M-Failure Group Replacement Model for Queueing Systems With Unreliable and Repairable Servers

Abstract

In this research we consider the group replacement problem for an M/M/N production/service system. The servers are unreliable with identically exponentially distributed failure times. The repair cost consists of a fixed cost and a variable cost proportional to the number of repaired machines. In addition there is a holding cost for each customer in the system per unit of time. We develop a specific class of m-failure group replacement policy where the repair is started as soon as the number of failed machines reaches a predetermined level m. In the repair process, we assume the positive repair time and allow server failures during replacement. Finally, we formulate a matrix-geometric model to perform the steady state analysis and to obtain the expected average number of customers and the expected average cost. Besides the mathematical analysis, we numerically demonstrate the properties of the optimal policy for various sets of parameter values.

Replacement Model for Street Lighting Systems

“…Such models include individual replacement model, repair limits replacement model, routine replacement model, age replacement model, and group replacement theory [20,25,26]. Several research works have been dedicated to solving replacement issues based on several policies [21,25,27]. Liu [25] described three categories of group replacement; these are:…”

“…Several research works have been dedicated to solving replacement issues based on several policies [21,25,27]. Liu [25] described three categories of group replacement; these are:…”

Customer-oriented group maintenance model for unreliable service system

“…The first type of group maintenance policy is m-failure. The general idea for this policy is that no repairs are performed until m failed servers have occurred, and then all failed machines in the system are fixed simultaneously ( [1], [12], [31]). The second one is T-age group maintenance policy.…”

“…Accordingly, the group maintenance problems considered in this paper will be classified as queuing systems with unreliable servers, which can be solved by the matrix-geometric method for steady state analysis of a certain class of continuous time Markov processes ( [6], [12], [17], [18], [29]). These related studies can only acquire the expected average number of customers, rather than allow the replacement decision to dynamically depend on the number of customers in system.…”