O R Queuing Theory

Abstract

There are times when queueing systems behave like fluid. A good newlinescenario is when customers of a busy bus station experience rush hour. Therein, newlinethe scenery looks highly saturated and stable or completely unstable. Either newlineway, the system dynamics resembles a continuous fluid flow rather than newlinediscrete. Medhi s analogy in of fluid flow of people coming out of a subway or newlinean electric train during rush hour is similar to the example above. The wide newlinesense approximate continuity in such traffic flows is created by the heaviness newlineof queueing traffic into the system. Broadly speaking, a heavy traffic queueing newlinesystem can be defined as a queueing system whose server occupation rate is newlinebarely less than unity and this phenomenon as Boxma et al. indicates is a newlinefeature in modern communications and computer systems today. Researches newlinehave shown that early investigation in this area was carried out by Kingman on newlinea general queue called the G/G/1 and the result is referred to as central limit newlinetheorem for queueing theory, see Medhi. newlineOur objective in this thesis is to survey works on queueing systems newlinegenerally in the light of both mathematical and statistical realities with newlineemphasis on those queues supporting the diffusion approximation. This newlineincludes their distributions, analyses, modeling and application. It is anticipated newlinethat a survey of this kind will provide an excellent background in heavy traffic newlinestudies especially in packets and internet traffic prevalent in computers, newlinecommunications and telecommunications systems. To achieve an optimum newlinesurvey process as in this case, it is essential that one bears in mind the Poisson newlinetraffic controversy now prevalent in telecommunications and computer traffic newlinemodeling not because the controversy is relevant or not, but because there are newlinediverse opinions worthy of sharing especially as regards the new traffic models newlinesuch as the self-similar model. Not only that, recent studies have shown that the newlinePoisson based models are equally relevant and could be used to describe the newlineinternet traffic.