PhD ThesisWe consider the problem of routing (incorporating local scheduling) in a distributed
network. Dedicated jobs arrive directly at their specified station for processing. The
choice of station for generic jobs is open. Each job class has an associated holding cost
rate. We aim to develop routing policies to minimise the long-run average holding cost
rate.
We first consider the class of static policies. Dacre, Glazebrook and Nifio-Mora (1999)
developed an approach to the formulation of static routing policies, in which the work at
each station is scheduled optimally, using the achievable region approach. The achievable
region approach attempts to solve stochastic optimisation problems by characterising
the space of all possible performances and optimising the performance objective over
this space. Optimal local scheduling takes the form of a priority policy. Such static
routing policies distribute the generic traffic to the stations via a simple Bernoulli routing
mechanism. We provide an overview of the achievements made in following this approach
to static routing. In the course of this discussion we expand upon the study of Becker et al.
(2000) in which they considered routing to a collection of stations specialised in processing
certain job classes and we consider how the composition of the available stations affects
the system performance for this particular problem. We conclude our examination of
static routing policies with an investigation into a network design problem in which the
number of stations available for processing remains to be determined.
The second class of policies of interest is the class of dynamic policies. General DP
theory asserts the existence of a deterministic, stationary and Markov optimal dynamic
policy. However, a full DP solution may be unobtainable and theoretical difficulties posed
by simple routing problems suggest that a closed form optimal policy may not be available.
This motivates a requirement for good heuristic policies. We consider two approaches to
the development of dynamic routing heuristics. We develop an idea proposed, in the
context of simple single class systems, by Krishnan (1987) by applying a single policy
improvement step to some given static policy. The resulting dynamic policy is shown
to be of simple structure and easily computable. We include an investigation into the
comparative performance of the dynamic policy with a number of competitor policies and
of the performance of the heuristic as the number of stations in the network changes. In
our second approach the generic traffic may only access processing when the station has
been cleared of all (higher priority) jobs and can be considered as background work. We
deploy a prescription of Whittle (1988) developed for RBPs to develop a suitable approach
to station indexation. Taking an approximative approach to Whittle's proposal results
in a very simple form of index policy for routing the generic traffic. We investigate the
closeness to optimality of the index policy and compare the performance of both of the
dynamic routing policies developed here