Teletraffic models beyond Erlang

Abstract

In the era where call-level traffic is not anymore of single and constant bandwidth per call, but multidimensional traffic with very different bandwidth per call requirements, or each call may have several alternative contingency bandwidth requirements, while in-service calls may have adaptive features of bandwidth and holding time, or may experience bandwidth compression-expansion, the term Erlang in teletraffic models seems to be obsolete, since it refers to telephone networks or, precisely speaking, to single service systems. Needless to mention the bursty nature of traffic and the necessity of considering apart from Poisson traffic, quasi-random traffic or Batched Poisson call arrival processes, while, in any case, the call admission can be based on several bandwidth sharing policies; all these are far from Erlang. Nevertheless, the term Erlang is still kept, even for multirate teletraffic loss models, thanks to a model, which is applicable when different service-classes are accommodated to a communication link, and provides the same results with the famous Erlang B-Formula, when only one service-class is accommodated to the link. Hence, we name this model Erlang Multirate Loss Model (EMLM). It becomes the springboard of teletraffic modeling for QoS assessment in the multidimensional traffic environment of contemporary communication networks, because of the accurate and efficient Call Blocking Probability (CBP) calculation through a recurrent formula (well-known as Kaufman-Roberts recursion). Recurrence is the most desirable computational feature of a teletraffic model in order to cope with the high bandwidth capacities of network links. In this chaotic traffic environment, we distinguish the calls according to: a) their arrival process, b) their bandwidth requirements upon arrival, and c) their behavior under service. Based on this categorization and relying on the EMLM, we have studied and proposed many efficient teletraffic loss models. We shall restrict on the review of the EMLM, of the so called Connection-Dependent Threshold Model (CDTM) that comprises call retries, and of the Batched Poisson Multirate Loss Model (BPMLM), in which the input process is Batched Poisson. The considered call admission policy is the complete sharing policy, as well as the bandwidth reservation policy, suitable for QoS guarantee.