TY - JOUR
T1 - An M/G/1 Queue with Repeated Orbit While in Service
AU - Hanukov, Gabi
AU - Barron, Yonit
AU - Yechiali, Uri
N1 - Publisher Copyright:
© 2024 by the authors.
PY - 2024/12
Y1 - 2024/12
N2 - 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.
AB - 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.
KW - orbit while in service
KW - patience time
KW - repeated trials
KW - supplementary variable
UR - http://www.scopus.com/inward/record.url?scp=85212078783&partnerID=8YFLogxK
U2 - 10.3390/math12233722
DO - 10.3390/math12233722
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AN - SCOPUS:85212078783
SN - 2227-7390
VL - 12
JO - Mathematics
JF - Mathematics
IS - 23
M1 - 3722
ER -