Asymptotically optimal trunk reservation for large trunk groups

A loss system with N servers, two types of customers, exponential service times, and Poisson arrivals is considered. Customers of class i generate a reward r_i when they enter service (r₁>r₂). The optimal policy has a threshold form known as trunk reservation. The behavior of the optimal trunk reservation level as N→∞ is considered, and it is shown that in a case of practical interest it grows as √N. The approximation to the optimal trunk reservation level obtained from the asymptotic analysis works extremely well