On Attributed Simulation Nets and Their Use in Simulation Studies for Detailed Design of Flexible Manufacturing Systems.

Kelvyn C.K. Chin, Frank DiCesare, Nai Choon Ho and Stephen S.G. Lee

Abstract --- The modeling and performance evaluation of flexible manufacturing systems (FMS) using ordinary Petri nets (PNs) or generalised stochastic Petri nets (GSPNs) becomes cumbersome for complex systems. In GSPNs, temporal specifications of systems are limited to negative exponential distributions. Complexity culminates in two problem areas. Firstly, structural complexity (nets with large state spaces) limits computation of a solution within a finite time. Secondly, details such as scheduling and process plans lends dyamic changes to the PN structure itself. In this paper, simulation nets (SN), a special class of PNs, are used to perform simulation for detailed planning and design of FMSs. A comparison of simulation nets versus classical net evaluative approaches is done. We will address the issue of constant modification of PN structures when FMS schedules and process plans are considered. Formerly, we had to assume average distributions and routings of parts through the system. While this may be viable at an aggregate level design stage, this lack of detail may prove detrimental at later design stages. We will introduce a subclass of coloured Petri nets called attributed simulation nets (ASN) to address this issue. We shall also demonstrate the mechanics of ASNs by modeling and simulating a hypothethical FMS. A brief description of PN-STM, a software which provides a Petri net based environment for modeling and simulation of FMSs, is given.

I. INTRODUCTION AND REVIEW.

A. Petri nets and the FMS.

Petri nets have been widely used in the modeling [Murata 19891, perfarmance evaluation [Viswanadham 19881, control [Zhou 19921 and recently, scheduling of FMSs [Lee 19931. The formal aspects of PN theory is well suited for representing causal dependencies and performing structural and high level quantitative analyses of a complex discrete event dynamic system like the FMS. Several problems are computational complexity in representation and obtaining steady state solutions of even moderately sized systems, and ~~ ~

Kelvyn Chin is a research engineer at Gintic Institute of Manufacturing Technology, Nanyang Technological Univ., Spore. Frank DiCesare is a profesor at the Electrical, Computer and Systems Engineering Dept at Rensselaer Polytechnic Institute, Troy, N.Y. Nai Choon Ho is the divisional director at Gintic Institute of Manufacturing Technology, Nanyang Technological Univ., Spore. Stephen S.G. Lee is a senior lecturer at the School of Mechanical and Production Engineering, Nanyang Technological Univ., Spore.

the need for use of exponential distributions in GSPN models to retain the isomorphism with Markov models [Marsan 19891. Coloured Petri nets (CPNs) reduce the structural complexity of ordinary PNs and allow for succinct descriptions of large systems without losing the formal aspects of PNs [Jensen 19901. In CPNs, the interactions of a system are represented not only by the net structure but by the color sets and arc expressions.

B. Simulation.

Simulation studies are conducted on FMSs to analyse and determine critical elements and issues, to evaluate designs and solutions and to predict behaviour of the system. There have been recent efforts to reconcile simulation techniques with net theory, for example the simulation net (SN) by [Tom 19911. SNs extend modeling capability of timed PNs because of the generality of timed distributions attached to the firing of transitions. Thus firing rates in SN models are not limited to just classes of memoryless distributions. However, SNs do not make use of coloured tokens. SNs can be used as an alternative method for analysing complex FMSs as no steady state solution is computed.

C. Motivation for research and layout ofpaper.

In the first section of this paper, we will use SNs to analyse an FMS. The later sections of this paper are logical extensions of previous work, which described FMS subnets which can be synthesised to form complete models of FMSs. The models' performance were analysed using Markovian techniques, which proved less than satisfactory. A set of six experiments ran for 120 hours. Also, the AGV subnet which was generated using an algorithm proposed in [Chin 1993b] only allows for probabilistic or average routing of parts through the FMS. The algorithm fails when process plans and scheduling of parts or AGVs are included. Strictly speaking, the subnet structure would differ substantially for different scenarios. We will propose attributed simulation nets (ASNs) as a special class of CPNs which will help us retain the genericity of these subnets under varying scenarios involving process plans and schedules. Thus, the subnet synthesis approach to modeling FMSs can be used. This paves the way for icon based manipulation of FMS elements which will reduce modeling lead times. We will then be able to create subnet libraries which are reusable and provide transparency to modelers. In

0-7803-2129-4194 $3.00 0 1994 IEEE

the final section of this paper, we describe a software developed called PN-SIM, which uses the subnets as modular building blocks, while SNs and ASNs are used for simulation of the synthesised model.

as rough cut values for aggregate level design. However, the steady state solutions for six experiments of differing scenarios ran for approximately 120 hours on a SUN360.

11. ORDINARY SIMULATION NETS.

Definition I : An ordinary simulation net (SN) is a 5-tuple SN = (P,T,:I,O,Mo,z) where (P,T,I,O,Mo) is a Petri net structure with addition that we (a) partition the set of places P such that P = PR v PE v Ps where PR is a set of resource places, PE is a set of event places and Ps is a set of sink places; and (b) partition the set of transitions such that T = TI v TR v TP where TI is a set of immediate transitions, TR is a set of transitions with randomly distributed firing times and TP is a set of transitions with probabilistic firing behaviour. We further define

Z:R[ M O ] x TR + ZRIVM ER[ Mo],Vt E TR as a marking dependent randomly distributed firing function. Strictly speaking the function ZR will associate each transition tE TR in every marking MER[Mo] any value of firing time, T =ZR(M, t), where T is a random variable sampled from any of the standard distributions whose p.d.f we denote as the firing function as follows: z R ( T ) = puni(T) , ZIri- (T),

z exp ( T ) ,zcns/(T), .&om(T)].

A SN reduces to an ordinary Petri net if the function Z is suppressed. Isomorphism with the Markov model is sacrificed in SNs.

;. 1. The Petri Net struelure of the reconjigured UPEFUS.

B. Detailed design of the MPEFMS using SNs.

111. SIMULATION OF THE MPEFMS.

A . The physical system andprevious work.

The MPEFMS was modeled by an ordinary PN in [Chin 1993al. The system produces paperweight souvenirs on which is affixed a plastic tag bearing the signature of the user. The FMS consists of an engraving station, a robotic cell where the plastic tag is fixed onto the aluminium base, a visual inspection station to verify the colour of the plastic tag, and a collection station. The two tier dual in-line material handling system consists of a working line which has the workstation at one end and the collection station at the other. The inspection station is situated in between these two and the flow of parts is configured in a loop. The retum line returns empty pallets to the holding area. There are four different colour tags on which the signature is engraved and four different base designs, making sixteen different part types possible. Using GSPNs, the performance of the MPEFMS was obtained using Markovian analysis. The results were discussed in [Chin 1993a1 and deemed suitable

By inserting the function Z in definition (l), a SN model of the MPEFMS was obtained using the same PN structure. The same experimental analyses were carried out on a PC. Results were collated within a day, and shows roughly the same accuracy as the corresponding results from GSPN analysis. The first set of experiments is largely capacity type planning, and the conclusions drawn are similar to the GSPN analyses. The results from the simulation showed that the throughput of the system is limited to 30 parts per day, even if additional mills are introduced in the FMS. Also, both the FMS and workstation are fully utilized when there are two pallets in the system. Modifications were made to the net structure, see fig. 1, which represented reconfiguration of both the FMS layout and its control scheme. In the original scheme, the data storage allowed only a single tag to be processed at any time. Also the FMS allowed one tag entry and would only be freed when the tag is glued on the base. The workstation allowed only one pallet in the input buffer. This configuration led to bottleneck of incoming tags and pallets into the FMS and

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workstation respectively. In the reconfigured FMS, we allow for a tag slot at the entry to the FMS for holding a number of tags, and a pallet buffer at the entry to the workstation to hold waiting pallets. Also, we allow several parts' data to be processed and placed in the controllers' data storage. As soon as a physical souvenir is loaded on the workstation, the information for the next part to be manufactured is processed. This will make the time taken for data validation by the user to run in parallel to waiting times for the workstation to be free.

A second set of simulation experiments was conducted. The results showed that throughput of the system generally improved as did utilizations of the FMS and workstation for the modified FMS control logic. Chart 1 shows the throughput of the FMS for both old and new configurations, with varying number of pallets and addition of a milling machine (M). The new configuration exploits the concurrent capability of flexible manufacturing, especially when we have additional resources in the system. The results for the scenario where an extra milling machine was added in the workspace showed that throughput was almost doubled, which was not possible with the original configuration. We conclude that the problems facing the earlier FMS configuration were: ( I ) the data for the souvenirs being processed one at a time and (2) not having input buffers at the FMS and workstation entry points thus causing a bottleneck for incoming tags and pallets. The new configuration gives better throughput and utilizations.

& old-M=l & old-M=2

I I I 0 1 2 3 4

Num pallets

gble I : Results for old and new configurations of the MPEFMS, wi varying number ofpallets and addition of a mill.

IV. ATTRIBUTED SIMULATION NETS.

A. Motivation

When a complex FMS is being simulated using SNs, for example the FMS in [Chin 3993b], two problems arise. The first stems directly from the state space problem. SNs do not reduce the size of the net. Secondly, the net structure itself is constantly being modified when different scenarios, such as process plans are introduced in the models' scope. We introduce ASNs as a special class of CPNs which can be used to perform discrete event simulation of PNs. ASNs extend the modeling capability of PNs by the natural use of the attributes in CPNs thus reducing the size of the PN structure. CPNs also provide a natural backbone for attaching simulation functions to augment the PN. For example, specific functions can be incorporated to the net such as AGV network routing. By using ASNs we retain PN structures as a formal paradigm for FMS modeling, structural validation and performance evaluation using traditional net theory while allowing discrete event simulation to be done for detail level analysis. Also, since information like part types and AGV ids are carried by the attribute sets, routing based on process plans and AGV scheduling will not change the structure of the subnets. Thus a modular approach for synthesising FMS models from a library of subnets can be achieved.

B. Definition.

From [Jensen90] and defmition (I), we introduce ASNs as a special class of CPNs as follows:

Definition 2: An attributed simulation net is a tuple ASN = ( C , P , T , A R , N , A , E , M o , Z ) where C is a set of finite and non-empty attribute sets; P = PR U PE U Ps is a finite set of places; T = TI v TRU TP is a finite set of transitions; AR is a finite set of input and output arcs; N : AR + P x T u T x P is the node function; A: P + C the attribute function; MO the initial marking; E the arc expression function and the marking dependent firing

function as before.

2: R[ MO] x TR + Z R ( V M E R[ Mo],V't E TR

C. Modeling an FMS using ASNs,

A hypothethical FMS will be used as a case study. The configuration of the FMS is shown in fig. 2, which consists of a load/ unload station (LUSTN); two process stations MI and M2; and a three section AGV network. Sections SI and S3 are bidirectional. We assume no workstation

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breakdowns. The FMS will produce three different part types- A, B and C, whose routing through the FMS is determined by a process plan. The time between arrivals to the FMS are exponentially distributed with means of 11.2, 10.6 and 11.0 minutes respectively. Part A will route through LUSTN, M1 and back to LUSTN; part B LUSTN, M2 and back to LUSTN; and part C from LUSTN, MI, M2 and back to LUSTN. Transportation and processing times are normally distributed. The machining time on the process stations depends on the part type.

S

M v h m MI

5. 2. Configuration ofthe hypofhethical FMS.

Prior to using ASNs, two methods of modeling the FMS were adopted. Method I : for each part types' processes and routing through the FMS, a separate and mostly sequential net is constructed. The three subnets are linked via the places representing shared resources. The resulting net consists of 56 places and 40 transitions, even with the shared resources subnet modeled as one macro place. This net models explicitly the routing of each of the three part types, but any changes in the process plans will make this net structure invalid. Method 2: probabilistic routing of part types across the FMS is assumed. The probabilities for the "decision" places in the AGV subnet is obtained using ad- hoc queueing type calculations. This may be applicable at the aggregate planning stage, but may prove detrimental at detailed stages of design. The PN in fig. 3 was created using this method.

While the net for the first method reflects explicitly the processes of the FMS, the non-genericity of the structure means that the basis for the "subnets as elemental building blocks" rationale for synthesising models of FMSs is forfeited. Using ASNs, the PN structure of the second

method is augmented by the attribute sets and functions to allow detailed modeling without losing genericity of the subnets.

D. Details of the ASN model.

The input and output sink places are p31 and p61 respectively. The input sink place p31 has an attribute set defined by EPart = <PartType, PartId, TimeCreat, TNow, CurProcess>. The node hnction schedules the creation of incoming parts based on the interarrival times. The output sink place p61 has the same attribute set and the node function disposes of tokens entering the place. We define the attribute set ZQueue = <qType, Index, where 1 <index<capacity. Places representing queues, such as p28 (the LUSTN output queue), p59 (M1 input queue) and p60 (M1 output queue) have an attribute set defined by the cross product CQueue x CPart.

For the AGV subnet, we first define CAgv = <Type, Id, Status>. The attributes of the event places in the subnet will be the resultant product CAgv x CPart. Routing of tokens through the subnet will model transportation of parts. The subnet structure consists of decision nodes and free choice transitions. The firing of the conflict transition is determined by a set of rules for "step-wise" routing of the AGV based on the attribute of the token in the decision place. The rules are externally tied to a static process plan. The "step-wise" routing strategy is based on these rules:

1 . if CAgv x CPart shows an empty AGV, fire the transition which moves AGV along shortest path back to Agv-Park or the nearest non-empty station output buffer to pick up part. if CAgv x CPart shows an AGV carrying a part, fire the transition that routes the AGV to the parts next process. AGVs at decision places at entry to process stations have several choices (example p58):

3.1. if CAgv x CPart shows the current station to be the next process defined in the process plan, and no part is waiting in the output buffer, fire transition allowing part into machine. The token "leaving" the decision node will have the element (CAgv, 0) i.e the AGV is empty.

3.2. if ZAgv x CPart shows an empty AGV, fire the transition indicating a move to the next destination (rule 1 above).

3.3. if CAgv x CPart shows an AGV carrying a part which does not require processing at the current station, fire transition moving the AGV onto the next section of the AGV network.

3.4. if CAgv x CPart shows an AGV carrying a part to be processed on this station, and there are parts waiting

2.

3.

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in the stations' output buffer, fire the transition to allow the part into the station and pick up the first part from the output buffer.

Schedule creat part B Schedule creat part C Part C created Schedule creat C 1:38 Schedule fire t28 fire immediate transition Schedule fire t29 now+l:OO Creat part B Sched creat part B Creat part B Sched creat part B tire t29

$1 min

Resource places are modeled as parallel mutual exclusions (PMEs), see for example [Zhou 19901, in the ASN. For this class of places, we may allow:

CResource = (.)(b'p E Pf(

ie, we allow resource places to hold tokens carrying no attributes. This permits intuitive representation of resources.

Delay times for the firing of the randomly distributed transitions are marking dependant. This means that the attribute of the token residing in a place determines the time taken for the firing of the transition. This is easily envisioned by noting that the firing of transition T2 (processing time on M 1) is dependent on the part type of the token's attribute in the transitions' input place.

Fig. 3 shows the ASN at the simulated time of 2:41 minutes. Tables 2a.-b. shows the (partial) scheduled event list and the event calendar.

- pending - X

X

X

X

X

X

X

X

X

X

X

X

X

Y

rble 2a. A X

E002 0.37 E003 0.35 E004 1.64 E006 1.33 E007 0.74 E008 1.51 E009 1.33 EO10 1.93 EO11 1.33 E012 1.33 E013 1.33 E0142.16 E015 6.80 E016 2.17

ial scheduled event list at

Description Creat Part A (1) Creat Part B ( I ) Creat Part C (1) Creat Part C (2) fire t29 Creat Part B (2) Creat Part B (3) fire t28 fire t29 (Finish load B (1) ) fire t30 fire t47 tire t33 (decision) <XAgv, C(1) > fire t 36 Creat A (2) Creat B (4) : 2:41 min

T clock I current event I Description 0:oo I Sched EO01 1:20 I Schedule creat part A I 0:oo 0:oo 0:21 0:21 0:2 I 0:2 I 0:2 1 0:22 0:22 0:44 0:44 1:21

Table 26.

Sched E002 0:22 Sched E003 0:21 E003 Sched E004 Sched E005 fire t28 E005 fire t28 Sched E006 tire t29 E002 Sched E007 E007 Sched E008 E006

'a1 event calendar at T =

V. PETRI NET SIMULATOR (PN-SIM)

A software called PNSIM is being developed that provides an environment for consistent representation and simulation of PN models of FMSs. ASNs are used as a theoretical basis for the simulation. The subnet library contains subnets for FMS elements (process stations, load/ unload stations and ASRS elements). The AGV network subnet is generated using the algorithm proposed in [Chin1993b]. Bottom up synthesis of subnets is handled by the inference engine. The details of synthesis procedures can be found, for example, in [Jeng1989]. The GUI is menu driven, whereby the model is built by picking and placing icon elements. The model is parametrized using the GUI. Here the user can specify whether he is performing aggregate level or detail level analysis. Aggregate level analysis requires only an ordinary SN description. Parametrization of this model is simpler than the detailed level model, which requires definition of the attribute sets and node functions for the ASN definition. The subnets are extracted from the library and the FMS model synthesised. The simulation engine performs simulation of the model and generates the results.

VI. CONCLUSIONS.

For complex systems, simulation nets provide faster solutions and allow the usage of non- exponentially distributed firing times. SNs can be used to perform detail simulation studies of FMSs. Thus, techniques associated with simulation, such as what- if analysis and experimental planning, can be applied using Petri net structures instead of shifting across paradigms for modeling and analyses. This approach was used to evaluate and improve the performance of the MPEFMS. ASNs were proposed as a special class of CPNs. ASNs can be used to model the dynamic information carried at the subnet level and ensure that the PN structure remains unchanged by factors such as process plans, AGV routing and schedules. From these principles, a simulator based on ASNs was also described.

ACKNOWLEDGMENT

The SN models were executed using the software SimNet described in [Tom1991]. Constructing the PN models on a PC was done using NetMan, a graphical editor for PNs developed by Michael R. Gile and Paul Kulp, Jr. at Rensselaer Polytechnic Institute, Troy, NY.

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g. 3. The ASN for the hypothetical FMS at simulated time T=2:41 min.

REFERENCES

[Chin1993a] Chin, K.C.K, DiCesare, F., Ho, N.C., "Modeling and Analysis of a Flexible Manufacturing System using Petri Nets", Journal of the Institution of Engineers. Singapore, Vo1.33 No.4, June 1993.

[Chin1993b] Chin, K.C.K, DiCesare, F., Ho, N.C., "On Petri Net Models of Workstations and Automated Guided Vehicle Systems and their Synthesis for Systems- Level Analysis of Flexible Manufacturing Systems". Proc. of the 2nd. Infernational Conference on Computer Integrated Manufacturing System, World Scientific Press, Singapore, Sept. 1993.

[Jengl989] Jeng, M.D. and DiCesare, F.,"Synthesis and Reduction of Petri Nets", Working Paper, ECSE, Rensselaer Polytechnic Institute, Troy, NY, 1989.

[Jensen I9901 Jensen, K., "Coloured Petri Nets: A High Level Language for System Design and Analysis", Advances in Petri Nets 1990 pp. 342 - 416 (G. Rozenberg ed.), Lecture Notes In Computer Science, vol. 483. Springer, Berlin Heidelberg New York 1990.

[Lee19931 Lee, Doo Yong and DiCesare, F.D,"Scheduling Flexible Manufacturing Systems with the Consideration of Setup Times", Proc. 32nd Conference on Decision and Confrol, San Antonio, Texas. Dec. 1993

[Marsan19891 Marsan, M.A.,"Stochastic Petri Nets: an Elementary Introduction", Advances in Petri Nets, Lecture Notes in Computer Science, vol. 424, Springer Verlag, 1989.

[Murata1989] Murata, T., "Petri Nets: Properties, Analysis and Applications", Proc. ofthe IEEE, vol. 77. no. 4. Apr. 1989.

[Tom1991] Torn, A., "Simulation Modeling", Reports on ('omputer Science and Mathematics, Ser. B, No. 12, Mar. 1991.

[Viswanadhaml988] Viswanadham, N., Narahari, Y., "Stochastic Petri Net Models for Performance Evaluation for Automated Manufacturing Systems", Information and Decision Technologies. Vol. 14, pp 125- 142, Elsevier Science Publishers B.V., North Holland, 1988.

[Zhou1990] Zhou, M.C. and DiCcsare, F., "Parallel and Sequential Mutual Exclusions for Petri Net Modeling of Manufacturing Systems and Shared Resources", Working Paper, ECSE. Rensselaer Polytechnic Institute, Troy, NY, Jan. 1990.

[Zhou1992] Zhou, M.C., DiCesare, F. and Rudolph, D., "Design and Implementation of a Petri Net Based Supervisor for a Flexible Manufacturing System", in Automafica, Vol. 28, No. 6, pp. 1199- 1208, 1992.

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