GA optimization of Petri net-modeled concurrent service systems

This paper deals with the performance modeling and the optimization of concurrent service systems. In large and complex service systems, asynchronous and concurrently occurring activities are common. Petri nets are ideal tools for modeling concurrent systems. However, Petri nets are lacking in time duration concept, in data collecting mechanism and in conjunctive logic on the preconditions of an event. These inherent limitations along with the state explosion problem severely restrict their scope of application. In this paper, we introduce the Client Server Petri net, which overcomes all these limitations. The Client Server Petri net is an extension of the Generalized Stochastic Petri net that allows greater flexibility in modeling and simulating concurrent systems.The total operational cost of service systems consists of service cost and waiting cost. The former is due to the hiring of service personnel, while the latter is due to the fact that customers weary of waiting may take their business somewhere else. The problem, in principle, can be formulated as a multi-objective optimization problem and then solved to obtain the Pareto-front. In this study, however, we formulate it as a single-objective optimization problem because optimization (minimization) of the total cost (service cost + waiting cost) is of paramount importance in economic models.Finding the optimal operational cost becomes a combinatorial optimization problem which we seek to minimize using the genetic algorithm, known for its robustness and versatility as an optimization meta-heuristic. We demonstrate the effectiveness of the novel Client Server Petri net model editor–simulator–optimizer with the practical example of an automobile purchase concurrent service system.