Applicability of the Extensions of the Erlang Multirate Loss Model on ABR Services in ATM Networks

In this paper, we evaluate three extensions of the Erlang Multirate Loss Model by comparing them, based on the resultant call blocking probabilities for ABR services in ATM networks. In the first extension, the retry models, blocked calls can retry with reduced resource requirements and increased arbitrary mean residency requirements. In the second one, the threshold models, request sizes and residency times are state dependent. We propose a third extension, the connection-dependent threshold model, which resembles the threshold models, but the state dependency is individualized among call connections. Our investigation shows that the retry models can hardly approach the behavior of ABR services, while the proposed model performs much better than the other two extensions. 1. Introduction ATM networks are designed to accommodate a variety of service-classes with different traffic description parameters and quality-of-service (QoS) requirements. We study the QoS assessment of call level traffic in the multi-service environment of ATM networks which is very important since it is basic requirement for several network/traffic controls like connection admission control, virtual path bandwidth control and network planning. In order to assess the call-level QoS of ABR and CBR services, we evaluate the call blocking probability (CBP). On the call level, ATM networks that accommodate CBR and VBR can be modeled as multi-rate circuit switched networks [1] due to the notion of equivalent bandwidth [2]. Therefore, we manage the call-level traffic of CBR and VBR services by using the Erlang Multirate Loss Model (EMLM) [3]. In the case of ABR services the notion of CBP needs to be reconsidered, because no resource allocation is made prior to the information transfer phase. The CBP depends strongly on the required holding (service) time of an ABR call-connection, while the holding time depends on the available bandwidth and it is not known in advance for ABR services. Nevertheless, it is possible to calculate the CBP of ABR and QoS guarantee services, by using the notion of “total” offered traffic-load [4]. The traditional models for calculation of CBP pay no attention to congestion control, which is quite important for ABR services. Two models, which comprise some kind of congestion control, are the retry and the threshold models [5,6]. In this paper we propose a generalization of the threshold models, called connectiondependent threshold model (CDTM), whereby we approach much better the behavior of ABR services. With application examples, we reveal the superiority of the CDTM in respect of CBP while simulation results in [7] show the validity of the CDTM. 2. The connection-dependent threshold model (CDTM) Consider k (k=1,2…K) independent service-classes of Poisson arriving calls, which offer traffic-load αk and request an integer valued bk bandwidth and μk mean holding time, and a transmission link (Virtual Path, VP) of bandwidth C (C servers). In the threshold model instead of waiting for calls to be blocked and then retry, bandwidth and service time requests depend on the total number of occupied bandwidth units, denoted by j. In other words, a call of service-class k, may attempt n+1 times to be connected; one initial attempt with parameters (bkc, μkc) and n more attempts, with parameters (bkcl, μkcl ), l= 1,…,n, where bkcn < …< bkc1 < bk and μkc1 -1 > …> μkcn -1 > μk; the pair (bkcl, μkcl ) is used when Jl < j ≤ Jl+1, Jn+1 = C, while the highest possible threshold is Jn = C-bkcn . According to [7] the final unconditional CBP for the threshold models, Bk, is defined as: Bk= Prob{ j > C-bkc } = Prob{ j > C-bkc | j > Jn } * Prob{ j > Jn }.and is given by: