Title: Joining strategy for double orbit retrial queue with imperfect service and vacation under N-policy

Authors: Palak Mehta; Madhu Jain

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

Abstract: Optimal joining policy for Markovian retrial queueing system operating under N-policy and having ordinary and premium orbits, has been investigated. There is provision of additional service to the unsatisfactory ordinary orbit customers whereas unsatisfactory executive orbit customers may re-join the queue as a feedback customer. The proposed queueing system is investigated by implementing probability generating function (PGF) approach and evaluating various performance measures. Numerical experiments are performed to validate the analytical metrics obtained. The adaptive neuro fuzzy inference system (ANFIS) approach has also been implemented to authenticate the feasibility of intelligence computing for various metrics. The optimal joining probability is obtained by maximising the profit function value using particle swarm optimisation (PSO). The sensitivity of the queueing indices along with cost function has also examined by conducting the numerical simulation.

Keywords: double orbit retrial queue; N-policy; imperfect service; feedback; joining strategy; particle swarm optimisation; PSO.

DOI: 10.1504/IJMOR.2025.146354

International Journal of Mathematics in Operational Research, 2025 Vol.30 No.4, pp.435 - 469

Received: 26 Jul 2023
Accepted: 01 Aug 2023
Published online: 27 May 2025 *

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