Optimal Control of a Two-Server Heterogeneous Queueing System with Breakdowns and Constant Retrials

Heterogeneous servers which can differ in service speed and reliability are getting more popular in 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 the two-level threshold control policy. This policy prescribes the usage of the less productive server if the number of customers in the queue becomes higher as a predefined level which depends on a state of 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.