Asymptotic Analysis of a Loss Model with Trunk Reservation I: Trunks Reserved for Fast Traffic

We consider a model for a single link in a circuit-switched network. The link has ð ¶ circuits, and the input consists of offered calls of two types, that we call primary and secondary traffic. Of the ð ¶ links, ð ‘… are reserved for primary traffic. We assume that both traffic types arrive as Poisson arrival streams. Assuming that ð ¶ is large and ð ‘… = ð ‘‚ ( 1 ) , the arrival rate of primary traffic is ð ‘‚ ( ð ¶ ) , while that of secondary traffic is smaller, of the order √ ð ‘‚ ( ð ¶ ) . The holding times of the primary calls are assumed to be exponentially distributed with unit mean. Those of the secondary calls are exponentially distributed with a large mean, that is, √ ð ‘‚ ( ð ¶ ) . Thus, the primary calls have fast arrivals and fast service, compared to the secondary calls. The loads for both traffic types are comparable ( ð ‘‚ ( ð ¶ ) ) , and we assume that the system is “critically loaded†; that is, the system's capacity is approximately equal to the total load. We analyze asymptotically the steady state probability that ð ‘› 1 (resp., ð ‘› 2 ) circuits are occupied by primary (resp., secondary) calls. In particular, we obtain two-term asymptotic approximations to the blocking probabilities for both traffic types.