A Heterogeneous Two-Server Queueing System with Balking and Server Breakdowns

Abstract

Abstract In this paper, we study an M/M/2 queueing system with balking and two heterogeneous servers, Server 1 and Server 2. Customers arrive according to a Poisson process and form a single waiting line. Two parallel servers provide heterogeneous exponential service to customers on a firstcome first-served basis. It is assumed that Server 1 is perfectly reliable and Server 2 is subject to breakdowns. For this system, we obtain the stationary condition where the system reaches a steady state. We also obtain the steady-state probabilities in a matrix form by using a matrix-geometric solution method. Finally, we produce explicit expressions of some performance measures such as the mean system size, the average balking rate and the probabilities that Server 2 is in various states. Numerical illustrations are also provided.

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