Performance Analysis of the N-Policy M/H(subscript k)/1 Queuewith Balking and Multiple Vacations

Abstract

This paper presents an analysis for an N-policy M/H(subscript k)/1 queuing system with balking and multiple vacations. The server takes multiple vacations when the system becomes empty. When a vacation is over, if N or more are present in system, the server must begin to serve the customers at once. Otherwise, the server can have another vacation. If customers on ar-rival find other customers in the system, they either decide to enter the queue or balk with a constant probability. By using the matrix geometric solution method, the matrix-geometric form solution for steady-state probability vectors is obtained and the computation of the boundary steady-state probability vectors is also discussed. Then, some performance mea-sures of the system are derived explicitly. Based on these performance analysis, we develop a cost model to determine numerically the system's optimal cost and optimal critical value, and perform a sensitivity analysis through numerical experiments. Finally, we introduce the case of the non-constant balking probability.