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

[摘要] We consider a model for a single link in a circuit-switchednetwork. The link hasCcircuits, and the input consistsof offered calls of two types, that we call primary and secondary traffic. Of theClinks,Rare reserved for primary traffic. Weassume that both traffic types arrive as Poisson arrival streams. Assuming thatCis large andR=O(1), the arrival rate of primary traffic isO(C), while that of secondary traffic is smaller, of the orderO(C). The holding times of the primary calls areassumed to be exponentially distributed with unit mean. Thoseof the secondary calls are exponentially distributed with a largemean, that is,O(C). Thus, the primary calls have fast arrivalsand fast service, compared to the secondary calls. The loads forboth traffic types are comparable(O(C)), and we assume that the system is “critically loaded”; that is, the system's capacity is approximatelyequal to the total load. We analyze asymptoticallythe steady state probability thatn1(resp.,n2) circuits are occupiedby primary (resp., secondary) calls. In particular, we obtaintwo-term asymptotic approximations to the blocking probabilitiesfor both traffic types.

[学科分类] 应用数学