ON A STOCHASTIC-MODEL OF A NON-MARKOVIAN TIME-DEPENDENT QUEUING SYSTEM WITH GENERAL INTERTRANSITION TIME DISTRIBUTION

This paper studies the stochastic behaviour of a non-Markovian queueing system in continuous and discrete time. The system deals with a non-Markovian type of a departure mechanism, wherein, the intertransition time distribution is general, so that results corresponding to the situation where intertransition times are governed by a particular process could be easily derived. Further, the arrival mechanism dealt with here is Markovian. The analysis of the system leads to Laplace transforms of the probability generating function of the time-dependent queue length distribution in transient and steady-states. Finally, some important particular cases are derived.