Developing Efficient and Effective Algorithms for Complete Analysis of a Class of Vacation Queueing Models

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Queueing delays are one of the most intolerable, yet inevitable, aspects of all service systems. Vacation queues are a major class of queues that occur very frequently in real life. They are applied to systems in which the server is often interrupted (including priority systems), and more specifically used to approximate polling systems - queues in which service is provided through access to a shared medium. Examples include: wireless local area network, processing of manufacturing pieces at a workstation, traffic intersection control systems, and scheduling of patients, based on priorities, for healthcare procedures such as surgery, echocardiogram, etc, and recently cognitive radio networks. In order to provide effective and efficient services that minimize costs while ensuring the quality of service is at an acceptable level to the system users, managers need mathematical models for analyzing these systems and estimating delays so they can work at reducing them. The existing mathematical models for vacation models are either too complex to implement or make unrealistic simplifying assumptions that render them not truly reflective of the actual systems being represented. Our main goal in this proposal is to develop computationally feasible, efficient and effective tools, based on the matrix-analytic methods, for analyzing this very important class of queueing models. We will construct the models that are truly more representative of commonly occurring vacation systems and explore mathematical structures that make the solutions realistically tractable in terms of creating implementable algorithms. The results of this research include providing tools for accurately studying several classes of protocols in communication systems. This will assist in designing more efficient and cost effective communication systems that guarantee users the quality of service they expect. The results can also be applied in the areas of healthcare, transportation and manufacturing.