Properties of Recurrent Equations for the Full‐Availability Group with BPP Traffic

Abstract

The paper proposes a formal derivation of recurrent equations describing the occupancy distribution in the full-availability group with multirate Binomial-Poisson-Pascal BPP traffic. The paper presents an effective algorithm for determining the occupancy distribution on the basis of derived recurrent equations and for the determination of the blocking probability as well as the loss probability of calls of particular classes of traffic offered to the system. A proof of the convergence of the iterative process of estimating the average number of busy traffic sources of particular classes is also given in the paper.

Analytical modelling of multiservice switching networks with multiservice sources and resource management mechanisms

“…In the case of Engset sources, the intensity of arrival of new calls of particular classes decreases with the increase in the number of serviced traffic sources (the occupancy state of the system), whereas in the case of Pascal sources, the intensity of arrival of new calls of particular classes increases along with the increase in the number of serviced traffic sources (the occupancy state of the system) [25,53]. Values A En, j,c (n) and A Pa,k,c (n) of traffic offered, respectively, by Engset sources from set Z En, j and Pascal sources from set Z Pa,k , generating calls of class c in state n of busy AUs, can then be determined as follows:…”

“…In the case of Erlang traffic streams, the intensity of arrival of new calls does not depend on the number of serviced traffic sources (the model assumes an infinite number of traffic sources) [25,53]. As a result, for the considered system, the average value of traffic generated by Erlang sources from set Z Er,i generating calls of class c is:…”

“…To solve a given set of confounded equations, it is necessary to use the iterative methods developed in [25,55]. Having determined the occupancy distribution in the limited-availability group with a reservation mechanism, the blocking probability for calls of class c that belong to set M = {1, 2, .…”

“…As a result, the area of application of the method is broad. The general approach to modelling multi-stage switching networks with Clos structure thus developed also permits us to take into consideration traffic streams generated by multiservice Erlang, Engset and Pascal sources [25].…”

“…[48]) is that inter-stage links can be described by the model of the so-called fullavailability group with multiservice traffic. The model of a full-availability group, without threshold mechanisms and/or reservation, was initially developed for Erlang traffic streams [27,28], and then was expanded to include systems that serviced Engset and Pascal traffic streams [25]. Gła˛bowski and Sobieraj [51] assumes that in the case of the introduction of threshold mechanisms to output directions of a network, inter-stage links can be modelled by the model of a fullavailability group with threshold mechanisms.…”