Mathematics and Computers in Simulation 34 (1992) 317-324 North-Holland

317

MATCOM 903

Diagrammatic representations of the conceptual simulation model for discrete event systems * Vlatko Ceric

Faculty of Economics, University of Zagreb, Trg J.F. Kennedyja 6, 41000 Zagreb, Croatia

Ray J. Paul Department of Information Systems, London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom

Abstract

Ceric, V. and R.J. Paul, Diagrammatic representations of the conceptual simulation model for discrete event systems, Mathematics and Computers in Simulation 34 (1992) 317-324.

Diagrammatic modelling representation methods in discrete event simulation are varied and can be classified as follows: simulation strategy neutral, simulation strategy oriented, simulation language oriented, and methods borrowed from other computer modelling areas. The main diagrammatic methods are described in some detail (augmented Petri nets, activity cycle diagrams, event graphs and GPSS block diagrams) and demonstrated by an example. The advantages and disadvantages of these representation methods are briefly discussed.

1. Introduction

The building of discrete event simulation models is not an easy task, bearing in mind some of the difficult problems that have to be handled: dynamic changes of system state at discrete time points, parallel asynchronous events, discrete objects and their interactions, common system resources, queuing for resources, etc. Therefore the need for conceptual model design prior to program development is even more significant than in many other areas of computer modelling. It helps in structuring the ideas about the problem tackled, in the communication between participants in the simulation process and in producing a valid simulation program in an efficient manner. The main purpose of a conceptual model is to show clearly the basic structure of a system and the relationships between its entities, whilst avoiding unnecessary details.

Conceptual modelling is an important part of the simulation process, because it influences the subsequent phases of the process. It has to be clearly distinguished from the programming

Correspondence to: Dr. R.J. Paul, Department of Information Systems, The London School of Economics and Political Sciences, Houghton Street, London WC2A 2AE, United Kingdom. * This joint research was supported by the Yugoslav Council for International Technical Cooperation and the

British Council.

0378-4754/92/$05.00 0 1992 - Elsevier Science Publishers B.V. All rights reserved

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phase; conceptual modelling is primarily aimed at human understanding of the problem, whilst programming is directed towards the complete coding of the problem that is necessary for a computer to translate and execute it. Conceptual modelling for discrete event simulation is also a part of a wider family of conceptual modelling methods in the general computer modelling area, where various methods have been developed for better understanding and validation of the problem.

A previous paper [3] discussed in detail the importance of discrete event simulation model representation, and made a survey of the commonly used representation methods in this area. These methods were classified into four basic groups: diagrammatic methods, formal specifica- tion languages, combined diagrammatic/formal specification languages, and structured ques- tionnaires. This paper classifies the diagrammatic model representation methods, describes and demonstrates the most significant among them, and discusses the main features of their representation capability.

This paper has the following structure. In Section 2 the key strength of diagrammatic methods is discussed, and a classification is offered. Section 3 gives a brief description of four representative diagrammatic methods: augmented Petri nets, activity cycle diagrams, event graphs and GPSS block diagrams. Section 4 makes a comparison of these diagrammatic methods before introducing the concept of comprehensive harmony in Section 5. Conclusions are drawn in the final section.

2. Diagrammatic modelling representation methods

Diagrammatic methods for representing discrete event simulation conceptual models are the most used and developed type of representation method. These methods are based on a system of symbols connected in diagrams.

The key reasons for their popularity seems to be the following [4,6]: - conceptually connected objects can be represented by physical proximity; - interactions between objects can be shown in two dimensions (compared with the sequential nature of procedural statements); - the parallelism of the human visual system enables the easier comprehension of the model; - the syntax and semantics of these methods are mostly rather simple; _ hierarchical descriptions of the model are often enabled; - and manual simulation using diagrammatical models is usually possible (which is helpful for model validation).

It is possible to classify diagrammatic modelling representation methods into the following four basic groups.

(1) Simulation strategy neutral methods. These methods do not belong to any of the simulation strategies, nor to any specific simulation language. Their neutrality enables the use of such methods in conjunction with any simulation language. This group includes various augmentations of Petri nets, as given in [4,9,12,13], and to activity cycle diagrams [7]. Whilst activity cycle diagrams are widely used by exponents of the three-phase method, the cycles naturally correspond to processes in the process method, and the end of activities to events in the event based method.

(2) Simulation strategy oriented methods. These methods are oriented towards a specific simulation strategy (using the latter’s key notions), but not to any specific simulation language.

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Hence these methods naturally lead to the writing of programs in a simulation language based on the appropriate simulation strategy. This group of methods includes event graphs [ll].

(3) Simulation language oriented methods. These methods often use a kind of flowchart of dynamic system entities (transactions) flowing through the blocks to represent system actions. Each symbol in such a diagrammatic approach is equivalent to one statement of a language. The two key versions of these methods are GPSS block diagrams [lo] and SLAM networks [S].

(4) Methods borrowed from other computer modelling areas. An example of these methods is an application of semantic nets for simulation model representation [2]. The model is created on a number of levels, starting with links between objects and activities and entities, assigning numerical values and providing a graphic user interface. This method is equipped with its own simulation programming support. Another example is the proposed use of entity-relationship modelling [5].

3. Description and demonstration of key diagrammatic methods

Four key diagrammatic methods are presented to illustrate and compare the above methods. These are augmented Petri nets, activity cycle diagrams, event graphs and GPSS block diagrams. The criteria for selection were the level of development and stability of the methods, their intensity of usage and availability of documentation. The main characteristics of the selected methods are described, and then explained by their application to a simple problem. The idea behind the example is to show how the methods work, not what their limitations are. The example problem is a simple job shop, which will be described for each of the methods immediately after the description of the method. This problem is a demonstration of a simple process-type open problem with arrivals of entities flowing through the system: a simple job shop consists of a single input flow of consumers or jobs who wait to be served by a single server or machine until the server is free.

3.1. Augmented Petri nets

The original Petri nets contain the following components: transitions (represented by bars), places (circles), directed arcs and tokens. Arcs join transitions and places, while tokens are dynamic elements moving from place to place. Places and transitions alternate in the net, so that each transition has its preceding (input) and succeeding (output) places. The net is activated by firing its transitions: firing is enabled when all input places of the transition have tokens. After firing, tokens are removed from their input places and shifted to the output places.

In augmented Petri nets used in simulation [4], time delays are added (using temporal events shown with a star symbol and which represents the condition for a transition firing). These time delays give individuality to tokens, which can therefore be created, destroyed, split or merged. Other additions are control arcs, route selection by AND and OR events etc. Transitions correspond to events in simulation, places to activities or states, and tokens to dynamic entities.

Figure 1, an augmented Petri net for the job shop, shows the customer process and server cycle. The start of service transition (event) can be fired only when there is a customer in a

320 V. Ceric, R.J. Paul / Diagrammatic representations of simulation models

customer * arrival

-?I-

customer departure

(SERVE ) \ I”LI

h

0 ph%S

- transitions

* passage of time . . w transition firing

.

customer process

Fig. 1. Augmented Petri net representation.

“wait” place (state) and a server in the “idle” place. Customer arrival and departure transitions (events) require the passage of time, shown by temporal events (star symbols).

3.2. Activity cycle diagrams

Activity cycle diagrams consist of a number of entity life cycles. In each life cycle, the entity cycles through alternating active and passive states, i.e., activities and queues. Activities are interaction points between different life cycles in an activity cycle diagram, where different types of entities cooperate, while queues represent states of entities waiting for some conditions to be fulfilled in order to move to an active state. Activity cycle diagrams are commonly used in the classical activity scanning simulation strategy or in its more recent variant of the three-phase strategy. However, the method has universal applicability.

Figure 2, the example activity cycle diagram, shows three life cycles. “Arrival” and “service” activities are the interaction points between different entities. For example, the “service” activity starts whenever both the customer queue “wait” and the server queue “idle” are nonempty.

3.3. Event graphs

Event graphs, as shown in Fig. 3, are a diagrammatical tool for the event scheduling simulation strategy. The events are described by nodes, while the relationships between events are described by directed arcs between events. The arcs can cause either event-scheduling or event-cancelling, and each of them can have attached the time delay and some condition for its activation.

Figure 3 shows the three events for the example system (customer arrivals, start of service and end of service), with the mutual scheduling event logic of the system. So the customer

K Ceric, R.J. Paul / Diagrammatic representations of simulation models 321

IDLE 0 server

Fig. 2. Activity cycle diagram representation.

active state

-.

queuing state

arrival event schedules both the following customer arrival event after an interarrival time delay, and the start of service event when the condition “server idle” is fulfilled.

3.4. GPSS block diagrams

This is a flowchart description for GPSS language-based simulation programs. Each symbol is equivalent to one GPSS block, which is a statement representing a block of code describing one simulation function. A sequence of connected blocks in a diagram represents a process. Permanent entities (resources> are captured and freed by temporary entities (transactions) in corresponding blocks. Transactions may be created, destroyed, split or merged.

1 (sewer idle)

(customers are waiting for

service)

Fig. 3. Event graph representation.

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GENERATE

QUEUE

SEIZE

inter-arrival time

wait

server

IKX B A DEPART wait

ADVANCE

RELEASE

TERMINATE

service-time

server

CUSTOMER PROCESS

Fig. 4. GPSS block diagram representation (notation of [ 141).

Figure 4 shows a customer process, where the start and finish of the server engagement is described by a simple designation of the server entity name in corresponding blocks (SEIZE and RELEASE). The passage of time is designated in the ADVANCE block. Situations arise in which the transactions cannot move to the next block (e.g., if the server is not available) or have to stay in a block for some time (e.g., for the service time). In such situations, the points at which transactions are waiting are called reactivation points, and transactions have to pause until the system conditions enable them to move on.

4. A comparison of the selected diagrammatic modelling methods

The selected diagrammatic modelling methods are briefly compared along the following lines: simplicity and ease of understanding, hierarchical modelling ability, ability of describing simulation complexity and possibility of automatic program generation. Precise comparison of the different diagrammatic methods is almost impossible because of the qualitative nature of such criteria, and because of the bias introduced by researcher’s own experience. The influence of previous experience and the time needed to master a new method produces a tendency to favour the method being used. However, some parameters are given for comparison of the methods.

(1) Simplicity and ease of understanding. Activity cycle diagrams and event graphs use the least number of concepts, closely followed by the augmented Petri nets, while GPSS block diagrams uses significantly more concepts (types of blocks). Our feeling is that the activity cycle diagram and GPSS block diagrams are easiest to understand - the other methods require more simulation technical knowledge to understand the diagram concepts. The most “natural” approach for computer scientists seems to be the GPSS block diagram transaction flow. Activity

V. Ceric, R.J. Paul / Diagrammatic representations of simulation models 323

cycle diagrams are claimed to be the easiest to explain to customers. Event graphs hide all the consequences of the events in the event routines and these do not appear on the diagram.

(2) Hierarchical modelling ability. An important feature of the representation method is its ability to represent complex systems on various levels - a hierarchical ability means that, starting from the rather simple highest level, lower levels can be introduced into the higher levels by extending parts of the higher level model. In such a way the gradual development of a complex conceptual model can be supported. Augmented Petri nets seems to be the only method for which the hierarchical modelling ability is used [12], although some research into activity cycle diagrams is reported [l].

(3) Ability t o d escribe simulation complexity. There are many sources of simulation complex- ity, principally connected with the various characteristics of contemporary technological sys- tems, which are the main candidates for simulation modelling. The only serious approach towards the structuring and description of simulation complexity is due to [4], although it is primarily focused on a comparison of simulation languages. According to this approach there are two groups of simulation complexities: linear complexities dealing with the linear sequence of the entities histories in a model, and nonlinear complexities, which are abilities of entities to follow more than one line of behaviour such as splitting, merging and autointeracting.

As might be expected, the GPSS block diagram, being a one-to-one description of the GPSS language, can describe most simulation complexities. Augmented Petri nets introduced a number of concepts for describing simulation complexities, but a similar augmentation has not emerged for activity cycle diagrams or for event graphs. However, while adding additional concepts augments the power of representation of a method, it also works against the simplicity of the method, which is a key requirement for conceptual modelling.

Further research is needed for a more complete comparison of the ability of diagrammatic modelling methods to handle simulation complexity.

(4) Possibility of automatic program generation. Automatic simulation program generation on the basis of the conceptual model enables the flexible usage of conceptual models in frequent reformulations of the problem [3]. Such a tool raises the importance of the conceptual models as a linguistic agent for communication between different participants in the simulation process, because of the ability to quickly convert the conceptual model into a simulation program. It appears that activity cycle diagrams are used as the conceptual modelling technique for nearly all known automatic program generators which are based on diagrammatic concep- tual modelling methods.

5. The principle of comprehensive harmony

Conceptual modelling in simulation was developed from the very beginning of simulation modelling. However, different methods offer different types of representation and different advantages. Which of them to use, and in which circumstances, is not clear. There is a need for a principle which adequately describes the essential requirements of modelling: a well-under- stood representation of complex systems as well as the development of the model with a full specification and hence the ability to validate.

This principle has been formulated as that of comprehensive harmony [3], which has two key constituents. (1) The modelling method has to be comprehensive, enabling the representation of

324 K Ceric, R.J. Paul / Diagrammatic representations of simulation models

complex technological and social systems. (2) The modelling has to be harmonized in such a way as to be an intelligible representation for all participants in the simulation process.

Simultaneous achievement of these two characteristics would lead to modelling which would both be powerful, as well as manageable by human beings. A lot of work has to be done by the simulation community in order to satisfy the challenging requirements of the principle of comprehensive harmony.

6. Conclusions

This paper describes diagrammatic methods for conceptual modelling in discrete event simulation. Besides the suggested taxonomy of these types of methods, four of the most used diagrammatic methods were selected, and each was applied to the modelling of a simple job shop. The most significant characteristics of these methods were described and compared showing their relative simplicity, modelling power and usefulness in the simulation process. Research is continuing into a more detailed comparison of existing diagrammatic modelling methods, including demonstrations of their application to a spectrum of different and charac- teristic simulation problems. The principle of comprehensive harmony is offered as a guide to the further development of conceptual modelling in simulation.

References

[l] G. Au and R.J. Paul, A complete graphical discrete event simulation environment, CASM Report, Dept. Information Systems, London School of Economics, 1990.

[2] M. Barakat and R.J. Paul, Semantic modelling for discrete event simulation, CASM Report, Dept. Information Systems, London School of Economics, 1989.

[3] V. Ceric and R.J. Paul, Methods of model representation in discrete event simulation: an overview, J. Oper. Res. Sot., submitted.

[4] J.B. Evans, Structures of Discrete Event Simulation: An Introduction to the Engagement Strategy (Ellis Horwood, Chichester, 1988).

[S] A.R. Hutchings, Introduction to entity - relationship modelling for OR analysts, J. Oper. Res. Sot. 41 (1990) 191-200.

[6] W. Kreutzer, System Simulation: Programming Styles and Languages (Addison-Wesley, Sydney, 1986). [7] M. Pidd, Computer Simulation in Management Science (Wiley, Chichester, 2nd ed., 1988). [8] A.A.B. Pritsker and CD. Pegden, Introduction to Simulation and SLAM (Wiley, New York, 1979). [9] G. Schiffner and H. Godbersen, Function nets: a comfortable tool for simulation database system architectures,

Simulation 46 (1986) 201-210. [lo] T.J. Schriber, Simulation Using GPSS (Wiley, New York, 19741. [ll] L. Schruben, Simulation modelling with event graphs, Comm. ACM 26 (1983) 957-963. [12] A.A. Torn, Simulation graphs: a general tool for modelling simulation designs, Simulation 37 (1981) 187-194. [13] A.A. Torn, Simulation nets, a simulation modelling and validation tool, Simulation 45 (1985) 71-75. [14] W. Young, M.A.P. Taylor and P.G. Gipps, Microcomputers in traffic engineering, Research Press Studies Ltd,

Taunton, United Kingdom, 1989.