Unreliable Server Mx/G/1 Queue with Loss-delay, Balking and Second Optional Service

Abstract

This investigation deals with MX/G/1 queueing model with setup, bulk- arrival, loss-delay and balking. The provision of second optional service apart from essential service by an unreliable server is taken into consideration. We assume that the delay customers join the queue when server is busy whereas loss customers depart from the system. After receiving the essential service, the customers may opt for the optional service with some probability or may leave the system. The server is unreliable and hence may breakdown in both essential and optional service cases and requires a setup time before being repaired. The service during essential service, setup times and repair times for both cases are general distributed while the service time during optional service is exponential. Using the supplementary variable technique, the equations governing the model are constructed. The steady state queue size distribution is then obtained using Laplace transform and probability generating functions. The numerical results for various performance indices have been obtained and illustrated graphically.