Title: Strategic behaviour for M/M/1 double orbit retrial queue with imperfect service and vacation

Authors: Sibasish Dhibar; Madhu Jain

Addresses: Department of Mathematics, Indian Institute of Technology Roorkee, Haridwar, Uttarakhand, 247667, India ' Department of Mathematics, Indian Institute of Technology Roorkee, Haridwar, Uttarakhand, 247667, India

Abstract: In this paper, optimal strategy for double orbit retrial queue with imperfect service and vacation interruption has been studied. Sometimes, when the waiting space appears to be congested, the incoming customers may decide not to join the system. If the server is busy, the arriving customers are compelled to enter the ordinary or premium class orbit as per willingness of the customers not to pay or pay for waiting in the queue. If some customers are unsatisfied with their service during the normal busy period, they may demand additional service. Chapman-Kolmogorov governing equations are structured and solved analytically by using the probability generating functions. Several performance indices and optimal social profit with joining strategy are derived explicitly. The numerical results are obtained to analyse the effects of system descriptors on the performance indices, joining probabilities, etc. Moreover, particle swarm optimisation technique has been used to establish the optimal service policy.

Keywords: retrial queue; imperfect service; vacation; equilibrium strategy; social profit; particle swarm optimisation.

DOI: 10.1504/IJMOR.2023.132479

International Journal of Mathematics in Operational Research, 2023 Vol.25 No.3, pp.369 - 385

Received: 16 May 2022
Accepted: 19 May 2022
Published online: 24 Jul 2023 *

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