Routing in the Presence of Breakdowns

Jobs from Poisson input stream can be routed through N alternative gateways, modelled as parallel M/M/1 queues. The servers at those queues are subject to random breakdowns and repairs. When a server fails, all jobs present in the corresponding queue are lost; moreover, no incoming jobs are directed to that queue during the subsequent repair period. The marginal queue size distributions are determined by finding the roots of a polynomial inside the unit disc, and solving a set of simultaneous linear equations. The optimal splitting of the input stream between the servers, as to minimize the job loss rate, is examined.