Modelling of state-dependent multirate systems carrying BPP traffic

Abstract

This paper presents a simple approximate calculation methodology of the occupancy distribution and the blocking probability in state-dependent systems with multirate Binomial-Poisson-Pascal traffic. The particular traffic streams are generated by an infinite, as well as by a finite, population of traffic sources. The proposed methodology is based on the generalized Kaufman-Roberts recursion. The model enables calculations to be carried out for the systems in which accepting a new call depends on an admission control algorithm (e.g., a model of a full-availability group with bandwidth reservation) as well as for those systems in which accepting a new call depends on the structure of a system (e.g., a model of a limited-availability group). The results of the analytical calculations have been compared with the simulation results of exemplary state-dependent systems.

Modelling of Cellular Networks with Traffic Overflow

“…It should be stressed, however, that the method can be easily adopted for modelling systems with traffic overflow in which direct resources are offered multiservice BPP (Bernoulli-Poisson-Pascal) call streams [23]. To achieve that, one can make use of the results of studies devoted to modelling (determination of occupancy distributions and the blocking probability) of systems with BPP traffic, such as [48][49][50].…”

Queuing Systems for the Internet

“…In [33] and [34], a model of a multiservice server with call streams of the batched Poisson type is developed. [35] and [36] propose a recursive generalisation of the distribution (6) for Erlang, Engset and Pascal traffic. Distribution (8) is proposed in [12] to be applied in an analysis of a multiservice server with limited traffic compression, and is then generalised in [13] to include a case of unlimited compression (C v → ∞), which means that each call can infinitely decrease its bit rate and increase its service time.…”

A Model of Erlang’s Ideal Grading with Multi-service Traffic Sources

“…Equations (11) and (12) and (9) form then a system of confounding equations. In order to solve a given system of confounding equations, we will apply the iterative method proposed in [30]. To achieve that, let us assume that…”