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

Abstract EN

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 primary traffic is O(C), while that of secondary traffic is smaller, of the order O(C).

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, O(C).

Thus, the primary calls have fast arrivals and fast service, compared to the secondary calls.

The loads for both traffic types are comparable (O(C)), 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 n1 (resp., n2) circuits are occupied by primary (resp., secondary) calls.

In particular, we obtain two-term asymptotic approximations to the blocking probabilities for both traffic types.