PARAMETRIC AND ALGORITHMIC SOLUTIONS FOR THE STEADY-STATE ANALYSIS OF MARKOVIAN QUEUEING SYSTEMS USING GRAPHICAL ENUMERATION
Abstract
This thesis directly exploits the structure contained in the transition diagrams of Markovian queueing systems to find steady-state queue length probabilities. The Matrix Tree Theorem is used to give a method of solution that relies on enumerating the intrees of the transition diagram. Decomposition of a transition diagram is the major tool used for this enumeration. Cutpoints are used to find "Block Product Form Solutions". A weaker concept of separability is then used to derive recursive solutions for the Erlang Systems. The solution procedure is amenable to both parametric and recursive solutions. Other systems that have separable transition diagrams are discussed. The results give considerable savings when compared to existing solutions, and solutions for some previously unsolved problems are considered. Since the underlying approach is topological, varying the weights or rates of the processes considered is easily accounted for in the solution procedure. Also, by considering the transition diagrams of the different systems, directional duality can be used to show the "equivalence" of different systems.
Degree
Ph.D.
Subject Area
Operations research
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