A single queue single server Markov processes model. – O. A. Ofem, E. E Williams, A. E. Edim and S. S. Akpan.
Several research efforts as well as developments have chosen queueing theories as a vital tool in the measurement and analysis of performance evaluation of system components that arrives at different time intervals, waiting to be serviced by a server. In this paper, we considered the important issue of planning the queueing system to minimize system cost. This is a non-trivial task, since it involves several sets of variables: the mean arrival rate of items in the queue, the mean service rate of the server to the items in the queue, and the queueing model type to be used and the efficiency of the model in terms of performance evaluation. The task is further complicated due to the presence of system performance constraints, and the inter-dependence among the variables. Our first contribution in this paper is the formulation of this problem in terms of the variables, constraints and the optimization criterion. Our second contribution is in identifying the dependencies among the variables and breaking down the problem into tractable sub-parts. In this process, we extensively used domain knowledge to strike a balance between tractability and practicality.