OPTIMAL-CONTROL OF A QUEUING NETWORK SYSTEM WITH 2 TYPES OF CUSTOMERS

We deal with an optimal control problem in a queuing network system. The system consists of the first stage with a server and the second stage with two servers each having its finite queue. Two types of customers are first served at the first stage server and subsequently proceed to the queue at the server corresponding to their types in the second stage. When the first stage server completes a service, he determines the type of customer to be next served. The optimal control problem is to select the type of customer to be next served in order to minimize the expected cost per hour. The problem is formulated as an undiscounted semi-Markov decision process. The monotonicity of the optimal policy is shown.