Abstract
This paper studies the optimal policy for joint control of admission, routing, service, and jockeying in a queueing system consisting of two exponential servers in parallel. Jobs arrive according to a Poisson process. Upon each arrival, an admission/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 inclusive 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 implementing control actions in practice.
Highlights
Controls are often applied to queueing systems to improve system performance
We study the optimal control of queueing systems with a Poisson arrival of jobs and two parallel exponential servers
With the structure properties of the optimal value function, we characterize the optimal control policy as a hedging point policy of which two monotone switching curves intersected at the hedging point and typically partitioned the state space into three decision zones
Summary
Queueing models are widely used to study the manufacturing systems, public service systems, distributed computer systems, data communication networks, traffic flow systems, healthcare operations management, etc. Xu et al [18] considered optimal control of routing and jockeying in a two-station queueing system which had a Poisson arrival of jobs and exponential service time at two stations in parallel. They formulated the queueing control problem as an MDP and used dynamic programming to characterize the optimal policy as a switching-curve policy for both discounted and long-run average cost criteria. Since our research is oriented towards applications in operations management which are more concerned with closely matching supply with customer orders, we study a more complex model which includes joint controls of admission, routing, service, and jockeying.
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