Research and Comparative Analysis of the Dual Pair of the E2/M/1 and M/E2/1 Systems

Abstract

Queueing theory is widely used in many branches of science and technology: in modeling active network equipment in telecommunications, to assess performance indicators of computer networks, to model traffic flows, in logistics problems, and much more. An alternative section of mathematical modelling - simulation modelling is also based on modelling the operation of queuing systems. In turn, in the theory of queueing, many results are obtained using the method of spectral expansion of the solution of the Lindley integral equation for a particular system. The paper proposes results on two dual queuing systems (QS) with general second-order Erlangian input distributions for which the author did not find information in the scientific literature. Thus, the paper presents spectral decompositions and formulas obtained on their basis for the main characteristic of the QS-average delay of incoming requests in the queue. The systems under consideration refer to systems of the G/M/1 and M/G/1 types, respectively. The obtained results of computational experiments indicate a significant difference between these systems and thus confirm the general theory of queueing. The adequacy of the obtained mathematical models is based on the correct use of the apparatus of the spectral decomposition method.