Routing and transfers amongst parallel queues

Abstract

This thesis is concerned with maximizing the performance of policies for routing and transferring jobs in systems of heterogeneous servers. The tools used are probabilistic modelling, optimization and simulation. First, a system is studied where incoming jobs are allocated to the queue belonging to one of a number of servers, each of which goes through alternating periods of being operative and inoperative. The objective is to evaluate and optimize performance and cost metrics. Jobs incur costs for the amount of time that they spend in a queue, before commencing service. The optimal routing policy for incoming jobs is obtained by solving numerical programming equations. A number of heuristic policies are compared against the optimal, and one dynamic routing policy is shown to perform well over a large range of parameters. Next, the problem of how best to deal with the transfer of jobs is considered. Jobs arrive externally into the queue attached to one of a number of servers, and on arrival are assigned a time-out period. Jobs whose time-out period expires before it commences service is instantaneously transferred to the end another queue, based on a routing policy. Upon transfer, a transfer cost is incurred. An approximation to the optimal routing policy is computed, and compared with a number of heuristic policies. One heuristic policy is found to perform well over a large range of parameters. The last model considered is the case where incoming jobs are allocated to the queue attached to one of a number of servers, each of which goes through periods of being operative and inoperative. Additionally, each job is assigned a time-out on arrival into a queue. Any job whose time-out period expires before it commences service is instantaneously transferred to the end of another queue, based on a transfer policy. The objective is to evaluate and optimize performance and cost metrics. Jobs incur costs for the amount of time that they spend in a queue, before commencing service, and additionally incur a cost for each transfer they experience. A number of heuristic transfer policies are evaluated and one heuristic which performs for a wide range of parameters is observed.