Optimal Policy for Controlling Two-Server Queueing Systems with Jockeying

This paper studies the optimal policy for joint control of admission,routing,service,and jockeying in a queueing sys-tem consisting of two exponential servers in parallel.Jobs arrive according to a Poisson process.Upon each arrival,an admis-sion/routing decision is made,and the accepted job is routed to one of the two servers with each being associated with a queue.After each service completion,the servers have an option of serving a job from its own queue,serving a jockeying job from another queue,or staying idle.The system performance is in-clusive of the revenues from accepted jobs,the costs of holding jobs in queues,the service costs and the job jockeying costs.To maximize the total expected discounted return,we formulate a Markov decision process(MDP)model for this system.The value iteration method is employed to characterize the optimal policy as a hedging point policy.Numerical studies verify the structure of the hedging point policy which is convenient for implement-ing control actions in practice.