Matrix-geometric Solutions in Stochastic Models [antikvár]

Preface This book is an outgrowth of a series of lectures I gave at The Johns Hopkins University, Baltimore, Maryland, from July 20 to July 24, 1979. It contains a variety of results on queues and other stochastic models with the unifying feature of ready algorithmic implementation. The material discussed in this book comes under the broader heading of computational probability, a subject area sufficiently young to require definition. As I perceive it, computational probability is not primarily concerned with the algorithmic questions raised by the direct numerical computation of existing analytic solutions. Such questions are best considered within the framework of classical numerical analysis. It is the concern of the probabilist, however, to ensure that the solutions he obtains are in the best, most natural, form for numerical computation. The expression of this concern is of recent date. Before the era of the modern computer, much of the best effort in applied mathematics was aimed at obtaining insight into the behavior of formal models, while avoiding the drudgery of computation by primitive machinery. On the other hand, the early difficulty of computation has also allowed the development of a large number of formal solutions from which few, if any, qualitative conclusions may be drawn, and whose appropriateness for algorithmic implementation has not been seriously considered. There is, in fact, an attitude that still pervades most of the teaching and the research literature on applied probability today and that does not view algorithmic implementation as an integral, challenging part of the solution process. We view this attitude as a legacy of history, but not as a constructive one. We therefore define computational probability as the study of stochastic models with a genuine added concern for algorithmic feasibility over a wide, realistic range of parameter values. We have imposed upon ix