Mathematical models for two kind of single-server queueing systems with arbitrary service-time distribution

Abstract

We propose here a analytical method for the study of queueing systems with generalized time distributions. The idea is to define a new type of stochastic process, called a generalized Markov renewal process, which aay describe the transition behavior of the stochastic process at non-regenerative points. By means of the GMRP method, Mathematical models are then developed for two kind of typical single-server queueing systems which are the M/G/l/N/N and M/G/l/N queueing systems. The system performance Measures, such as the steady-state probability distribution of the number of customers in the system, expected queue length, expected number of customers in the system, average waiting time, mean busy period lengths, and so on, are derived for both the queueing systems.