Optimal admission policies for small star networks

Abstract

In this thesis admission stationary policies for small Symmetric Star telecommunication networks in which there are two types of calls requesting access are considered. Arrivals form independent Poisson streams on each route. We consider the routing to be fixed. The holding times of the calls are exponentially distributed periods of time. Rewards are earned for carrying calls and future returns are discounted at a fixed rate. The operation of the network is viewed as a Markov Decision Process and we solve the optimality equation for this network model numerically for a range of small examples by using the policy improvement algorithm of Dynamic Programming. The optimal policies we study involve acceptance or rejection of traffic requests in order to maximise the Total Expected Discounted Reward. Our Star networks are in some respect the simplest networks more complex than single links in isolation but even so only very small examples can be treated numerically. From those examples we find evidence that suggests that despite their complexity, optimal policies have some interesting properties. Admission Price policies are also investigated in this thesis. These policies are not optimal but they are believed to be asymptotically optimal for large networks. In this thesis we investigate if such policies are any good for small networks; we suggest that they are. A reduced state-space model is also considered in which a call on a 2-link route, once accepted, is split into two independent calls on the links involved. This greatly reduces the size of the state-space. We present properties of the optimal policies and the Admission Price policies and conclude that they are very good for the examples considered. Finally we look at Asymmetric Star networks with different number of circuits per link and different exponential holding times. Properties of the optimal policies as well as Admission Price policies are investigated for such networks.