Optimal probabilistic allocation of customer types to servers

The model under consideration consists of n customer types attended by m parallel non-identical servers. Customers are allocated to the servers in a probabilistic manner; upon arrival customers are sent to one of the servers according to an m × n matrix of routing probabilities. We consider the problem of finding an allocation that minimizes a weighted sum of the mean waiting times. We expose the structure of an optimal allocation and describe for some special cases in detail how the structure may be exploited in actually determining an optimal allocation.