Optimal Admission Control to Two Multiserver Queues in Series with Two Arrival Streams

Abstract

We consider a loss system of two queues in series with finite system capacity. The first queue is a self-service queue and the second is a multiserver queue. There are two types (type 1 and 2) of customers that are generated according to independent Poisson processes. A type 1 customer requires the service at the first queue then at the second queue and a type 2 customer requires service at the second queue only, while an arriving type 2 customer finding that all servers at the second queue are busy will leave the system. Assume that service times at both queues are exponentially distributed. This system is similar to a phonebanking center. A reward is earned by the system for each entering customer, however there is a holding cost per unit time for each customer staying in the system and a cost for each lost type 2 customer at the second queue. We study the optimal admission policy by accepting or rejecting the arriving type 1 customers and the objective is to maximize the expected total discounted profits. keywords: Queues, admission control, Markov decision process.