Simulation–optimization of complex tandem queue systems with reneging and server breakdowns considering budget constraints

Abstract

This paper presents a simulation–optimization model for tandem G/G/K queuing systems with infinite capacity considering reneging and server breakdowns. In this problem, the entities that enter each queue after a certain amount of waiting time renege from the queue. Moreover, each of the servers may break down based on the failure rates and will be repaired immediately according to the repair rates. Owing to the complexity of these systems, the OptQuest approach that combines the scatter search (SS) and tabu search (TS) algorithms is employed to determine the optimal number of servers in each queue according to the capacity of resources as well as budget constraints. The main objective of this optimization is to minimize the total time in the system by keeping the average waiting time in each queue below the allowable waiting time. Finally, 20 distinct samples of tandem G/G/K queuing systems are used to evaluate the validity of the proposed simulation model and the optimization algorithm. To the best of our knowledge, this is the first study that both simulates and optimizes tandem G/G/K queuing systems by simultaneously considering reneging and server breakdowns such that budget constraints are satisfied.