Level Crossing Methods in Stochastic Models

This is a complete update of the first edition of Level Crossing Methods in Stochastic Models, which was published in 2008. Level crossing methods are a set of sample-path based mathematical tools used in applied probability to establish reliable probability distributions.

Since its inception in 1974, the level crossing approach for analyzing a large class of stochastic models has become increasingly popular among researchers. This volume traces the evolution of level crossing theory for obtaining probability distributions of state variables and demonstrates solution methods in a variety of stochastic models including: queues, inventories, dams, renewal models, counter models, pharmacokinetics, and the natural sciences.

From 1972 to 1974, I was working on a PhD thesis entitled Multiple Server Queues with Service Time Depending on Waiting Time.

This volume contains research papers on topics in stochastic processes, with specific applications to problems in underwater acoustics. Topics treated in this book are familiar problems in diverse areas. Models and algorithms developed in this volume can be used in applications other than those of underwater acoustics.