Modeling Erlang′s Ideal Grading with Multirate BPP Traffic

Abstract

This paper presents a complete methodology for modeling gradings (also called non-full-availability groups) servicing single-service and multi-service traffic streams. The methodology worked out by the authors makes it possible to determine traffic characteristics of various types of gradings with state-dependent call arrival processes, including a new proposed structure of the Erlang’s Ideal Grading with the multirate links. The elaborated models of the gradings can be used for modeling different systems of modern networks, for example, the radio interfaces of the UMTS system, switching networks carrying a mixture of different multirate traffic streams, and video-on-demand systems. The results of the analytical calculations are compared with the results of the simulation data for selected gradings, which confirm high accuracy of the proposed methodology.

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

“…To solve them, the iterative process proposed in [57] has to be applied. Thus determined occupancy distribution allows us then to determine the blocking probability for each of the m service classes.…”

Modelling of the access part of a multi-service mobile network with service priorities

“…Let us consider an EIG to which a mixture of call streams M with different bit rates is offered. The group is defined by the demands of individual call classes The EIG group is a particular instance of a non-fullavailability groups [14,29] that was defined by Erlang for a single-service case as early as in the beginning of the twentieth century [30]. An approximated model of the group for a multi-service case is proposed in [13].…”

“…These models are essentially based on the model of the multi-service full-availability group [11,12]. In this paper, however, to model the wideband code division multiple access (WCDMA) interface, a model of a multi-service Erlang's ideal grading is used [13,14]. In addition, the paper proposes a model of the non-fullavailability group with priorities based on the approach that has been earlier adopted for the analysis of priorities in the full-availability group [5,6].…”

“…The non-full-availability group is the so-called statedependent system [14,15]. This dependence results from the particular structure of the system in which calls arriving at the input have access to a limited amount of resources, substantially lower than the total capacity of the system.…”

“…This model is then expanded to include the possibility of performing calculations for non-integer vales of availability [31]. The most extensive description of multi-service non-full-availability groups is provided in [14] in which different models of multi-service ideal non-full-availability groups, defined for different types of call streams and different structures of groups, are presented.…”