Customer routing to parallel servers with different rates

We consider the problem of routing customers to parallel servers having different rates. There are no buffers in the system. Each customer must be rooted to a server immediately upon its arrival and if the server to which it is routed is occupied, then the customer is aborted. The aim is to maximize throughput (the proportion of customers which are successfully routed to a free server), when the routing must be done without knowing which servers are occupied and which are free. An upper bound on the throughput is found for a general renewal arrival process and geometric service times. Furthermore, a new routing policy, the golden ratio policy, is suggested and shown to approach a limit which is within at least 98.4 percent of the upper bound. The golden ratio policy is a generalization of the round robin policy, when the service rates of the servers are different.