Computing steady state probabilities in λ( n)/G/1/ K queue

Abstract

In this paper a recursive method is developed to obtain the steady state probability distribution of the number in system at arbitrary and departure time epochs of a single server state-dependent arrival rate queue λ( n)/G/1/ K in which the arrival process is Markovian with arrival rates λ( n) which depend on the number of customers n in the system and general service time distribution. It is assumed that there exists an integer K such that λ( n) > 0 for all 0 ⩽ n < K and λ( n) = 0 for all n ⩾ K. Numerical results have been presented for many queueing models by suitably defining the function λ( n). These include machine interference model, queues with balking, queues with finite waiting space and machine interference model with finite waiting space. These models have wide application in computer/communication networks.