Numerical Methods in Optimization and Performance Analysis of Queueing Networks

We consider control problems in many-server queueing networks, with impatient customers. We focus on models with two customer classes and one or two service stations. Our objective is to find a policy minimizing the expected discounted holding cost of waiting customers. The technique we used is Markov Decision Process. Our conclusions are: 1. an optimal policy depends on the total number of customers only; 2. it is optimal to keep idleness in the station with lower service rate; 3. an optimal policy is to arrange only one type of customers waiting at any moment. The decision depends on whether the derivative of optimal cost function is greater than the ratio (c1-c2)/(θ1-θ2); with ci and θi being the cost rate and abandonment rate of class i respectively. The thesis also introduces an algorithm for simulating G/G/N queues, which is then extended to more complex networks.