On the analysis of single server finite queue with state dependent arrival and service processes:M(n)/G(n)/1/K

Abstract

This paper discusses the analysis of a single server finite queue with Poisson arrival and arbitrary service time distribution, wherein the arrival rates are state dependent which are all distinct or all equal, service times are conditioned on the system length at the moment of service initiation. The analytic analysis of the queue is carried out and the final results have been presented in the form of recursive equations which can be easily programmed on any PC to obtain the distributions of number of customers in the system at arbitrary, departure and pre-arrival epochs. It is shown that the method works for all service time distributions including the non-phase type and also for low and high values of the model parameters. Some performance measures, and relations among the state probabilities at arbitrary, departure and pre-arrival epochs are also discussed. Furthermore, it is shown that results for a number of queueing models can be obtained from this model as special cases. To demonstrate the effectiveness of our method some numerical examples have been presented.