Mathematics and Computer Science, Volume 2

23Analysis of a Multiserver System of Queue-Dependent Channel Using Genetic Algorithm

Anupama^1⋆ and Chandan Kumar²

¹Department of Mathematics, Darbhanga College of Engineering, Darbhanga, Bihar, India

²Department of Mechanical Engineering, BIT Sindri, Jharkhand, India

Abstract

In the present work, a M/M/3 Queuing system with a Queue-dependent multi-server has been considered. Here, a number of failed machines form a queue and repairmen consider a service provider or service channel which starts its service when the queue length is N. We found a generating function for breakdown machines. Afterwards, some performance measures including idle time and busy time for the system have been evaluated. At last, cost is optimized using a genetic algorithm.

Keywords: M/M/3, repairmen, queue dependent server, genetic algorithm

23.1 Introduction

The concept of a multiserver queueing system with queue-dependent servers is not new. Hahn and Sivazlian, in 1990, developed the M/M/2 model with service stations [5]. Yadin and Naor, in 1963, invented the N policy concept for the single server system [9]. The (0, K, N, M) rule in a two server system used by Rhee and Sivazlian in 1990 helps to derive the working period distribution [12].

Natarajan studied a system for warm stand-bys in 1968 [13]. With one online unit and two standbys with failure and repair time exponentially distributed, this model assumes only one condition, namely that the system will fail if spares are not present for the breakdown ...