A Model for a Vacation Queuing Policy Considering Server’s Deterioration and Recovery

Abstract

In this paper, we present a vacation queue model in which the service rate of the server deteriorates during the service period (e.g., due to the fatigue of a human server or the wear and ageing of machinery) and recovers during the vacation period (e.g., following a recuperation period for a human sever or the servicing of a machine). During the recuperation period, the main server is replaced with a temporary server with inferior capabilities. Using the multi-dimensional Markov process, we analyze the effects of different vacation policies on the target function and focus on the scheduling of the vacation period as a function of the deterioration and recovery rates. It is shown that the use of vacations to allow the server to rest and regain efficiency has a strong and valuable effect on the mean customer waiting time, to the extent that switching servers may be beneficial for the system, even when implemented at a point in time when the main server’s service rate is still much higher than that of the temporary server.

Keywords

• queuing theory
• vacation queue
• deterioration
• recovery