Link access blocking in very large multi-media networks

Abstract

This paper is concerned with performance models and approximations for very large, multi-media networks. Blocking is the traditional performance measure in circuit-switched networks, and will remain as such in multi-rate circuit-switched networks. It is also considered a likely performance measure candidate for resource management and dimensioning in broadband fast packet-switched networks, operated under virtual circuit mode. To gain some insight into network-wide blocking phenomena, we study in this paper the basic building block of any network, a single link. Multi-media traffic calls with Poisson arrivals, arbitrarily distributed service times, and different bandwidth requirements (in number of circuits), are offered to a system (link) of finite capacity. A call is rejected when the sharing policy doesn't allow it to be accommodated by the system. Under complete sharing policy, an aggregate state describing the number of occupied circuits is shown to exhibit a product form solution in steady state, when the capacity and traffic intensities become very large asymptotically. This structural property leads to the main result of this paper, an approximation which reduces the computation of the blocking probabilities for the different classes of traffic to the evaluation of a single Erlang formula and the determination of the root of a monotonous polynomial function. We provide comparison curves of the exact blocking probabilities and the approximations for some examples with 3 classes of traffic.