Stochastic Analytical Modeling Based on Queuing Systems

Abstract

The subject of discussion in this chapter is the stochastic approach to model investigation of queuing systems (QS) with waiting buffer (queue) and server (service unit). Two types of QS are presented: single-channel and multi-channel QS. Single-channel QS is discussed in the first part of the chapter with presentation of main characteristics such as workload of the resource, queuing length, total number of requests in system, waiting time and time for presence in the system. The second part deals with organization of analytical investigation of QS and in particular presentation of discrete and continuous time Markov chains. The two possibilities for investigation were considered – during the development of a transient regime and the conditions for reaching a steady state regime. Three versions of QS are presented in QS – with an infinite buffer, with a limited buffer, and QS with request rejections in the absence of a buffer. Some examples for stochastic model investigation are presented in the last part.