Compensating for failures with flexible servers

We consider the problem of maximizing capacity in a queueing network with flexible servers, where the classes and servers are subject to failure. We assume that the interarrival and service times are independent and identically distributed, that routing is probabilistic, and that the failure state of the system can be described by a Markov process that is independent of the other system dynamics. We find that the maximal capacity is tightly bounded by the solution of a linear programming problem and that the solution of this problem can be used to construct timed, generalized round-robin policies that approach the maximal capacity arbitrarily closely. We then give a series of structural results for our policies, including identifying when server flexibility can completely compensate for failures and when the implementation of our policies can be simplified. We conclude with a numerical example that illustrates some of the developed insights.