Asymptotic Analysis of a Loss Model with Trunk Reservation II: Trunks Reserved for Slow Traffic

Abstract

We consider a model for a single link in a circuit switched network. The link has C circuits, and the input consists of offered calls of two types, that we call primary and secondary traffic. Of the C links R are reserved for primary traffic. We assume that both traffic types arrive as Poisson arrival streams. Assuming that C is large and R=O(1), the arrival rate of secondary traffic is O(C) while that of primary traffic is smaller, of the order . The holding times of the secondary calls are assumed exponentially distributed with unit mean. Those of the primary calls are exponentially distributed with a large mean, that is . The loads for both traffic types are thus comparable (O(C)) and we assume that the system is “critically loaded,” i.e., the system's capacity is approximately equal to the total load. We analyze asymptotically the steady state probability that n2 (resp. n1) circuits are occupied by primary (resp. secondary) calls. In particular, we obtain two‐term asymptotic approximations to the blocking probabilities for both traffic types. This work complements part I, where we assumed that the secondary traffic had an arrival rate that was and a service rate that was . Thus in part I the R trunks were reserved for the “fast traffic,” whose arrival and service rates were O(C) and O(1).