Optimal routing of customers with general independent interarrival times in deterministic parallel queues

A queueing system consisting of two parallel heterogeneous servers is considered. Customers ran arrive at discrete-valued instants and, upon their arrivals, they are immediately routed to one of the server buffers. The interarrival times are assumed to be integer, independent, identically distributed random variables, whereas the service times of the servers are assumed to be integer and deterministic. The optimization problem considered is the minimization of the customer mean flow time over an infinite horizon. The existence of a stationary optimal policy with a switchover structure is established.<
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