A CRITICALLY LOADED MULTIRATE LINK WITH TRUNK RESERVATION

We consider a loss system model of interest in telecommunications. The re is a single service facility with N servers and no waiting room. Th ere are K types of customers, with type i customers requiring Ai serve rs simultaneously. Arrival processes are Poisson and service times are exponential. An arriving type i customer is accepted only if there ar e R-i (greater than or equal to A(i)) idle servers. We examine the asy mptotic behavior of the above system in the regime known as critical l oading where both N and the offered load are large and almost equal. W e also assume that R-1, ..., RK-1 remain bounded, while R-K(N) --> inf inity and R-K(N)/root N --> 0 as N --> infinity. Our main result is th at the K dimensional ''queue length'' process converges, under the app ropriate normalization, to a particular K dimensional diffusion. We sh ow that a related system with preemption has the same limit process. F or the associated optimization problem where accepted customers pay, w e show that our trunk reservation policy is asymptotically optimal whe n the parameters satisfy a certain relation.