Analysis of discrete-time multi-server queue with balking

Abstract

This paper analyses a discrete-time multi-server queue with balking behavior. The inter-arrival and service times are assumed to be independent and geometrically distributed. If all the servers are busy, an arriving customer either enters with probability b or balks with probability 1 − b. Otherwise, the service of the arriving customer commences immediately. The system is analysed under the assumptions of an early arrival system and a late arrival system with delayed access. Closed-form expressions for the steady-state probabilities at arbitrary epochs and an outside observer's observation epoch probabilities are obtained. Various performance measures along with some numerical results in the form of a table and graphs are presented. Some special cases of the model have also been discussed. We have shown that the obtained results converge to the results of the continuous-time counterparts in the limiting case.