A Single-Server Bulk-Service Queue With Varying Capacity And Erlang Input

Abstract

AbstractThis paper deals with a bulk-service queuing model denoted by It is assumed that the interarrival times are i.i,d.r,v,’s each having the A-phase Erlangian distribution, the service is in bulk, and there is a single exponential server of capacity b. The random variable X denotes the number of units already present with the server at a service epoch, and if X = m (≤ b), then the server takes (b - m) more units or the whole queue length, whichever is smaller. Under the assumption that at a service epoch the server does not wait for the units to arrive if he finds the queue empty, we derive limiting distributions of queue sizes at random, post-departure, and pre-arrival epochs. The first two moments of the distributions are listed. The results are specialized to suit the case of deterministic input. One of the main features of this study is that the results are expressed in terms of a unique real root of the characteristic equation and are thus easy to compute numerically. A sample listing of the root...