Scheduling and stability analysis of Cambridge Ring
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Multiclass queueing networks are widely used to model complex manufacturing systems and communications networks. In this dissertation we describe and analyze a multiclass queueing network model known as the Cambridge Ring. As the name suggest this network has a circular topology with unidirectional routing. In many cases the analysis of a stochastic model is a difficult task. For a few special cases of this network we show that all non-idling policies are throughput optimal for this system. One of the major differences between this work and precious literature is that we prove throughput optimality of all non-idling policies, whereas most of the previous work has been on establishing throughput optimality for a specific policy (usually First-In-First-Out). We use a macroscopic technique known as fluid model to identify optimal policies with respect to work in process. In one case we consider, the discrete scheduling policy motivated by the optimal fluid policy is indeed optimal in the discrete network. For the other special case we show by means of a deterministic counterexample that the discrete policy most naturally suggested by the fluid optimal policy may not be optimal for the queueing network. We also formulate the fluid holding cost optimization problem and present its solution for a simple version of the Cambridge Ring. Further we establish that the optimal policy under a class of policies known as "non-ejective" policies may be an idling policy. We use an example of the Cambridge Ring with a single vehicle to show that the optimal policy for this example has to be an idling policy.