Analysis of M<SUP align="right">[X]</SUP>/G<SUB align="right">k/1 retrial queue with Bernoulli-2 vacation, search for customers and hot stand-by

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 ith stage of service, the customer may have the option to choose (i + 1)th stage of service with probability θi or may leave the system with probability qi = 1 − θi, I = 1, 2, …, k − 1 and qk = 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 Lq, Ls, Wq and Ws are discussed. Simulation results are given using MATLAB.