An M/G/1 Queue with Repeated Orbit While in Service

Gabi Hanukov (), Yonit Barron and Uri Yechiali
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Gabi Hanukov: Department of Industrial Engineering & Management, Ariel University, Ariel 40700, Israel
Yonit Barron: Department of Industrial Engineering & Management, Ariel University, Ariel 40700, Israel
Uri Yechiali: Department of Statistics and Operations Research, Tel Aviv University, Tel Aviv 69978, Israel

Mathematics, 2024, vol. 12, issue 23, 1-22

Abstract: Orbit and retrial queues have been studied extensively in the literature. A key assumption in most of these works is that customers “go to orbit” when they are blocked upon arrival. However, real-life situations exist in which customers opt to go to orbit to efficiently use their orbit time rather than residing dormant at the service station while waiting for their service to be completed. This paper studies such a system, extending the scope of traditional orbit and retrial queues. We consider an M/G/1 queue where customers repeatedly go to orbit while their service remains in progress. That is, if a customer’s service is not completed by within a specified “patience time”, the customer goes to orbit for a random “orbit time”. When the customer orbits, the server continues rendering her/his service. If, on return, the service is already completed, the customer leaves the system. Otherwise, s/he waits for another patience time. This policy is repeated until service completion. We analyze such an intricate system by applying the supplementary variable technique and using Laplace–Stieltjes transforms. Performance measures are derived, and a comparison analysis is provided between various service time distributions.

Keywords: orbit while in service; patience time; repeated trials; supplementary variable (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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