Title: Analysis of M^[X]/G_k/1 retrial queue with Bernoulli-2 vacation, search for customers and hot stand-by

Authors: J. Radha; K. Indhira; V.M. Chandrasekaran

Addresses: School of Advanced Sciences, VIT, Vellore-14, India ' School of Advanced Sciences, VIT, Vellore-14, India ' School of Advanced Sciences, VIT, Vellore-14, India

Abstract: A batch arrival retrial queueing model with k optional stages of service, extended Bernoulli vacation and stand-by is studied. After completion of the i^th stage of service, the customer may have the option to choose (i + 1)^th stage of service with probability θ_i or may leave the system with probability q_i = 1 − θ_i, I = 1, 2, …, k − 1 and q_k = 1. After service completion of each customer, the server may take a vacation with probability v₁ and extend a vacation with probability v₂ or rejoin the system after the first vacation with probability 1 − v₂. Busy server may get to breakdown and the stand-by server provides service only during the repair times. At the completion of service, vacation or repair, the server searches for the customer in the orbit (if any) with probability α or remains idle with probability 1 − α. By using the supplementary variable method, steady state probability generating function for system size, some system performance measures like L_q, L_s, W_q and W_s are discussed. Simulation results are given using MATLAB.

Keywords: retrial; k-optional service; orbital search; standby; extended vacation; supplementary variable technique.

DOI: 10.1504/IJPMB.2020.106139

International Journal of Process Management and Benchmarking, 2020 Vol.10 No.2, pp.196 - 223

Received: 11 Jul 2017
Accepted: 28 Jan 2018
Published online: 01 Apr 2020 *

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