Analysis of M[X]/Gk/1 Retrial Queueing Model and Standby

Abstract

A batch arrival retrial queueing model with k optional stages of service is studied. Any arriving batch of customer finds the server free, one of the customers from the batch enters into the first stage of service, and the rest of them join into the orbit. 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 \({q_{i} =\left \{\begin {array}{l} {1-\theta _{i} ,i=1,2,\ldots k-1} {1,i=k} \end {array}\right \}}\,{ }_{.}\) Busy server may get to breakdown, and the standby server provides service only during the repair times. At the completion of service, the server remains idle to provide the service. By using the supplementary variable method, steady-state probability generating function for system size, some system performance measures are discussed. Simulation results are given using MATLAB.