A Solution of Single Server and Multiserver General Queueing Systems Using a Linear Algebraic Approach

Performance evaluation of computer systems and communication networks is very important due to the essential need of finding such systems which can meet all the objectives, for which these resources are built, at an acceptable cost. Many methods h ave been applied to describe the performance of these resources and to find possible ways of improving performance. Each of these methods has its own characteristics and procedure in dealing with the performance concept. These procedure describe these systems such that a previously specified technique can be used to evaluate useful performance measurements which will help decision making. The queueing network model is the most widely used computer systems and communication networks description method. Traditional techniques used in solving the above method use unrelated mathematical techniques. The linear algebraic approach has been chosen as the mathematical approach in this thesis. This approach transforms the queuing theory problems from those of integral equations into those of algebraic equations over a finite dimensional vector space. The solutions obtained using this approach can now make use of the high-speed parallel processors since the components of these solutions are in matrixvector format. In this research, the linear algebraic approach is used to derive explicit solutions for single server and multi server general queueing systems.

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