The General Queue G/G/1 and Approximations

Abstract

The use of Markov models in queueing theory is very common because they are appropriate for basic systems and lend themselves for easy applications. But often the real-world systems are so complex and so general that simple Markov and renewal process models do not represent them well. The presentation of matrix-analytic models of Chapter 8 is an introductory attempt to go beyond the basic models discussed earlier. The computer and communication systems which have had a major role in advancing technology in the past three decades require queueing models that go well beyond those we have seen so far in the last eight chapters. Their full discussion is beyond the scope of this text. Here we provide an introduction to the analysis of the waiting time process in the general queue and a few approximation techniques that have proved useful in handling emerging complex applications. Readers who are not prepared for the complexities of the derivations may use this chapter for the fundamental concepts and the results it presents.