Quasi cut-through: New hybrid switchingtechnique for computer communication

networksM. llyas, M.S., Ph.D., Mem.I.E.E.E., and H.T. Mouftah, M.Sc, Ph.D.,

Sen.Mem.I.E.E.E.

Indexing terms: Switches and switching theory, Networks, Hybrid switching, Packet switching, Queueing theory.Resource sharing, Reassembly delay

Abstract: A novel hybrid switching technique for computer networks is proposed and analysed in this paper.This hybrid switching technique combines packet switching and cut-through switching. Partial cuts are intro-duced to improve the performance of a network from a practical point of view. Messages are segmented intopackets using a threshold-based segmentation rule. A method to calculate reassembly delay for noisy channelsis described and has been used in the analysis of the hybrid switching. Several numerical results are reported atthe end which depict the practical versatility of the proposed hybrid switching. Some simulation results are alsoreported in order to verify the analytical formulation.

1 Introduction

The importance of remote processing is growing rapidly.Computer networks are used to accomplish this task.Optimisation of the performance of computer networkshas been an extremely important area of research eversince the evolution of the concept of packet-switched net-works. Efforts in this field have been primarily directedtowards the design of efficient algorithms so as to achievethe highest possible throughput and lowest possiblenetwork transit delay.

Dynamic resource sharing is the most basic and crucialaspect of computer communication networks. For accom-plishing this task three basic switching techniques areused: packet switching, message switching and circuitswitching. A few hybrid (i.e. combinations of more thanone) switching techniques have also been proposed:PACUIT (PACket + circUIT) switching [4], [11] and cut-through (also known as virtual cut-through) switching [9],[10]. Hybrid switching techniques came into existencebecause no single switching technique gives favourableperformance for all types of traffic. The performance ofcircuit switching is degraded due to the call set-up timedelay. Therefore this method is good for only longer mes-sages (file transfers) and human communication (telephonesystems). Message and packet switching techniques belongto a larger class known as store-and-forward switching.Message switching suffers from the excessive waitingdelays at the switching nodes when relatively longer mes-sages are involved. However, for smaller messages it isacceptable. Packet-switching poses the formidable problemof reassembly of packets back to messages at the destina-tion node. As a result hybrid switching techniques cameinto existence. PACUIT switching integrates packet andcircuit switching and aims at combining the advantages ofboth switching techniques. The cut-through switchingtechnique is essentially a combination of circuit andmessage switching. The degree of integration dependsupon the traffic intensity of the network. Several tradeoffstudies have been carried out to compare different switch-ing techniques quantitatively [9, 15].

Paper 28O5E, first received 25th April 1983 and in revised form 2nd September 1983The authors are with the Department of Electrical Engineering, Queens University,Kingston, Canada, K7L 3N6

IEE PROCEEDINGS, Vol. 131, Pt. E, No. I, JANUARY 1984

2 Quasi cut-through switching

This paper presents the analysis of a novel hybrid switch-ing technique for computer communication networks. Thishybrid switching technique is essentially a combination ofcut-through switching and packet switching. It also incor-porates a very useful aspect called 'partial cuts'. In the cut-through switching technique a message is submitted to thenetwork as if it will travel from its source node to its desti-nation node using the message switching technique inwhich a message is stored at every intermediate node.However, a message is not stored at an intermediate nodeif the node is found empty. When this happens, themessage is said to have made a 'full cut1. The hybridswitching technique being proposed in this paper goes onestep further and assumes that a message is not completelystored at an intermediate node if it finds only one messagein the node, which will be, of course, in the service facility.Thus the message can start its onward journey as soon asthe service of the preceding message is finished. When thishappens, a message is said to have made a 'partial cut'.The only difference between performing cuts and not per-forming cuts is that the processor does not hold transmis-sion of a packet till all the bits of that packet have arrived,but starts transmission as soon as a packet's header hasbeen processed. This does not need any extra processortime.

In addition to the provision of partial cuts, this hybridswitching technique introduces a threshold-based rule forthe segmentation of messages into packets. If a newlyarrived message has its length less than or equal to thethreshold value, it is not segmented into packets and ishanded over to the network as such after appending afixed number of bits as its header for identification anderror control. On the other hand, if a newly arrivedmessage has its length greater than the threshold value,then it is segmented into smaller packets before handing itover to the network. In the latter case every packet has itsown header of fixed length. The threshold-based segmen-tation rule is illustrated in Fig. 1. This segmentation rulehas advantages and disadvantages. Before going into thediscussion of these merits and demerits it is necessary tounderstand the nature of this rule. First of all the thresholdvalue should be greater than or equal to the maximumallowable packet length because the opposite case isredundant and complicates the analysis. Secondly if the

threshold value is equal to the maximum allowable packetlength then it is tantamount to packet switching. Thus the

fy(x)»-M*

fy(x)

fx(x)

^no segmentation segmentation

fx(x)

Xth

V

N^no segmentation

X

fxW

Xth x

af ter segmentation

PDF overall

Ip Xth x

Fig. 1 Threshold-based segmentation process

threshold-based segmentation rule gives rise to a com-bination of packet and message switching. When full andpartial cuts are allowed, a flavour of circuit switching isalso introduced. This hybrid switching is, therefore, a com-bination of all three basic switching techniques. The use ofpacket or message switching is controlled by the thresholdvalue and that of circuit switching is controlled by thetraffic intensity. Now let us return to the pros and cons ofthreshold-based segmentation. The main items affected bythis segmentation rule are:

reassembly delaybuffer efficiencyoverheaderror controldeadlocks

The reassembly delay per message decreases because theaverage number of packets per message are fewer in thethreshold-based segmentation than that in conventionalsegmentation. The buffer efficiency [2] decreases a littlebecause there will be a few packets of larger length. Theoverhead decreases dramatically for the same reason as forreassembly delay. Because of a few longer packets, errorperformance degrades a little. Deadlocks are less likely tooccur because there is a smaller number of packets permessage.

The analysis of the new hybrid switching technique ispresented in the next Section. A nonzero probability oferror is assumed over the network channels so as to havemore realistic performance evaluation of this switchingtechnique. The network is modelled as M/G/l queues intandem. Lateral arrivals are allowed at the intermediatenodes which help the use of independence assumption[12].

3 Mathematical formulation

An exact mathematical representation of various per-formance evaluation parameters for large computer net-

2

works is almost impossible. Most of the time one has tomake use of a few assumptions which make the mathe-matical analysis tractible. Commonly used assumptionsinclude Poisson arrivals of external messages and exponen-tial service times. These assumptions are very close to thereal behaviour of network traffic for the case of messageswitching. When messages are segmented into packets, theassumption of exponential service times is violated andone has to use other methods to include the effects of seg-mentation. The model and assumptions used to analysethe new hybrid switching are discussed in Section 3.1.Then the formulation for the case of non-noisy channelsand that for noisy channels are discussed separately.

3.1 Model and assumptionsFor a message switched network the average delay permessage is

T= X ±T( (1)

where M is the number of channels in the network, )H isthe total traffic on the ith channels, y is the total externaltraffic entering the network and T( is the average delay permessage on the ith channel. For a balanced network it canbe shown that eqn. 1 can also be written as [12, 20]:

T = nTi

where(2)

(3)

represents the average number of store-and-forward nodesvisited by a message while travelling from its source nodeto the destination. This number depends upon the routingstrategy and the topology of the network. Once this quan-tity is known, one can come up with a tandem network ofn nodes for the purpose of the analysis. That is exactlywhat has been used in this study. The analytical model isshown in Fig. 2. It consists of n nodes (source and destina-tion nodes included). It has been reported that the solution[1] of tandem networks is not so easy because it is hard toapply the assumption of Poisson arrivals at every node. Itwas, however, shown by using simulation that if thenetwork topology is quite complex then the independenceassumption [12] can be used without altering the resultssignificantly from the true ones. In this study lateralarrivals and departures are allowed at every intermediatenode to facilitate the use of the independence assumption.Arrivals are assumed to be Poisson at every intermediatenode while service times are general. Hence the analyticalmodel consists of M/G/l queues in tandem. The buffercapacity at each node is assumed to be very large. It is alsoassumed that balanced traffic conditions exist in thenetwork. Moreover, the propagation delay over thenetwork channels and the nodal processing delay is con-sidered to be negligible as compared to the total nodaldelay.

£)—i—°destinationn-1

'1 ^ 2 ^n-1

Fig. 2 Analytical Model of M/G/l queues in tandemi = 1i = 2 , 3 , . . . , H

q

/.f = /., + A,,.

1EE PROCEEDINGS, Vol. 131, Pt. E, No. 1, JANUARY 1984

3.2 Formulation for non-noisy channelsThe threshold-based segmentation rule can be formallystated as follows:

(a) If an externally arriving message has service require-ment less than or equal to the threshold value Xth, themessage will not be segmented into packets and will behanded over to the network as such.

(b) If an externally arriving message has service require-ment greater than the threshold value Xth, the messagewill be segmented into smaller packets of maximum servicetime lp before it starts its journey through the network

[*,* > y.If the service times of the external messages are assumed tofollow exponential distribution with an average of \/p.s permessage, then the following relations can be shown to betrue:

P(A) = P[x: x ^ X J = 1 - exp (- / i

P(B) = P[x: x > Xlh] = exp (-p.Xth)

(4a)

(4b)

If £[JV] is the expected number of packets per messagethen

£[JV | A~] = 1 no segmentation

E[N | B] = D +exp [ —

(5a)

(56)

where D is the smallest integer greater than XJlp. E\_N~\ isthen given by (see Appendix 7 for proof):

£[AT] = £[N | A]P(A) + E[N | B]P{B) (6a)

or

£[N] = 1 + (D - 1) exp (-nXth) + (6b)

Now let Y be the length of a packet chosen at random(after segmentation or no segmentation) then the probabil-ity distribution of packet lengths is:

P(Y1 -exp(-i

1 — exp ( — p.

P(L <Y <y) = exp (-filp) - exp ( -

<L

xt

P(y < xth) = i

where PA is the probability that a packet belongs to non-segmented messages, PBl is the probability that a packetbelongs to segmented messages and has a constant lengthand PB2 is the probability that a packet belongs to seg-mented messages and its length is less than lp. These prob-abilities are:

P. =E[N\A~]P(A)

{£[Nlfi]-l}P(fi)

P(B)82 (7)

The probability density function (PDF) can be found by

IEE PROCEEDINGS, Vol. 131, Pt. E, No. 1, JANUARY 1984

differentiating the probability distribution function (eqn. 7)and is given by

B2

-exp(-i

[TZ^>0

0 ^ y < lp

>' = ' ,

< y < x,h

otherwise

Using this probability density function, one can find outthe average service requirement of packets x, and secondmoment of packet service requirements x2 [6].

In order to calculate the average network delay permessage, one needs the average number of full and partialcuts made. The probability of performing a full cut at anode is the same as that of the nodal queue being empty.However, a partial cut is made when a node has onepacket therein, and the service requirement of the arrivingpacket is more than the remaining service requirement ofthe arriving packet. On average an arriving packet willfind the latter condition satisfied [12, 20], especially whenthe average message length is considerably larger than lp.Therefore, the probability of performing a partial cut canbe approximated to be equal to the probability of nodalqueue having one packet in it which will, of course, be inthe service facility. These probabilities can be found byusing the probability generating function G,,(z) for M/G/lqueues:

Gn(z) =(\ - p)(z - \)A(z)

z - A(z)p = Lx (9)

where X is the average arrival rate of packets per second, xis the average service requirement per packet including theheader service time, p is the line utilisation and A(z) is theLaplace transform of the probability density function ofpacket lengths calculated at s = X — Xz. The probability Pk

of having k packets in the nodal buffer is

dkGn(z)/dkzk\

(10)

where Gn(z) is given by eqn. 9.By using the independence assumption, the delay at

each node can then be calculated by the Pollaczek-Khinchin formula. Multiplying this delay per node by thenumber of nodes gives the network delay per packet. Forsingle packet messages this will be the delay per message.But for multipacket messages one has to calculate thereassembly delay as well, in order to calculate the averagenetwork delay per message.

The analytical model shown in Fig. 2 consists of n store-and-forward nodes. The number of nodes where either afull cut or a partial cut can be made is equal to n — 1. Theaverage number of nodes where full cuts are made is

= p 0 ( n - \ ) = ( l - (11)

Similarly the average number of nodes where a partial cutcan be made is

N=Pl(n-\) (12)

Note that (Nf + Np) <(n — 1) and that equality occurswhen p = 0. If no cuts are made the average delay per

message for single packet messages is

(13)

where T[^oc stands for the average network delay permessage for single-packet messages when no cuts are per-formed. The average saving on the network transit delaydue to a full cut is

Sf = x - (14)

where x0 is the service requirement of the header. Similarlythe average saving on the network transit delay due to apartial cut is [12, 20]

= x - — + xo\ (15)

Using eqns. 11-15 the network delay per message forsingle-packet messages using hybrid switching will be

T-'(s) _1 we — (16)

For multipacket messages, as said earlier, one has to takecare of reassembly delay. For calculating this delay anapproximation [2] will be used. The approximation saysthat the interpacket gap among the consecutive packets ofthe same message after travelling through n nodes is:

X.

i = qkx

(17a)

(176)

where p,- stands for the traffic intensity of interferingpackets at the intermediate nodes and q is the fraction ofthe traffic arriving laterally. If the expected number ofpackets per message is N, then the total gap gt between itsfirst and the last packet, which also represents the reassem-bly delay, is

9, = (N - (18)

If no cuts are made the average delay per message formultipacket messages is

(N- l)(a + x) (19)

where T^l stands for the average network delay permessage for multipacket messages when no cuts are made.When full and partial cuts are performed the effectivenumber of nodes is decreased and is given by

= (l - P o - P i X " - 1)+ (20)

Using this effective number of nodes in eqn. 17 and addingto it the contribution due to partial cuts, one can write theeffective interpacket gap as

(21)(i - Pd

Then the network delay per message for multipacket mes-sages using the quasi-cut-through switching is

(22)

(23a)

(23b)

(N- \){ge + x)

Then the average delays per message are:

Twoc = P(A)T[?0C + P{B)TZl

Twc = P(A)T[?C + P(B)T%>

Twoc and Twc are the average network delays per messagewithout and with cuts, respectively.

3.3 Formulation for noisy channelsThe calculation of the network delay for noisy channels isa very involved task. The problem becomes difficult tohandle because one has to consider the acknowledgmentand retransmission of packets. In the case of the hybridswitching the analysis becomes even more complicatedbecause of full and partial cuts. In this case one has tokeep track of the node which will retransmit a packetwhen requested to do so by a node which received thepacket in error. To keep the analytical complicationsunder control, instantaneous positive and negativeacknowledgment strategy is assumed. It is also assumedthat the network traffic remains balanced even after theretransmissions of packets which are found in error. Net-works with noisy channels experience the following effects:

(i) the network traffic intensity is increased due toretransmissions of packets which are found in error

(ii) the average number of nodes visited by a packet isincreased because of retransmissions

(iii) in the case of quasi-cut-through switching the prob-abilities of making full and/or partial cuts are also affectedbecause these probabilities depend on the traffic intensity

If one can find the average number of nodes visited by apacket, the effective traffic intensity and the new probabil-ities of making full and partial cuts, then the same methodas used for non-noisy channels can be used to calculate thenetwork delays. To calculate the effective number of nodesvisited by a packet, one should know the probability ofmaking k continuous (full and partial) cuts. These prob-abilities follow geometric distribution. If prime (') indicatesthe parameters pertaining to noisy channels, then theprobability of making a (full or partial) cut at any node is

P'c = P'o + P\ (24)

Note that p'o, p\ and p'c are functions of effective networktraffic intensity p' after retransmissions. The probabilitydensity function of making k continuous cuts is, therefore,

P["c\k) =(P'e

0 < k < n - 1k = n - \

(25)

where Pl"c\k) denotes the discrete probability of making kcontinuous cuts when the actual number of nodes is n. Tocalculate the average number of nodes visited by a packetafter retransmissions, a recursive formula is developed [9],and then effective traffic intensity is

(26)

where Nn(n) represents the average number of nodesvisited by a packet for noisy channels when the actualnumber of nodes is n. If Pe is the probability that a packetis found in error after travelling over one hop then

NtM \nee = k a n d n o error) = k + 1 + N,,(i — k — \)(27a)

N,,(i \ncc =k and error) = k + 1 + N,,{i) (27b)

where ncc is the number of continuous cuts made. Combin-ing eqns. 27a and 276,

Nlt(i\ncc = k) = Ik + 1 + N,,(i - k - 1)](1 - Pe)k + i

and(28)

(29)

IEE PROCEEDINGS, Vol. 131, Pt. E, No. I, JANUARY 1984

Substituting eqn. 28 in eqn. 29 and collecting similar terms,

N( , S ! = o C(fc + 1) + N,Jjn - k - 1X1 - Pc)fc + 1]^'(/c)

(30)

Similarly the number of cuts performed is

(31)

The effective number of nodes contributing to the reassem-bly delay in the case of multipacket messages is

- Nc(n) (32)

The number of full cuts N'f and the number of partial cutsN'p are

and

p\Ne{n)

Pc

(33a)

(336)

One should notice that the effective number of nodes givenby eqn. 30 depends upon the probability density functionof making k continuous cuts (eqn. 25) which, in turn,depends upon the effective traffic intensity. But the trafficintensity itself depends upon the average number of nodesvisited by a packet (eqn. 26). This interdependence oftraffic intensity and average number of nodes leads to iter-ative calculation of these two parameters in order toobtain the reasonably converged solution. It was observedthat for a probability of error Pe of 0.005, about five iter-ations were enough to attain reasonable convergence.These parameters were then utilised to calculate theaverage network delays.

The formulation presented here is quite general and canbe used in the case of no cuts (e.g. traditional packet ormessage switching). For this purpose the probabilitydensity function of making k continuous cuts is used suchthat the probability of making zero cuts is unity and all therest of the probabilities are zero. When this is used eqn. 26and eqn. 30 reduce to

1P =

- PeP

Nlt(n) =" Pe)

(34)

Moreover if Pe = 0.0 then all noisy channel equationsbecome similar to those of non-noisy channels.

Once the effective line utilisation p', effective number ofnodes n'e, total number of nodes Ntl(n) and other relatedparameters have been calculated, then a procedure similarto that used for non-noisy channels can be used to calcu-late the average network delays for single-packet andmultipacket messages.

4 Numerical results

The results of this study are presented in a variety of formsso as to illustrate the performance of the quasi-cut-throughswitching and its versatility.

Fig. 3 shows the effect of the traffic intensity on the totalsaving in network delay, when the quasi-cut-through

switching is used. The contributions of partial and full cutstowards the saving in delay are also shown separately. The

0.100

* 0.010

0.0010.2 0.4 0.6 0.8 1.0

Fig. 3 Reduction in delay against traffic intensity

q = 0.6 n = 5/„ = 1000 bits X,h = 2500 bits

1/// = 2000 bits .vo = 100 bitsC = 50 kbit/s

saving in delay due to partial cuts increases initially,reaches its peak at about p = 0.4 and then drops as thevalue of p is further increased. It eventually becomes zerowhen p is near unity. The saving due to full cuts decreasesas the value of p is increased and so does the totalreduction in delay. It can be seen that the partial cuts givea helping hand to improve the network performanceexactly at the moment of need. Fig. 4 shows the same

100

80

60

20

0.2 0.4 0.6 0.8 1.0

Fig. 4 Percentage reduction in delay against traffic intensityq = 0.6 » = 5/„ = 1000 bits l/n = 2000 bits

X,h = 2500 bits Xo = 50 bitsC = 50 kbit/s

quantities as those in Fig. 3, but now these are in the formof percentage of total reduction in delay against trafficintensity. It can be seen that the percentage reductionachieved due to partial cuts increases, and that due to fullcuts decreases as the traffic intensity is increased.

IEE PROCEEDINGS, Vol. 131, Pt. E, No. /, JANUARY 1984

Fig. 5 shows the actual delays in the three cases: nocuts, full cuts and full and partial cuts. It can be seen thatthe delay in the case of the hybrid switching (full andpartial cuts) is the lowest for all values of traffic intensity.

0.6 r

0.4

0.2

no cutsfull cuts,

full and partial cuts

0.2 O.A 0.6 0.8 1.0

Fig. 5 Average message delay against traffic intensityq = 0.6 n = 5lp = 1000 bits l//< = 2000 bits

Xlh = 2500 bits x0 = 100 bitsC = 50 kbit/s

0.9

0.8

Q7

0.6

p=0.40

1K 10K 20K

Fig. 6 Ratio of delays with, or without, cuts against Xlh

q = 0.5 n = 5/„ = 1000 bits x0 = 50 bits

l//i = 2000 bits C = 50 kbit/s

Fig. 6 shows the plot of the ratio of the network delaywith cuts: the delay without cuts as a function of thethreshold value for different values of traffic intensity. Foreach value of traffic intensity, there exists one optimalpoint where this ratio is minimum. It implies that the per-formance of quasi-cut-through switching is optimum atthat particular value of the threshold. It can also beobserved that this optimum value does not change muchas the value of traffic intensity is varied from 0.4 to 0.7.This aspect of quasi-cut-through switching implies its prac-tical utility and ease of implementation, in the sense that

the threshold value does not have to be adjusted dynami-cally.

The ratio of the network delay with cuts to the delaywithout cuts as a function of the threshold value is plotted

0.80

0.75

0.70-

0.655 10

threshold value, k bits20 30

Fig. 7 Ratio of delays with, or without, cuts against Xlhfor different lp

q = 0.5 n = 5l//< = 2000 bits .v0 = 50 bits

C = 50 kbit/s p = 0.5

in Fig. 7, for different maximum packet length lp expressedin terms of threshold value A",,,. It can be observed that thesag is bigger in the case when lp = XJX.5 and lp = XtJ2S).However, the value of the ratio is less (for smaller values ofthreshold) in the cases when lp = Xth and lp = constant =1000 bits. It can also be seen that the two cases of lp = Xth

and lp = 1000 bits show almost the same performance forthe entire range of threshold values. At a very high value ofthreshold, all the four cases converge to the same point.This is because no segmentation takes place at such a highvalue of threshold and hence the value of lp does not affectthe average packet length any more. However, it has to benoted that, in Fig. 7, the ratio of the two delays merelyindicates the relative performance. The actual delays for allthese four cases are plotted in Fig. 8. One can see from thisFigure that the delay in the case of lp = 1000 bits (i.e. thecase of quasi-cut-through switching) is the lowest for mostof the threshold values.

Fig. 9 shows the plot of the network delay with cuts tothe delay without cuts against traffic intensity for differentpath lengths. As the value of traffic intensity approachesunity, all the curves converge at the same point because, ata higher value of traffic intensity, packets cannot performcuts and hence there is no reduction in delay due to cuts.

The percentage of reduction in the network delay due topartial cuts is plotted in Fig. 10 as a function of the thresh-old for different values of traffic intensity. As the value ofthe threshold increases, the percentage reduction in delaydue to partial cuts decreases. This effect is more profoundat higher values of traffic intensity. At a very high thresh-old value, the curves level off and the threshold value doesnot affect the performance of partial cuts.

Fig. 11 shows the actual delays for noisy channels. Itcan be seen that the delay due to quasi-cut-throughswitching is less than that without cuts. The ratio of thedelay with cuts to the delay without cuts is plotted in Fig.12, as a function of the threshold value for different prob-abilities of error.

IEE PROCEEDINGS, Vol. 131, Pt. E, No. 1, JANUARY 1984

Some simulation results are given in Figs. 13 and 14.Analytical and simulation results regarding average packet

0.35r

0.30 -

0.055 10

threshold value, k bits

Fig. 8 Average message delay against Xlh for different lp

In = 2000 bits .x0 = 50 bitsC = 50 bits p = 0.5

1.0

I 0-8

2 0.6a>

BI 0.4

o

•o 0.2

0.2 0.4 0.6 0.8 10

Fig. 9 Ratio of delays with, and without, cuts against p for different nq = 0.6 C = 50 kbit/s/„ = 1000 bits \/n = 2000 bits

X.k = 2500 bits xn = 100 bits

length and average number of packets per message (usingthreshold-based segmentation) are plotted against thethreshold value (Fig. 13). Both results show an excellentagreement. Actual network delay against traffic intensity isplotted in Fig. 14 along with the respective simulationresults. Both results again exhibit a very reasonable agree-ment.

5 Conclusions

In this paper a novel hybrid switching technique for com-puter communication networks has been proposed andanalysed. According to this switching technique a messageis not segmented into smaller packets if its service require-ment is less than or equal to a predefined threshold. If,however, the service requirement is larger than the thresh-

IEE PROCEEDINGS, Vol. 131, Pt. E, No. 1, JANUARY 1984

old, it is segmented into smaller packets with maximumservice requirement equal to a value less than, or equal to,

30

25

20

15

5 10

threshold value, k bits

20 30

Fig. 10 Percentage reduction in delay due to partial cuts against Xth

q = 0.5 n = 5\/H = 2000 bits C = 50 kbit/s

/„ = 1000 bits Pe = 0.010xn = 50 bits

0.6 r

0.4

0.2no cuts

full and partial cuts

0.2 0.4 0.6 0.8 1.0

Fig. 11 Average message delay against p for different Pe

p , = o.O Pe = 0.005q = 0.6 n = 5/„ = 1000 bits l//< = 2000 bits

Xlh = 2500 bits .x0 = 100 bitsC = 50 kbit/s

the threshold value. Apart from this, a packet is not storedat an intermediate node if that node is empty or has onepacket in the service facility. The hybrid switching tech-nique has been analysed for noisy as well as non-noisychannels. M/G/l queues in tandem have been used tomodel the network for the purpose of analysis. A usefulmethod of calculating the reassembly delay for this hybridswitching technique has been presented in both cases ofnoisy and non-noisy channels.

Numerical results are presented in terms of a variety ofparameters. These results establish the integrity of thishybrid switching which integrates all the three basicswitching techniques for computer networks: packet,

0.80

0.75

0.70

0.65

=0.005

5 10 20 30threshold value . k bits

Fig. 12 Ratio of delays with, or without, cuts against Xlh, Pe ^ 0

q = 0.5 n = 5I //< = 2000 bits x0 = 50 bits/. = 1000 bits p = 0.5

3.0

2.5

2.0

1.5

1.0

0.5

4 6 8 10threshold value,k bits

12

Fig. 13 Average packet length and average number of packets permessage, simulation and analytical resultsO Expected number of packets/message• Average packet length (kbits)/„ = 1000 bits l//< = 2000 bils

message and circuit switching. Results have shown thatthere is always an optimal value of the threshold whichminimises the network delay for almost all levels of trafficintensity. Some simulation results are also reported incomparison with the analytical results. Both results showan excellent agreement and, in turn, verify the accuracy ofthe analytical formulation.

6 References

1 BURKE, P.J.: 'Output process and tandem queues'. Proceedings ofthe symposium on computer networks and teletraffic, New York,1972, pp. 419-428

1.0r

" 0.8

0.6

L. 0.4

0.2

0.2 0.4 0.6traffic intensity

0.8 1.0

Fig. 14 Average message delay against p, simulation and analyticalresults

O no cuts• full cuts• full and partial cuts

q = 0.5 n = 5\/n = 2000 bits X,h = 2500 bits

lp = 1000 bits x0 = 50 bitsC = 50 kbit/s Pc = 0.0

2 COLE, G.D.: 'Computer network measurements: Techniques andexperiments. Computer Science Department, UCLA, Report UCLA-ENG-7165, October 1971

3 FRANK, H., KAHN, R.E., and KLEINROCK, L.: 'Computer com-munication network design: Experience with theory and practice' inLarge scale networks: Theory and design' (IEEE Press, New York,1976) pp. 135-166

4 GERLA, M., and MULLER, D.: 'PACUIT: The integrated packetand circuit alternate to packet switching'. Proceedings of springcompcon., 1978, pp. 153-156

5 ILYAS, M., and MOUFTAH, H.T.: 'A new hybrid switching tech-nique for computer networks'. Records of the eleventh biennial sym-posium on communications, May-June 1982, pp. A4.5-A4.6

6 ILYAS, M.: 'Quasi cut-through: A novel hybrid switching techniquefor computer networks'. Ph.D. thesis, Department of Electrical Engi-neering, Queen's University at Kingston, Ontario, Canada, February1983

7 ILYAS, M., and MOUFTAH, H.T.: 'Analysis of cut-through switch-ing for multipacket messages'. Digest of the IEEE Canadian commu-nications and energy conference, Montreal, October 1982, pp.370-374

8 INOSE, H., and SAITO, T.: Theoretical aspects in the analysis andsynthesis of packet communication networks', Proc. IEEE, 1978, 66,pp. 1409-1422

9 KERMANI, P.: 'Switching and flow control techniques in computercommunication networks'. Computer Science Department, UCLA,Report UCLA-ENG-7802, February 1978

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11 KEYES, N., and GERLA, M.: 'Hybrid packet and circuit switching',Telecommunications, 1978, pp. 65-71

12 KLEINROCK, L.: 'Communication nets' (McGraw-Hill, New York,1964)

13 KLEINROCK, L.: 'Queueing systems Vol. 1 and 2', (Wiley 1976)14 KLEINROCK, L.: 'Principles and lessons in packet communica-

tions', Proc. IEEE, 1978, 66, pp. 1320-132915 MIYAHARA, H., HASEGAWA, T., and TESHIGAWARA, Y.:

'Comparative analysis of switching methods in computer networks'.Technical Report N74-3, University of Hawaii, Honolulu.

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IEE PROCEEDINGS, Vol. 131, Pt. E, No. I, JANUARY 1984

7 Appendix

£[N | A] = 1 no segmentation

For the case of event B, the following can be shown to be true:

Number of packets/message Probability

DD+ 1D + 2

[exp (-fiDlp) - exp (-^D + l)/p)]/P(B)[exp (-M£> + l)/p) - exp (-K

D + n [exp ( -

Summing up all the possibilities gives

+ n - \)lp) - exp {-

2)/p)]/P(fi)

+ n)/p)]/P(B)

£[JV | B] = = K | B)

exp(-/i/c/p)fc =

exp [ - ^ ( D / , - * , „ ) ]

H.T. Mouftah received the B.Sc. degree inelectrical engineering, and the M.Sc. degreein computer science from the University ofAlexandria, Alexandria, Egypt in 1969 and1972, respectively; and the Ph.D. degree inelectrical engineering from Laval Uni-versity, Quebec, Canada in 1975.

From 1969 to 1972 he was an instructorat the University of Alexandria, a researchand teaching assistant at Laval Universityfrom 1973 to 1975, a postdoctoral fellow

for the year 1975-76 at the University of Toronto and SeniorDigital Systems Engineer and then Chief Engineer at AdaptiveMicroelectronics Ltd., Thornhill, Ontario from 1976 to 1977.From 1977 to 1979 he worked with the Data System PlanningDepartment at Bell-Northern Research, Ottawa on several pro-jects related to computer communication networks. In 1979 hejoined the Department of Electrical Engineering, Queen's Uni-versity at Kingston, Ontario, Canada where he is presently anassociate professor. He has consulted for government andindustry in the areas of computer communications and digitalsystems. He holds a number of patents and published a largenumber of technical articles in the area of computer communica-tions, digital systems and multiple-valued logic.

Mohammad Ilyas received his B.Sc. degreein electrical engineering in 1976 from theUniversity of Engineering and Technology,Lahore, Pakistan. He worked with theWater and Power Development Authorityin Pakistan for about two years. In 1978 hewas awarded an RCD scholarship for post-graduate studies at Shiraz University inIran, where he completed his M.S. in Elec-trical and Electronic Engineering in 1980.He obtained his Ph.D. degree in electrical

engineering from Queen's University at Kingston, Canada in1983. Presently he is a visiting assistant professor at the Depart-ment of Electrical Engineering, Florida Atlantic University, BocaRaton, Florida. His research interests include computer commu-nication networks, switching and flow control techniques andsimulation etc.

IEE PROCEEDINGS, Vol. 13J, Pt. E, No. 1, JANUARY 1984