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

Gabi Hanukov () and Shraga Shoval
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Gabi Hanukov: Department of Industrial Engineering and Management, Ariel University, Kiriat Hamada, 3, Ariel 40700, Israel
Shraga Shoval: Department of Industrial Engineering and Management, Ariel University, Kiriat Hamada, 3, Ariel 40700, Israel

Mathematics, 2023, vol. 11, issue 12, 1-21

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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