Abstract
Heterogeneous servers which can differ in service speed and reliability are becoming more popular in the modelling of modern communication systems. For a two-server queueing system with one non-reliable server and constant retrial discipline we formulate an optimal allocation problem for minimizing a long-run average cost per unit of time. Using a Markov decision process formulation we prove a number of monotone properties for the increments of the dynamic-programming value function. Such properties imply the optimality of a two-level threshold control policy. This policy prescribes the usage of a less productive server if the number of customers in the queue becomes higher than a predefined level which depends on the state of a non-reliable more powerful server. We provide also a heuristic solution for the optimal threshold levels in explicit form as a function of system parameters.
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