컴퓨터 시뮬레이션을 이용한 병렬 대기행렬 시스템의 최적 서버 배치 방안

Abstract

A queueing system with 2 parallel workstations is common in the field. Typically, the workstations have different features in terms of the inter arrival times of customers and the service times for the customers. Computer simulation study on the optimal server allocation for parallel heterogeneous queueing systems with fixed number of identical servers is presented in this paper. The queueing system is optimized with respect to minimizing the weighted system time of the customers served by 2 parallel workstations. The system time formula for the M/M/c systems in Kendall’s notation is known. Thus, we first compute the optimal allocation for parallel M/M/c systems, comparing the results with those from the computer simulation experiments, and have the same results. The CETI rule is devised through optimizing M/M/c cases, which allocates the servers based on Close or Equal Traffic Intensities between workstations. Traffic intensity is defined as the arrival rate divided by the service rate times the number of servers. The CETI rule is shown to work for M/G/c, G/M/c queueing systems by numerous computer simulation experiments, even if the rule cannot be proven analytically. However, the CETI rule is shown not to work for some of G/G/c systems.