Calculating Expected Incomes in Open Markov Networks with Requests of Different Classes and Different Peculiarities

Abstract

A system of difference-differential equations for the expected incomes of open Markov queueing networks with different peculiarities is considered. The number of network states and also the number of equations in this system are both infinite. The incoming flows of requests are elementary and independent while their service times have exponential distributions. The incomes from transitions between different states of the network are deterministic functions that depend on its states; the incomes gained by the queuing server systems per unit time under the invariable states also depend on these states only. The system of the difference-differential equations is solved using the modified method of successive approximations combined with the series method. An example of a Markov G-network with signals and the group elimination of positive requests is studied. As demonstrated below, the expected incomes can be increasing and decreasing time-varying functions; can take positive and negative values.