grid and High Performance Computing 2012 4(1)67ndash8023 Sinnen O Sousa LA Communication contention in task scheduling IEEE Transactions on Parallel and Distributed

Systems 2005 16(6) 503ndash51524 Dorigo M Blum C Ant colony optimization theory a survey Theoretical Computer Science 2005 344(2ndash3)

243ndash27825 Dorigo M Ant colony optimization http wwwaco-metaheuristicorg26 Braun TD Sigel HJ Beck N A comparison of eleven static heuristic for mapping a class of independent tasks

onto heterogeneous distributed computing systems Journal of Parallel and Distributed Computing 2001 61810ndash837

27 Parhami B Introduction to Parallel Processing Algorithms and Architectures Plenum NewYork NY 199928 Silverschatz A Galvin PB Gange G Operating Systems Concepts John Wiley amp Sons New Delhi India 200729 Raja Z Vidyarthi DP A computational grid scheduling model to minimize turnaround time using modified GA In-

ternational Journal of Artificial Intelligence 2009 3(49)86ndash10630 Raja Z Vidyarthi DP A GA based scheduling model for computational grid to minimize turnaround International

Journal of Grid and High Performance Computing 2009 1(4)70ndash9031 Kokilavani T George DI Load balanced min-min algorithm for static metatask scheduling in grid computing

International Journal of Computer Applications 2011 20(2)43ndash4932 Hemamalini M Review on grid task scheduling in distributed heterogeneous environment International Journal of

Computer Applications 2012 40(2)24ndash3033 Sarker BK Tripathi AK Vidyarthi DP Yang LT Uehara K Multiple task allocation in arbitrarily connected

distributed computing systems using A algorithm and genetic algorithm LNCS 2006 4331279ndash29034 Topcuoglu H Hariri S Wu M-Y Performance-effective and low-complexity task scheduling for heterogeneous

computing IEEE Transaction on Parallel and Distributed Systems 2002 13(3)260ndash27435 Xhafa F Carretero J Abraham A Genetic algorithm based schedulers for grid computing systems International

Journal of Innovative Computing Information and Control 2007 3(6)1053ndash1071



269

APPENDIX A

Ant 1 (12) (45) (312) (68) (711) (26) (53)Without communication=MAX(178997) (147085) (72048) (80128) (97427) (341286)= 341286Ant 2 (72) (45) (512) (38) (211) (12) (66)For without communication T=MAX(63560+178997) (147085) (290364) (131602) (84710)(83471)= 290364For each task we will require total communication timeFor example for Ant 2 total communication time required by task 1 isCT1(11) =Communication time between task 1 and task 1=DF(22)CTCM(11) = (0)(0)

APPENDIX BDelay factor (DF) matrix of example explained at step 11 for all 12 nodes is calculated through Dijkstra

algorithm at each instance of time

DF=1 2 3 4 5 6 7 8 9 10 11 12

1 0 17942 34733 20804 14001 27659 25883 10292 29487 19565 31687 282682 17942 0 24149 18581 25384 26569 15299 07650 31539 21618 29464 103273 34733 24149 0 27485 24117 20119 08849 29869 19297 15168 38368 294184 20804 18581 27485 0 06803 19880 18636 26231 25673 15752 10883 082545 14001 25384 24117 06803 0 17043 15268 24293 18871 08949 17686 150576 27659 26569 20119 19880 17043 0 11270 32289 18016 08094 30763 178837 25883 15299 08849 18636 15268 11270 0 21019 16240 06318 29519 205688 10292 07650 29869 26231 24293 32289 21019 0 37259 27338 37114 179769 29487 31539 19297 25673 18871 18016 16240 37259 0 09922 36557 2417110 19565 21618 15168 15752 08949 08094 06318 27338 09922 0 26635 1425011 31687 29464 38368 10883 17686 30763 29519 37114 36557 26635 0 1913812 28268 10327 29418 08254 15057 17883 20568 17976 24171 14250 19138 0


Execution task matrix (ETM) for all seven tasks on each 12 machines at some instance of time (whichincludes machine ready time is)

ETM=1 2 3 4 5 6 7

1 308961 115982 181503 225824 401058 99368 1097092 178997 67195 105154 130832 232354 57569 635603 262914 98697 154452 192168 341286 84558 933584 283177 106303 166356 206979 367589 91075 1005545 201234 75542 118218 147085 261220 64721 714566 259533 97427 152466 189697 336896 83471 921587 338170 126948 198663 247174 438975 108762 1200818 224017 84095 131602 163738 290794 72048 795469 881521 330919 517862 644318 1144293 283515 31302010 914887 343444 537463 668706 1187605 294246 32486811 225655 84710 132564 164935 292921 72575 8012812 223686 83971 131407 163496 290364 71942 79429

For Variable Network Constant Message case we have considered 25Mb interprocess communication(IPC) of message is required for each task that is allocated on different nodesmachines Although thetask that is allocated on the same nodemachines required IPC= 0 Mb CTCM is the communicationrequired between different tasks of a job in CNCM and VNCM case It is a (lxl) matrix where l isthe number of tasks in a job

CTCM=1 2 3 4 5 6 7

1 0 25 25 25 25 25 252 25 0 25 25 25 25 253 25 25 0 25 25 25 254 25 25 25 0 25 25 255 25 25 25 25 0 25 256 25 25 25 25 25 0 257 25 25 25 25 25 25 0


CT1(12) =Communication time between task 1 and task 2=DF(211)CTCM(12) = (29464) (25)CT1(13) =Communication time between task 1 and task 3=CT1(14) =Communication time between task 1 and task 4=CT1(15) =Communication time between task 1 and task5=CT1(16) =Communication time between task 1 and task 6=CT1(17) =Communication time between task 1 and task7=CT1=MAXCT1(11) CT1(12) CT1(13) CT1(14) CT1(15) CT1(16) CT1(17)CT2=MAXCT2(21) CT2(22) CT2(23) CT2(24) CT2(25) CT2(26) CT2(27)Ω=MAXCT1 CT2 CT3 CT4 CT5 CT6 CT7Variable Network Constant Message turnaround time for Ant 2 = 290364+CT=1218214For Ant 2 T+Ω=1218214 (Eq 11 of formula)F=Min(T+Ω) (our objective is to minimize F)It should be noted here that we have already calculated the shortest route for going from one machine toanother for IPC through Dijkstrarsquos algorithm and its final value is stored in DF matrixSimilar will be the case of Variable Network VariableMessage turnaround time only CTCMmatrix will bechanged For constant network case DF matrix will be changed in both the cases It should also be notedthat DFmatrix is dynamically changing with respect to time as the load on network increases or decreases



Grid scheduling is a well-known NP-class problem having a very large search space of possiblesolutions [6] To find the near optimal solution many soft computing techniques have been appliedas discussed in literature [20 22 29 30] Ant colony optimization (ACO) is one such technique Inthe ant algorithm category it is the latest successful algorithm [24 25] ACO can provide a betteroptimal solution for all combinatorial optimization problems but the mapping of the parameters ofthis technique with the tuned constraint of the problem is a tough task [7ndash11]

Many models that use ACO for solving grid scheduling problem are focused on the minimizationof turnaround time (TAT) Task scheduling for minimization of TAT in computational grid is afundamental issue for fetching high-end capacity to achieve better performance It is discussed in[12ndash15] The optimal usage of large number of resources is the main objectives of these scheduling policies

Interprocess communication (IPC) plays an important role in scheduling the jobs over the grid IPCaffects the time taken in job execution and thus warrants a proper grid scheduling Very few studieshave been made to study the effect of IPC in scheduling Communication contention in task schedulinghas been discussed by Sinnen and Sousa [23] In [22] effect of IPC has been observed using anothersoft computing techniques genetic algorithm (GA) We have proposed a grid scheduler using a variantof ACO and observed the effect of IPC on the performance of grid scheduling

The outline of the paper is as follows After the introduction in Section 1 the problem is stated andelaborated in Section 2 Auto controlled ACO-based scheduling model is presented in Section 3whereas experimental evaluation and observation is described in Section 4 Conclusion of the workis drawn in Section 5

2 THE PROBLEM

Scheduling of the tasks is an integrated part of any computing systems An intensive research has beencarried out in this area and the results have been widely publicized With the emergence of Open GridService Architecture (OGSA) in computational grid newer scheduling models and algorithms are indemand for addressing new concerns in the grid environment The complexity of schedulingincreases with the size of the grid that makes it highly infeasible

Three phases of scheduling are involved in grid Phase one discovers the set of different resourcesaccording to the specialty of the jobtask Phase two collects the information of queuing lengthreliability and the speed of the node to match it with the application In the third phase allocationand execution takes place [12]

A global grid scheduler often called resource broker acts as an interface between the user and thedistributed resources and hide the complexities of computational grid It performs all the three phasesof scheduling in grid environment Besides it is also responsible for monitoring and tracking theprogress of application execution along with adapting to the changes in the run time environment ofthe grid variation in resource share availability and failures Grid environment is composed bydifferent types of processing nodes storage units scientific instrumentation and informationbelonging to different research organizations and so forth Each time a virtual organization usersubmits a job in the grid it has to make a reference with resource broker There is also a localscheduler on each site of the nodes that takes care of the scheduling inside the node In our problemwe have assumed that local scheduler works in first come first serve manner [1ndash4 16 17] althoughit may adopt in any other local policy

The scheduling parameters might be throughput system utilization TAT waiting time responsetime fairness level of security availability and so forth [12] The factors that may affect thescheduling decisions are as follows

Speed of the node Speed of the node plays an important role in optimizing most of the aforemen-tioned discussed parameters

Number of the nodes It is expected that as the number of node increases grid will becomemore powerful for doing different type of jobs in a faster way There is a tradeoff in costmanagement and execution time



243












31 Turnaround time


32 Fitness function







Ti frac14Xljfrac141


1mi

Njwji (1)








1mi

Njwji

(3)




L frac14 1T

(5)







1mki

Crs (7)



Xlrfrac141

Xlsfrac14rthorn1

Crswkrwislki


(8)



Xlrfrac141

Xlsfrac14rthorn1


0BB

1CCACrswkrwis

2664

3775 (9)




245




Xlrfrac141

Xlsfrac14rthorn1

Xhd kieth THORN1


( )Crswkrwis

(10)









(12)


33 The model













ifrac141Ti THORN










247













(





T itemin

0legle1



























249























251


























253




























(a)

(b)


speed lower)


255

Co




























257


















259

























261















263

















265












1 As the ratio lki





267




6 CONCLUSION



REFERENCES


































269

APPENDIX A




DF=1 2 3 4 5 6 7 8 9 10 11 12

1 0 17942 34733 20804 14001 27659 25883 10292 29487 19565 31687 282682 17942 0 24149 18581 25384 26569 15299 07650 31539 21618 29464 103273 34733 24149 0 27485 24117 20119 08849 29869 19297 15168 38368 294184 20804 18581 27485 0 06803 19880 18636 26231 25673 15752 10883 082545 14001 25384 24117 06803 0 17043 15268 24293 18871 08949 17686 150576 27659 26569 20119 19880 17043 0 11270 32289 18016 08094 30763 178837 25883 15299 08849 18636 15268 11270 0 21019 16240 06318 29519 205688 10292 07650 29869 26231 24293 32289 21019 0 37259 27338 37114 179769 29487 31539 19297 25673 18871 18016 16240 37259 0 09922 36557 2417110 19565 21618 15168 15752 08949 08094 06318 27338 09922 0 26635 1425011 31687 29464 38368 10883 17686 30763 29519 37114 36557 26635 0 1913812 28268 10327 29418 08254 15057 17883 20568 17976 24171 14250 19138 0



ETM=1 2 3 4 5 6 7

1 308961 115982 181503 225824 401058 99368 1097092 178997 67195 105154 130832 232354 57569 635603 262914 98697 154452 192168 341286 84558 933584 283177 106303 166356 206979 367589 91075 1005545 201234 75542 118218 147085 261220 64721 714566 259533 97427 152466 189697 336896 83471 921587 338170 126948 198663 247174 438975 108762 1200818 224017 84095 131602 163738 290794 72048 795469 881521 330919 517862 644318 1144293 283515 31302010 914887 343444 537463 668706 1187605 294246 32486811 225655 84710 132564 164935 292921 72575 8012812 223686 83971 131407 163496 290364 71942 79429


CTCM=1 2 3 4 5 6 7

1 0 25 25 25 25 25 252 25 0 25 25 25 25 253 25 25 0 25 25 25 254 25 25 25 0 25 25 255 25 25 25 25 0 25 256 25 25 25 25 25 0 257 25 25 25 25 25 25 0





243












31 Turnaround time


32 Fitness function







Ti frac14Xljfrac141


1mi

Njwji (1)








1mi

Njwji

(3)




L frac14 1T

(5)







1mki

Crs (7)



Xlrfrac141

Xlsfrac14rthorn1

Crswkrwislki


(8)



Xlrfrac141

Xlsfrac14rthorn1


0BB

1CCACrswkrwis

2664

3775 (9)




245




Xlrfrac141

Xlsfrac14rthorn1

Xhd kieth THORN1


( )Crswkrwis

(10)









(12)


33 The model













ifrac141Ti THORN










247













(





T itemin

0legle1



























249























251


























253




























(a)

(b)


speed lower)


255

Co




























257


















259

























261















263

















265












1 As the ratio lki





267




6 CONCLUSION



REFERENCES


































269

APPENDIX A




DF=1 2 3 4 5 6 7 8 9 10 11 12

1 0 17942 34733 20804 14001 27659 25883 10292 29487 19565 31687 282682 17942 0 24149 18581 25384 26569 15299 07650 31539 21618 29464 103273 34733 24149 0 27485 24117 20119 08849 29869 19297 15168 38368 294184 20804 18581 27485 0 06803 19880 18636 26231 25673 15752 10883 082545 14001 25384 24117 06803 0 17043 15268 24293 18871 08949 17686 150576 27659 26569 20119 19880 17043 0 11270 32289 18016 08094 30763 178837 25883 15299 08849 18636 15268 11270 0 21019 16240 06318 29519 205688 10292 07650 29869 26231 24293 32289 21019 0 37259 27338 37114 179769 29487 31539 19297 25673 18871 18016 16240 37259 0 09922 36557 2417110 19565 21618 15168 15752 08949 08094 06318 27338 09922 0 26635 1425011 31687 29464 38368 10883 17686 30763 29519 37114 36557 26635 0 1913812 28268 10327 29418 08254 15057 17883 20568 17976 24171 14250 19138 0



ETM=1 2 3 4 5 6 7

1 308961 115982 181503 225824 401058 99368 1097092 178997 67195 105154 130832 232354 57569 635603 262914 98697 154452 192168 341286 84558 933584 283177 106303 166356 206979 367589 91075 1005545 201234 75542 118218 147085 261220 64721 714566 259533 97427 152466 189697 336896 83471 921587 338170 126948 198663 247174 438975 108762 1200818 224017 84095 131602 163738 290794 72048 795469 881521 330919 517862 644318 1144293 283515 31302010 914887 343444 537463 668706 1187605 294246 32486811 225655 84710 132564 164935 292921 72575 8012812 223686 83971 131407 163496 290364 71942 79429


CTCM=1 2 3 4 5 6 7

1 0 25 25 25 25 25 252 25 0 25 25 25 25 253 25 25 0 25 25 25 254 25 25 25 0 25 25 255 25 25 25 25 0 25 256 25 25 25 25 25 0 257 25 25 25 25 25 25 0










1mi

Njwji

(3)




L frac14 1T

(5)







1mki

Crs (7)



Xlrfrac141

Xlsfrac14rthorn1

Crswkrwislki


(8)



Xlrfrac141

Xlsfrac14rthorn1


0BB

1CCACrswkrwis

2664

3775 (9)




245




Xlrfrac141

Xlsfrac14rthorn1

Xhd kieth THORN1


( )Crswkrwis

(10)









(12)


33 The model













ifrac141Ti THORN










247













(





T itemin

0legle1



























249























251


























253




























(a)

(b)


speed lower)


255

Co




























257


















259

























261















263

















265












1 As the ratio lki





267




6 CONCLUSION



REFERENCES


































269

APPENDIX A




DF=1 2 3 4 5 6 7 8 9 10 11 12

1 0 17942 34733 20804 14001 27659 25883 10292 29487 19565 31687 282682 17942 0 24149 18581 25384 26569 15299 07650 31539 21618 29464 103273 34733 24149 0 27485 24117 20119 08849 29869 19297 15168 38368 294184 20804 18581 27485 0 06803 19880 18636 26231 25673 15752 10883 082545 14001 25384 24117 06803 0 17043 15268 24293 18871 08949 17686 150576 27659 26569 20119 19880 17043 0 11270 32289 18016 08094 30763 178837 25883 15299 08849 18636 15268 11270 0 21019 16240 06318 29519 205688 10292 07650 29869 26231 24293 32289 21019 0 37259 27338 37114 179769 29487 31539 19297 25673 18871 18016 16240 37259 0 09922 36557 2417110 19565 21618 15168 15752 08949 08094 06318 27338 09922 0 26635 1425011 31687 29464 38368 10883 17686 30763 29519 37114 36557 26635 0 1913812 28268 10327 29418 08254 15057 17883 20568 17976 24171 14250 19138 0



ETM=1 2 3 4 5 6 7

1 308961 115982 181503 225824 401058 99368 1097092 178997 67195 105154 130832 232354 57569 635603 262914 98697 154452 192168 341286 84558 933584 283177 106303 166356 206979 367589 91075 1005545 201234 75542 118218 147085 261220 64721 714566 259533 97427 152466 189697 336896 83471 921587 338170 126948 198663 247174 438975 108762 1200818 224017 84095 131602 163738 290794 72048 795469 881521 330919 517862 644318 1144293 283515 31302010 914887 343444 537463 668706 1187605 294246 32486811 225655 84710 132564 164935 292921 72575 8012812 223686 83971 131407 163496 290364 71942 79429


CTCM=1 2 3 4 5 6 7

1 0 25 25 25 25 25 252 25 0 25 25 25 25 253 25 25 0 25 25 25 254 25 25 25 0 25 25 255 25 25 25 25 0 25 256 25 25 25 25 25 0 257 25 25 25 25 25 25 0





245




Xlrfrac141

Xlsfrac14rthorn1

Xhd kieth THORN1


( )Crswkrwis

(10)









(12)


33 The model













ifrac141Ti THORN










247













(





T itemin

0legle1



























249























251


























253




























(a)

(b)


speed lower)


255

Co




























257


















259

























261















263

















265












1 As the ratio lki





267




6 CONCLUSION



REFERENCES


































269

APPENDIX A




DF=1 2 3 4 5 6 7 8 9 10 11 12

1 0 17942 34733 20804 14001 27659 25883 10292 29487 19565 31687 282682 17942 0 24149 18581 25384 26569 15299 07650 31539 21618 29464 103273 34733 24149 0 27485 24117 20119 08849 29869 19297 15168 38368 294184 20804 18581 27485 0 06803 19880 18636 26231 25673 15752 10883 082545 14001 25384 24117 06803 0 17043 15268 24293 18871 08949 17686 150576 27659 26569 20119 19880 17043 0 11270 32289 18016 08094 30763 178837 25883 15299 08849 18636 15268 11270 0 21019 16240 06318 29519 205688 10292 07650 29869 26231 24293 32289 21019 0 37259 27338 37114 179769 29487 31539 19297 25673 18871 18016 16240 37259 0 09922 36557 2417110 19565 21618 15168 15752 08949 08094 06318 27338 09922 0 26635 1425011 31687 29464 38368 10883 17686 30763 29519 37114 36557 26635 0 1913812 28268 10327 29418 08254 15057 17883 20568 17976 24171 14250 19138 0



ETM=1 2 3 4 5 6 7

1 308961 115982 181503 225824 401058 99368 1097092 178997 67195 105154 130832 232354 57569 635603 262914 98697 154452 192168 341286 84558 933584 283177 106303 166356 206979 367589 91075 1005545 201234 75542 118218 147085 261220 64721 714566 259533 97427 152466 189697 336896 83471 921587 338170 126948 198663 247174 438975 108762 1200818 224017 84095 131602 163738 290794 72048 795469 881521 330919 517862 644318 1144293 283515 31302010 914887 343444 537463 668706 1187605 294246 32486811 225655 84710 132564 164935 292921 72575 8012812 223686 83971 131407 163496 290364 71942 79429


CTCM=1 2 3 4 5 6 7

1 0 25 25 25 25 25 252 25 0 25 25 25 25 253 25 25 0 25 25 25 254 25 25 25 0 25 25 255 25 25 25 25 0 25 256 25 25 25 25 25 0 257 25 25 25 25 25 25 0









ifrac141Ti THORN










247













(





T itemin

0legle1



























249























251


























253




























(a)

(b)


speed lower)


255

Co




























257


















259

























261















263

















265












1 As the ratio lki





267




6 CONCLUSION



REFERENCES


































269

APPENDIX A




DF=1 2 3 4 5 6 7 8 9 10 11 12

1 0 17942 34733 20804 14001 27659 25883 10292 29487 19565 31687 282682 17942 0 24149 18581 25384 26569 15299 07650 31539 21618 29464 103273 34733 24149 0 27485 24117 20119 08849 29869 19297 15168 38368 294184 20804 18581 27485 0 06803 19880 18636 26231 25673 15752 10883 082545 14001 25384 24117 06803 0 17043 15268 24293 18871 08949 17686 150576 27659 26569 20119 19880 17043 0 11270 32289 18016 08094 30763 178837 25883 15299 08849 18636 15268 11270 0 21019 16240 06318 29519 205688 10292 07650 29869 26231 24293 32289 21019 0 37259 27338 37114 179769 29487 31539 19297 25673 18871 18016 16240 37259 0 09922 36557 2417110 19565 21618 15168 15752 08949 08094 06318 27338 09922 0 26635 1425011 31687 29464 38368 10883 17686 30763 29519 37114 36557 26635 0 1913812 28268 10327 29418 08254 15057 17883 20568 17976 24171 14250 19138 0



ETM=1 2 3 4 5 6 7

1 308961 115982 181503 225824 401058 99368 1097092 178997 67195 105154 130832 232354 57569 635603 262914 98697 154452 192168 341286 84558 933584 283177 106303 166356 206979 367589 91075 1005545 201234 75542 118218 147085 261220 64721 714566 259533 97427 152466 189697 336896 83471 921587 338170 126948 198663 247174 438975 108762 1200818 224017 84095 131602 163738 290794 72048 795469 881521 330919 517862 644318 1144293 283515 31302010 914887 343444 537463 668706 1187605 294246 32486811 225655 84710 132564 164935 292921 72575 8012812 223686 83971 131407 163496 290364 71942 79429


CTCM=1 2 3 4 5 6 7

1 0 25 25 25 25 25 252 25 0 25 25 25 25 253 25 25 0 25 25 25 254 25 25 25 0 25 25 255 25 25 25 25 0 25 256 25 25 25 25 25 0 257 25 25 25 25 25 25 0





247













(





T itemin

0legle1



























249























251


























253




























(a)

(b)


speed lower)


255

Co




























257


















259

























261















263

















265












1 As the ratio lki





267




6 CONCLUSION



REFERENCES


































269

APPENDIX A




DF=1 2 3 4 5 6 7 8 9 10 11 12

1 0 17942 34733 20804 14001 27659 25883 10292 29487 19565 31687 282682 17942 0 24149 18581 25384 26569 15299 07650 31539 21618 29464 103273 34733 24149 0 27485 24117 20119 08849 29869 19297 15168 38368 294184 20804 18581 27485 0 06803 19880 18636 26231 25673 15752 10883 082545 14001 25384 24117 06803 0 17043 15268 24293 18871 08949 17686 150576 27659 26569 20119 19880 17043 0 11270 32289 18016 08094 30763 178837 25883 15299 08849 18636 15268 11270 0 21019 16240 06318 29519 205688 10292 07650 29869 26231 24293 32289 21019 0 37259 27338 37114 179769 29487 31539 19297 25673 18871 18016 16240 37259 0 09922 36557 2417110 19565 21618 15168 15752 08949 08094 06318 27338 09922 0 26635 1425011 31687 29464 38368 10883 17686 30763 29519 37114 36557 26635 0 1913812 28268 10327 29418 08254 15057 17883 20568 17976 24171 14250 19138 0



ETM=1 2 3 4 5 6 7

1 308961 115982 181503 225824 401058 99368 1097092 178997 67195 105154 130832 232354 57569 635603 262914 98697 154452 192168 341286 84558 933584 283177 106303 166356 206979 367589 91075 1005545 201234 75542 118218 147085 261220 64721 714566 259533 97427 152466 189697 336896 83471 921587 338170 126948 198663 247174 438975 108762 1200818 224017 84095 131602 163738 290794 72048 795469 881521 330919 517862 644318 1144293 283515 31302010 914887 343444 537463 668706 1187605 294246 32486811 225655 84710 132564 164935 292921 72575 8012812 223686 83971 131407 163496 290364 71942 79429


CTCM=1 2 3 4 5 6 7

1 0 25 25 25 25 25 252 25 0 25 25 25 25 253 25 25 0 25 25 25 254 25 25 25 0 25 25 255 25 25 25 25 0 25 256 25 25 25 25 25 0 257 25 25 25 25 25 25 0


























249























251


























253




























(a)

(b)


speed lower)


255

Co




























257


















259

























261















263

















265












1 As the ratio lki





267




6 CONCLUSION



REFERENCES


































269

APPENDIX A




DF=1 2 3 4 5 6 7 8 9 10 11 12

1 0 17942 34733 20804 14001 27659 25883 10292 29487 19565 31687 282682 17942 0 24149 18581 25384 26569 15299 07650 31539 21618 29464 103273 34733 24149 0 27485 24117 20119 08849 29869 19297 15168 38368 294184 20804 18581 27485 0 06803 19880 18636 26231 25673 15752 10883 082545 14001 25384 24117 06803 0 17043 15268 24293 18871 08949 17686 150576 27659 26569 20119 19880 17043 0 11270 32289 18016 08094 30763 178837 25883 15299 08849 18636 15268 11270 0 21019 16240 06318 29519 205688 10292 07650 29869 26231 24293 32289 21019 0 37259 27338 37114 179769 29487 31539 19297 25673 18871 18016 16240 37259 0 09922 36557 2417110 19565 21618 15168 15752 08949 08094 06318 27338 09922 0 26635 1425011 31687 29464 38368 10883 17686 30763 29519 37114 36557 26635 0 1913812 28268 10327 29418 08254 15057 17883 20568 17976 24171 14250 19138 0



ETM=1 2 3 4 5 6 7

1 308961 115982 181503 225824 401058 99368 1097092 178997 67195 105154 130832 232354 57569 635603 262914 98697 154452 192168 341286 84558 933584 283177 106303 166356 206979 367589 91075 1005545 201234 75542 118218 147085 261220 64721 714566 259533 97427 152466 189697 336896 83471 921587 338170 126948 198663 247174 438975 108762 1200818 224017 84095 131602 163738 290794 72048 795469 881521 330919 517862 644318 1144293 283515 31302010 914887 343444 537463 668706 1187605 294246 32486811 225655 84710 132564 164935 292921 72575 8012812 223686 83971 131407 163496 290364 71942 79429


CTCM=1 2 3 4 5 6 7

1 0 25 25 25 25 25 252 25 0 25 25 25 25 253 25 25 0 25 25 25 254 25 25 25 0 25 25 255 25 25 25 25 0 25 256 25 25 25 25 25 0 257 25 25 25 25 25 25 0

















251


























253




























(a)

(b)


speed lower)


255

Co




























257


















259

























261















263

















265












1 As the ratio lki





267




6 CONCLUSION



REFERENCES


































269

APPENDIX A




DF=1 2 3 4 5 6 7 8 9 10 11 12

1 0 17942 34733 20804 14001 27659 25883 10292 29487 19565 31687 282682 17942 0 24149 18581 25384 26569 15299 07650 31539 21618 29464 103273 34733 24149 0 27485 24117 20119 08849 29869 19297 15168 38368 294184 20804 18581 27485 0 06803 19880 18636 26231 25673 15752 10883 082545 14001 25384 24117 06803 0 17043 15268 24293 18871 08949 17686 150576 27659 26569 20119 19880 17043 0 11270 32289 18016 08094 30763 178837 25883 15299 08849 18636 15268 11270 0 21019 16240 06318 29519 205688 10292 07650 29869 26231 24293 32289 21019 0 37259 27338 37114 179769 29487 31539 19297 25673 18871 18016 16240 37259 0 09922 36557 2417110 19565 21618 15168 15752 08949 08094 06318 27338 09922 0 26635 1425011 31687 29464 38368 10883 17686 30763 29519 37114 36557 26635 0 1913812 28268 10327 29418 08254 15057 17883 20568 17976 24171 14250 19138 0



ETM=1 2 3 4 5 6 7

1 308961 115982 181503 225824 401058 99368 1097092 178997 67195 105154 130832 232354 57569 635603 262914 98697 154452 192168 341286 84558 933584 283177 106303 166356 206979 367589 91075 1005545 201234 75542 118218 147085 261220 64721 714566 259533 97427 152466 189697 336896 83471 921587 338170 126948 198663 247174 438975 108762 1200818 224017 84095 131602 163738 290794 72048 795469 881521 330919 517862 644318 1144293 283515 31302010 914887 343444 537463 668706 1187605 294246 32486811 225655 84710 132564 164935 292921 72575 8012812 223686 83971 131407 163496 290364 71942 79429


CTCM=1 2 3 4 5 6 7

1 0 25 25 25 25 25 252 25 0 25 25 25 25 253 25 25 0 25 25 25 254 25 25 25 0 25 25 255 25 25 25 25 0 25 256 25 25 25 25 25 0 257 25 25 25 25 25 25 0

















253




























(a)

(b)


speed lower)


255

Co




























257


















259

























261















263

















265












1 As the ratio lki





267




6 CONCLUSION



REFERENCES


































269

APPENDIX A




DF=1 2 3 4 5 6 7 8 9 10 11 12

1 0 17942 34733 20804 14001 27659 25883 10292 29487 19565 31687 282682 17942 0 24149 18581 25384 26569 15299 07650 31539 21618 29464 103273 34733 24149 0 27485 24117 20119 08849 29869 19297 15168 38368 294184 20804 18581 27485 0 06803 19880 18636 26231 25673 15752 10883 082545 14001 25384 24117 06803 0 17043 15268 24293 18871 08949 17686 150576 27659 26569 20119 19880 17043 0 11270 32289 18016 08094 30763 178837 25883 15299 08849 18636 15268 11270 0 21019 16240 06318 29519 205688 10292 07650 29869 26231 24293 32289 21019 0 37259 27338 37114 179769 29487 31539 19297 25673 18871 18016 16240 37259 0 09922 36557 2417110 19565 21618 15168 15752 08949 08094 06318 27338 09922 0 26635 1425011 31687 29464 38368 10883 17686 30763 29519 37114 36557 26635 0 1913812 28268 10327 29418 08254 15057 17883 20568 17976 24171 14250 19138 0



ETM=1 2 3 4 5 6 7

1 308961 115982 181503 225824 401058 99368 1097092 178997 67195 105154 130832 232354 57569 635603 262914 98697 154452 192168 341286 84558 933584 283177 106303 166356 206979 367589 91075 1005545 201234 75542 118218 147085 261220 64721 714566 259533 97427 152466 189697 336896 83471 921587 338170 126948 198663 247174 438975 108762 1200818 224017 84095 131602 163738 290794 72048 795469 881521 330919 517862 644318 1144293 283515 31302010 914887 343444 537463 668706 1187605 294246 32486811 225655 84710 132564 164935 292921 72575 8012812 223686 83971 131407 163496 290364 71942 79429


CTCM=1 2 3 4 5 6 7

1 0 25 25 25 25 25 252 25 0 25 25 25 25 253 25 25 0 25 25 25 254 25 25 25 0 25 25 255 25 25 25 25 0 25 256 25 25 25 25 25 0 257 25 25 25 25 25 25 0
















(a)

(b)


speed lower)


255

Co




























257


















259

























261















263

















265












1 As the ratio lki





267




6 CONCLUSION



REFERENCES


































269

APPENDIX A




DF=1 2 3 4 5 6 7 8 9 10 11 12

1 0 17942 34733 20804 14001 27659 25883 10292 29487 19565 31687 282682 17942 0 24149 18581 25384 26569 15299 07650 31539 21618 29464 103273 34733 24149 0 27485 24117 20119 08849 29869 19297 15168 38368 294184 20804 18581 27485 0 06803 19880 18636 26231 25673 15752 10883 082545 14001 25384 24117 06803 0 17043 15268 24293 18871 08949 17686 150576 27659 26569 20119 19880 17043 0 11270 32289 18016 08094 30763 178837 25883 15299 08849 18636 15268 11270 0 21019 16240 06318 29519 205688 10292 07650 29869 26231 24293 32289 21019 0 37259 27338 37114 179769 29487 31539 19297 25673 18871 18016 16240 37259 0 09922 36557 2417110 19565 21618 15168 15752 08949 08094 06318 27338 09922 0 26635 1425011 31687 29464 38368 10883 17686 30763 29519 37114 36557 26635 0 1913812 28268 10327 29418 08254 15057 17883 20568 17976 24171 14250 19138 0



ETM=1 2 3 4 5 6 7

1 308961 115982 181503 225824 401058 99368 1097092 178997 67195 105154 130832 232354 57569 635603 262914 98697 154452 192168 341286 84558 933584 283177 106303 166356 206979 367589 91075 1005545 201234 75542 118218 147085 261220 64721 714566 259533 97427 152466 189697 336896 83471 921587 338170 126948 198663 247174 438975 108762 1200818 224017 84095 131602 163738 290794 72048 795469 881521 330919 517862 644318 1144293 283515 31302010 914887 343444 537463 668706 1187605 294246 32486811 225655 84710 132564 164935 292921 72575 8012812 223686 83971 131407 163496 290364 71942 79429


CTCM=1 2 3 4 5 6 7

1 0 25 25 25 25 25 252 25 0 25 25 25 25 253 25 25 0 25 25 25 254 25 25 25 0 25 25 255 25 25 25 25 0 25 256 25 25 25 25 25 0 257 25 25 25 25 25 25 0




















257


















259

























261















263

















265












1 As the ratio lki





267




6 CONCLUSION



REFERENCES


































269

APPENDIX A




DF=1 2 3 4 5 6 7 8 9 10 11 12

1 0 17942 34733 20804 14001 27659 25883 10292 29487 19565 31687 282682 17942 0 24149 18581 25384 26569 15299 07650 31539 21618 29464 103273 34733 24149 0 27485 24117 20119 08849 29869 19297 15168 38368 294184 20804 18581 27485 0 06803 19880 18636 26231 25673 15752 10883 082545 14001 25384 24117 06803 0 17043 15268 24293 18871 08949 17686 150576 27659 26569 20119 19880 17043 0 11270 32289 18016 08094 30763 178837 25883 15299 08849 18636 15268 11270 0 21019 16240 06318 29519 205688 10292 07650 29869 26231 24293 32289 21019 0 37259 27338 37114 179769 29487 31539 19297 25673 18871 18016 16240 37259 0 09922 36557 2417110 19565 21618 15168 15752 08949 08094 06318 27338 09922 0 26635 1425011 31687 29464 38368 10883 17686 30763 29519 37114 36557 26635 0 1913812 28268 10327 29418 08254 15057 17883 20568 17976 24171 14250 19138 0



ETM=1 2 3 4 5 6 7

1 308961 115982 181503 225824 401058 99368 1097092 178997 67195 105154 130832 232354 57569 635603 262914 98697 154452 192168 341286 84558 933584 283177 106303 166356 206979 367589 91075 1005545 201234 75542 118218 147085 261220 64721 714566 259533 97427 152466 189697 336896 83471 921587 338170 126948 198663 247174 438975 108762 1200818 224017 84095 131602 163738 290794 72048 795469 881521 330919 517862 644318 1144293 283515 31302010 914887 343444 537463 668706 1187605 294246 32486811 225655 84710 132564 164935 292921 72575 8012812 223686 83971 131407 163496 290364 71942 79429


CTCM=1 2 3 4 5 6 7

1 0 25 25 25 25 25 252 25 0 25 25 25 25 253 25 25 0 25 25 25 254 25 25 25 0 25 25 255 25 25 25 25 0 25 256 25 25 25 25 25 0 257 25 25 25 25 25 25 0
















259

























261















263

















265












1 As the ratio lki





267




6 CONCLUSION



REFERENCES


































269

APPENDIX A




DF=1 2 3 4 5 6 7 8 9 10 11 12

1 0 17942 34733 20804 14001 27659 25883 10292 29487 19565 31687 282682 17942 0 24149 18581 25384 26569 15299 07650 31539 21618 29464 103273 34733 24149 0 27485 24117 20119 08849 29869 19297 15168 38368 294184 20804 18581 27485 0 06803 19880 18636 26231 25673 15752 10883 082545 14001 25384 24117 06803 0 17043 15268 24293 18871 08949 17686 150576 27659 26569 20119 19880 17043 0 11270 32289 18016 08094 30763 178837 25883 15299 08849 18636 15268 11270 0 21019 16240 06318 29519 205688 10292 07650 29869 26231 24293 32289 21019 0 37259 27338 37114 179769 29487 31539 19297 25673 18871 18016 16240 37259 0 09922 36557 2417110 19565 21618 15168 15752 08949 08094 06318 27338 09922 0 26635 1425011 31687 29464 38368 10883 17686 30763 29519 37114 36557 26635 0 1913812 28268 10327 29418 08254 15057 17883 20568 17976 24171 14250 19138 0



ETM=1 2 3 4 5 6 7

1 308961 115982 181503 225824 401058 99368 1097092 178997 67195 105154 130832 232354 57569 635603 262914 98697 154452 192168 341286 84558 933584 283177 106303 166356 206979 367589 91075 1005545 201234 75542 118218 147085 261220 64721 714566 259533 97427 152466 189697 336896 83471 921587 338170 126948 198663 247174 438975 108762 1200818 224017 84095 131602 163738 290794 72048 795469 881521 330919 517862 644318 1144293 283515 31302010 914887 343444 537463 668706 1187605 294246 32486811 225655 84710 132564 164935 292921 72575 8012812 223686 83971 131407 163496 290364 71942 79429


CTCM=1 2 3 4 5 6 7

1 0 25 25 25 25 25 252 25 0 25 25 25 25 253 25 25 0 25 25 25 254 25 25 25 0 25 25 255 25 25 25 25 0 25 256 25 25 25 25 25 0 257 25 25 25 25 25 25 0





















261















263

















265












1 As the ratio lki





267




6 CONCLUSION



REFERENCES


































269

APPENDIX A




DF=1 2 3 4 5 6 7 8 9 10 11 12

1 0 17942 34733 20804 14001 27659 25883 10292 29487 19565 31687 282682 17942 0 24149 18581 25384 26569 15299 07650 31539 21618 29464 103273 34733 24149 0 27485 24117 20119 08849 29869 19297 15168 38368 294184 20804 18581 27485 0 06803 19880 18636 26231 25673 15752 10883 082545 14001 25384 24117 06803 0 17043 15268 24293 18871 08949 17686 150576 27659 26569 20119 19880 17043 0 11270 32289 18016 08094 30763 178837 25883 15299 08849 18636 15268 11270 0 21019 16240 06318 29519 205688 10292 07650 29869 26231 24293 32289 21019 0 37259 27338 37114 179769 29487 31539 19297 25673 18871 18016 16240 37259 0 09922 36557 2417110 19565 21618 15168 15752 08949 08094 06318 27338 09922 0 26635 1425011 31687 29464 38368 10883 17686 30763 29519 37114 36557 26635 0 1913812 28268 10327 29418 08254 15057 17883 20568 17976 24171 14250 19138 0



ETM=1 2 3 4 5 6 7

1 308961 115982 181503 225824 401058 99368 1097092 178997 67195 105154 130832 232354 57569 635603 262914 98697 154452 192168 341286 84558 933584 283177 106303 166356 206979 367589 91075 1005545 201234 75542 118218 147085 261220 64721 714566 259533 97427 152466 189697 336896 83471 921587 338170 126948 198663 247174 438975 108762 1200818 224017 84095 131602 163738 290794 72048 795469 881521 330919 517862 644318 1144293 283515 31302010 914887 343444 537463 668706 1187605 294246 32486811 225655 84710 132564 164935 292921 72575 8012812 223686 83971 131407 163496 290364 71942 79429


CTCM=1 2 3 4 5 6 7

1 0 25 25 25 25 25 252 25 0 25 25 25 25 253 25 25 0 25 25 25 254 25 25 25 0 25 25 255 25 25 25 25 0 25 256 25 25 25 25 25 0 257 25 25 25 25 25 25 0















263

















265












1 As the ratio lki





267




6 CONCLUSION



REFERENCES


































269

APPENDIX A




DF=1 2 3 4 5 6 7 8 9 10 11 12

1 0 17942 34733 20804 14001 27659 25883 10292 29487 19565 31687 282682 17942 0 24149 18581 25384 26569 15299 07650 31539 21618 29464 103273 34733 24149 0 27485 24117 20119 08849 29869 19297 15168 38368 294184 20804 18581 27485 0 06803 19880 18636 26231 25673 15752 10883 082545 14001 25384 24117 06803 0 17043 15268 24293 18871 08949 17686 150576 27659 26569 20119 19880 17043 0 11270 32289 18016 08094 30763 178837 25883 15299 08849 18636 15268 11270 0 21019 16240 06318 29519 205688 10292 07650 29869 26231 24293 32289 21019 0 37259 27338 37114 179769 29487 31539 19297 25673 18871 18016 16240 37259 0 09922 36557 2417110 19565 21618 15168 15752 08949 08094 06318 27338 09922 0 26635 1425011 31687 29464 38368 10883 17686 30763 29519 37114 36557 26635 0 1913812 28268 10327 29418 08254 15057 17883 20568 17976 24171 14250 19138 0



ETM=1 2 3 4 5 6 7

1 308961 115982 181503 225824 401058 99368 1097092 178997 67195 105154 130832 232354 57569 635603 262914 98697 154452 192168 341286 84558 933584 283177 106303 166356 206979 367589 91075 1005545 201234 75542 118218 147085 261220 64721 714566 259533 97427 152466 189697 336896 83471 921587 338170 126948 198663 247174 438975 108762 1200818 224017 84095 131602 163738 290794 72048 795469 881521 330919 517862 644318 1144293 283515 31302010 914887 343444 537463 668706 1187605 294246 32486811 225655 84710 132564 164935 292921 72575 8012812 223686 83971 131407 163496 290364 71942 79429


CTCM=1 2 3 4 5 6 7

1 0 25 25 25 25 25 252 25 0 25 25 25 25 253 25 25 0 25 25 25 254 25 25 25 0 25 25 255 25 25 25 25 0 25 256 25 25 25 25 25 0 257 25 25 25 25 25 25 0
















265












1 As the ratio lki





267




6 CONCLUSION



REFERENCES


































269

APPENDIX A




DF=1 2 3 4 5 6 7 8 9 10 11 12

1 0 17942 34733 20804 14001 27659 25883 10292 29487 19565 31687 282682 17942 0 24149 18581 25384 26569 15299 07650 31539 21618 29464 103273 34733 24149 0 27485 24117 20119 08849 29869 19297 15168 38368 294184 20804 18581 27485 0 06803 19880 18636 26231 25673 15752 10883 082545 14001 25384 24117 06803 0 17043 15268 24293 18871 08949 17686 150576 27659 26569 20119 19880 17043 0 11270 32289 18016 08094 30763 178837 25883 15299 08849 18636 15268 11270 0 21019 16240 06318 29519 205688 10292 07650 29869 26231 24293 32289 21019 0 37259 27338 37114 179769 29487 31539 19297 25673 18871 18016 16240 37259 0 09922 36557 2417110 19565 21618 15168 15752 08949 08094 06318 27338 09922 0 26635 1425011 31687 29464 38368 10883 17686 30763 29519 37114 36557 26635 0 1913812 28268 10327 29418 08254 15057 17883 20568 17976 24171 14250 19138 0



ETM=1 2 3 4 5 6 7

1 308961 115982 181503 225824 401058 99368 1097092 178997 67195 105154 130832 232354 57569 635603 262914 98697 154452 192168 341286 84558 933584 283177 106303 166356 206979 367589 91075 1005545 201234 75542 118218 147085 261220 64721 714566 259533 97427 152466 189697 336896 83471 921587 338170 126948 198663 247174 438975 108762 1200818 224017 84095 131602 163738 290794 72048 795469 881521 330919 517862 644318 1144293 283515 31302010 914887 343444 537463 668706 1187605 294246 32486811 225655 84710 132564 164935 292921 72575 8012812 223686 83971 131407 163496 290364 71942 79429


CTCM=1 2 3 4 5 6 7

1 0 25 25 25 25 25 252 25 0 25 25 25 25 253 25 25 0 25 25 25 254 25 25 25 0 25 25 255 25 25 25 25 0 25 256 25 25 25 25 25 0 257 25 25 25 25 25 25 0












1 As the ratio lki





267




6 CONCLUSION



REFERENCES


































269

APPENDIX A




DF=1 2 3 4 5 6 7 8 9 10 11 12

1 0 17942 34733 20804 14001 27659 25883 10292 29487 19565 31687 282682 17942 0 24149 18581 25384 26569 15299 07650 31539 21618 29464 103273 34733 24149 0 27485 24117 20119 08849 29869 19297 15168 38368 294184 20804 18581 27485 0 06803 19880 18636 26231 25673 15752 10883 082545 14001 25384 24117 06803 0 17043 15268 24293 18871 08949 17686 150576 27659 26569 20119 19880 17043 0 11270 32289 18016 08094 30763 178837 25883 15299 08849 18636 15268 11270 0 21019 16240 06318 29519 205688 10292 07650 29869 26231 24293 32289 21019 0 37259 27338 37114 179769 29487 31539 19297 25673 18871 18016 16240 37259 0 09922 36557 2417110 19565 21618 15168 15752 08949 08094 06318 27338 09922 0 26635 1425011 31687 29464 38368 10883 17686 30763 29519 37114 36557 26635 0 1913812 28268 10327 29418 08254 15057 17883 20568 17976 24171 14250 19138 0



ETM=1 2 3 4 5 6 7

1 308961 115982 181503 225824 401058 99368 1097092 178997 67195 105154 130832 232354 57569 635603 262914 98697 154452 192168 341286 84558 933584 283177 106303 166356 206979 367589 91075 1005545 201234 75542 118218 147085 261220 64721 714566 259533 97427 152466 189697 336896 83471 921587 338170 126948 198663 247174 438975 108762 1200818 224017 84095 131602 163738 290794 72048 795469 881521 330919 517862 644318 1144293 283515 31302010 914887 343444 537463 668706 1187605 294246 32486811 225655 84710 132564 164935 292921 72575 8012812 223686 83971 131407 163496 290364 71942 79429


CTCM=1 2 3 4 5 6 7

1 0 25 25 25 25 25 252 25 0 25 25 25 25 253 25 25 0 25 25 25 254 25 25 25 0 25 25 255 25 25 25 25 0 25 256 25 25 25 25 25 0 257 25 25 25 25 25 25 0





267




6 CONCLUSION



REFERENCES


































269

APPENDIX A




DF=1 2 3 4 5 6 7 8 9 10 11 12

1 0 17942 34733 20804 14001 27659 25883 10292 29487 19565 31687 282682 17942 0 24149 18581 25384 26569 15299 07650 31539 21618 29464 103273 34733 24149 0 27485 24117 20119 08849 29869 19297 15168 38368 294184 20804 18581 27485 0 06803 19880 18636 26231 25673 15752 10883 082545 14001 25384 24117 06803 0 17043 15268 24293 18871 08949 17686 150576 27659 26569 20119 19880 17043 0 11270 32289 18016 08094 30763 178837 25883 15299 08849 18636 15268 11270 0 21019 16240 06318 29519 205688 10292 07650 29869 26231 24293 32289 21019 0 37259 27338 37114 179769 29487 31539 19297 25673 18871 18016 16240 37259 0 09922 36557 2417110 19565 21618 15168 15752 08949 08094 06318 27338 09922 0 26635 1425011 31687 29464 38368 10883 17686 30763 29519 37114 36557 26635 0 1913812 28268 10327 29418 08254 15057 17883 20568 17976 24171 14250 19138 0



ETM=1 2 3 4 5 6 7

1 308961 115982 181503 225824 401058 99368 1097092 178997 67195 105154 130832 232354 57569 635603 262914 98697 154452 192168 341286 84558 933584 283177 106303 166356 206979 367589 91075 1005545 201234 75542 118218 147085 261220 64721 714566 259533 97427 152466 189697 336896 83471 921587 338170 126948 198663 247174 438975 108762 1200818 224017 84095 131602 163738 290794 72048 795469 881521 330919 517862 644318 1144293 283515 31302010 914887 343444 537463 668706 1187605 294246 32486811 225655 84710 132564 164935 292921 72575 8012812 223686 83971 131407 163496 290364 71942 79429


CTCM=1 2 3 4 5 6 7

1 0 25 25 25 25 25 252 25 0 25 25 25 25 253 25 25 0 25 25 25 254 25 25 25 0 25 25 255 25 25 25 25 0 25 256 25 25 25 25 25 0 257 25 25 25 25 25 25 0























269

APPENDIX A




DF=1 2 3 4 5 6 7 8 9 10 11 12

1 0 17942 34733 20804 14001 27659 25883 10292 29487 19565 31687 282682 17942 0 24149 18581 25384 26569 15299 07650 31539 21618 29464 103273 34733 24149 0 27485 24117 20119 08849 29869 19297 15168 38368 294184 20804 18581 27485 0 06803 19880 18636 26231 25673 15752 10883 082545 14001 25384 24117 06803 0 17043 15268 24293 18871 08949 17686 150576 27659 26569 20119 19880 17043 0 11270 32289 18016 08094 30763 178837 25883 15299 08849 18636 15268 11270 0 21019 16240 06318 29519 205688 10292 07650 29869 26231 24293 32289 21019 0 37259 27338 37114 179769 29487 31539 19297 25673 18871 18016 16240 37259 0 09922 36557 2417110 19565 21618 15168 15752 08949 08094 06318 27338 09922 0 26635 1425011 31687 29464 38368 10883 17686 30763 29519 37114 36557 26635 0 1913812 28268 10327 29418 08254 15057 17883 20568 17976 24171 14250 19138 0



ETM=1 2 3 4 5 6 7

1 308961 115982 181503 225824 401058 99368 1097092 178997 67195 105154 130832 232354 57569 635603 262914 98697 154452 192168 341286 84558 933584 283177 106303 166356 206979 367589 91075 1005545 201234 75542 118218 147085 261220 64721 714566 259533 97427 152466 189697 336896 83471 921587 338170 126948 198663 247174 438975 108762 1200818 224017 84095 131602 163738 290794 72048 795469 881521 330919 517862 644318 1144293 283515 31302010 914887 343444 537463 668706 1187605 294246 32486811 225655 84710 132564 164935 292921 72575 8012812 223686 83971 131407 163496 290364 71942 79429


CTCM=1 2 3 4 5 6 7

1 0 25 25 25 25 25 252 25 0 25 25 25 25 253 25 25 0 25 25 25 254 25 25 25 0 25 25 255 25 25 25 25 0 25 256 25 25 25 25 25 0 257 25 25 25 25 25 25 0





ETM=1 2 3 4 5 6 7

1 308961 115982 181503 225824 401058 99368 1097092 178997 67195 105154 130832 232354 57569 635603 262914 98697 154452 192168 341286 84558 933584 283177 106303 166356 206979 367589 91075 1005545 201234 75542 118218 147085 261220 64721 714566 259533 97427 152466 189697 336896 83471 921587 338170 126948 198663 247174 438975 108762 1200818 224017 84095 131602 163738 290794 72048 795469 881521 330919 517862 644318 1144293 283515 31302010 914887 343444 537463 668706 1187605 294246 32486811 225655 84710 132564 164935 292921 72575 8012812 223686 83971 131407 163496 290364 71942 79429


CTCM=1 2 3 4 5 6 7

1 0 25 25 25 25 25 252 25 0 25 25 25 25 253 25 25 0 25 25 25 254 25 25 25 0 25 25 255 25 25 25 25 0 25 256 25 25 25 25 25 0 257 25 25 25 25 25 25 0




Observing the effect of interprocess communication in auto controlled ant colony optimization-based...

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