Analysis of Two-Channel Multi-Flow Queuing System with Resequence Customers and Distributions of Phase Type

The two-channel finite-capacity queuing system with several Poisson flows of customers of different types is considered. The service time is distributed according to phase-type which depends on the type of customers and the device of which it is served. On leaving the system there is a buffer in which there is a resequence of customers according to order of their receipt. Functioning of the system is described by uniform Markov process. In the assumption that intensity of flows and service of customers are positive and finite the final probabilities of statuses of Markov process exist, are strictly positive, don’t depend on initial distribution and match the stationary probabilities. For search of these probabilities the equilibrium system of equations is removed. Then possibility of convergence of the received equations to the similar equations for queuing system with resequence of customers with one Poisson flow of summary intensity and the subsequent determination of the type of customers just before arrival on service is set. The last circumstance allowed using results of the previous operations of authors for calculation of stationary distribution of queue length. As a result the recurrent matrix algorithm was developed for calculation of probabilities of statuses of considered system in the conditions of a stationary operation mode.

queuing system, phase type distribution, stationary probabilities, resequence customers