Optimal Dynamic Allocation of Heterogeneous Servers Under the Condition of Total Overload

We consider the following model, which arises in applications as diverse as satellite communications and emergency services. There are M servers in a service system, with no additional waiting space. The m sup th server has exponentially distributed service times with rate mu sub m, 1 = m = M. There are N customer types. Type n customers arrive to the service system in a Poisson process of rate lambda sub n = q sub n LAMBDA (with q sub i >= O, q sub (1) + ... + qN = 1) If a type n customer is placed into service in server m, a reward r(m,n) is received. If the customer is rejected, no reward is received. Exiting customers (upon service completion or rejection) never return, and preemption of customers in service is not allowed.