Recurrent Method for Blocking Probability Calculation in Multi-service Switching Networks with BPP Traffic

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

“…In the case of multiservice systems with multiservice traffic sources, in turn, a single source can generate different traffic streams that correspond to the classes related to the given source. The first attempts to apply the effective availability method to multiservice traffic sources with single-service Engset and Pascal traffic sources were presented in [47,48]. Over time, these have been extended to include multiservice switching networks with single-service Engset traffic sources and derived resource access control mechanisms such as, for example, threshold mechanisms [49].…”

“…This method is a modification of the recurrent method described in [48] and developed to determine pointto-group and point-to-point blocking probability in switching networks with single-service traffic sources.…”

“…5]. For the purpose of the discussed recurrent method, to determine effective availability d z (c) for a traffic stream of class c in z-stage equivalent network, the following formula can be used [48]: Parameter π z (c) determines the probability of an event in which a connection of class c between a given switch of the first stage and a given switch of the last stage cannot be set up. The determination of this parameter is based on the analysis of a channel graph for the equivalent switching network [32,59], -υ-the number of output links in a given direction, -η-the value that defines which part of fictitious traffic, in a switch of the first stage, is serviced by the considered direction.…”

“…The computational process [48] starts with the determination of blocking probability E 1 (c). Assuming a non-blocking nature of a switch of the first stage, we get that d 1 (c) = υ and, in consequence:…”

“…The assumption in most works devoted to analytical modelling of switching networks (e.g. [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].…”