Admission control for a multi-server queue with abandonment

In a M/M/N+M queue, when there are many customers waiting, it may be preferable to reject a new arrival rather than risk that arrival later abandoning without receiving service. On the other hand, rejecting new arrivals increases the percentage of time servers are idle, which also may not be desirable. We address these trade-offs by considering an admission control problem for a M/M/N+M queue when there are costs associated with customer abandonment, server idleness, and turning away customers. First, we formulate the relevant Markov decision process (MDP), show that the optimal policy is of threshold form, and provide a simple and efficient iterative algorithm that does not presuppose a bounded state-space to compute the minimum infinite horizon expected average cost and associated threshold level. Under certain conditions, we can guarantee that the algorithm provides an exact optimal solution when it stops; otherwise, the algorithm stops when a provided bound on the optimality gap...

• Type: Journal
• Year: 2010
• Where: QUESTA
• Authors: Yasar Levent Koçaga, Amy R. Ward
• Keywords: Customer, Optimal Solution, QUESTA 2010, Threshold Level