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

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 is of order 1, the arrival rate of secondary traffic is of order C while that of primary traffic is smaller, of the order of the square root of C. 

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 of the order of the square root of C. The loads for both traffic types are thus comparable (the order of 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 joint steady state probability of the number of circuits are occupied by the primary and secondary calls. 

Particular, we obtain two-term asymptotic approximations to the blocking probabilities for both traffic types. This work compliments part I, where we assumed that the secondary traffic had an arrival rate that was of the order of the square root of C and a service rate that was of the order of the reciprocal of the square root of C. Thus in part I the R trunks were reserved for the "fast traffic", whose arrival and service rates were of the order of C and of 1.