Limited Capacity Variable Queuing System Analysis

A non-markovian queueing system with finite waiting room and variable channels is studied in this paper.Multi-channel queueing system with finite waiting room has been studied by a lot of researchers in the past few years,but a model with finite waiting room and variable channels has not been seen in open literatures.For this reason we do some research on two models.For the first model with variable channels,the customers arrive singly.The inter-arrival and service times are arbitrarily and exponentially distributed,respectively.The distribution of the number of customers in the system at prearrival and arbitrary epochs are obtained using imbedded Markov chain and semi-regenerative method.We also get the distribution of waiting time at prearrival epochs.Model two is in the base of model one.The only difference is that in model two batch arrivals are considered.Since the system has finite waiting room,when a new batch arrives,we have a partial batch rejection if there is not enough room to hold the new batch customers.That's mean the customers of new batch is not allowed to come into the system when the system is full,then the surplus customers have to leave.In this model we also first do some research on its imbedded markov chain.Then suppose we have got the distribution of the number of customers at the prearrival epochs,using semi-regenerative method we get the distribution of the number of customers at arbitrary epochs.