Advanced Markovian Queueing Models

This chapter examines the development of models that are amenable to analytic methods and is concerned especially with Markovian problems of the non-birth death type. Difference-equation methods are often used instead to solve the problem when the maximum batch is small. It is the job of one worker to make the necessary adjustments to put the assembly back into the stream of the process. The number of defects per item is registered automatically, and it exceeds two an extremely small number of time. The exponential assumptions may be rather limiting, especially the assumption concerning service times being distributed exponentially. In practical situations, the Erlang family provides more flexibility in fitting a distribution to real data than the exponential family provides. The Erlang distribution is also useful in queuing analysis because of its relationship to the exponential distribution. The concept of phases can be generalized to include a much wider class of distributions than just the Erlang. Other distributions that use the concept of phases are the hyperexponential, or generalized Erlang, and Coxian distributions.