Property of optimal resource sharing policy in systems with N types of competing customer

The problem of capacity allocation to a number of different types of customer is considered. The model is an N-dimensional generalisation of the Erlang loss model. Assuming infinite population for each type of customer, the problem is to improve the system performance which is measured as low probability. A structural property of the optimal policy is derived. It follows that the optimally scheduled system, with nonzero probability, will have to use all its capacity.