Combination of queueing systems of different types with common buffer: A theoretical treatment

Abstract

In the paper, we investigate a combination of two following different queueing systems connected via common limited buffer space: (1) the system of M/G/1-type, in which service time does not depend on demand volume; (2) the processor-sharing system, in which demand length arbitrarily depends on its volume. For such combination, we determine the steady-state loss probability and distribution of number of demands present in each system of the combination.