Physical Sciences and Mathematics Commons^™

First Passage Processes In Queuing System Mx/Gr/1 With Service Delay Discipline, Lev M. Abolnikov, Jewgeni H. Dshalalow, Alexander M. Dukhovny

Mathematics and System Engineering Faculty Publications

This article deals with a general single-server bulk queueing system with a server waiting until the queue will reach level r before it starts processing customers. If at least r customers are available the server takes a batch of the fixed size r of units for service. The input stream is assumed to be a compound Poisson process modulated by a semi-Markov process and with a multilevel control of service time. The authors evaluate the steady state probabilities of the queueing processes with discrete and continuous time parameter preliminarily establishing necessary and sufficient conditions for the ergodicity of the processes. …