Acorrelation study on markov Modulated arrivals with varying Service rates using matrix Geometric method

Abstract

The complexity of data transfer in communication system affects in framing a mathematical model to study and compute their performance values. In this thesis we aim to study the correlation on arrival and service rate to some tractable queuing models under block matrix structure. The matrix geometric method provides a simple approach to derive the steady-state probabilities of complex queueing systems, particularly those involving Markovian processes. newlineMarkovian arrival process is a rich class of point process that include Markov Modulated Poisson Process(MMPP) which can model burstiness in arrival particularly in teletraffic modeling. newlineWe propose the models MMPP/PH/1,MMPP/H2/1,MMPP/M/1 and MMPP/MSP/1 under quasi-birth-death environment to study the arrival correlation with varying service rates. newlineThe models considered are numerically stable and computationally flexible even in complex circumstances. Apart from the service processes like phase type and hyper-exponential services, we propose Markovian service process for modulated arrival and deduce the steady state equations of the system to obtain the performance measures. newlineFinally, we illustrate the applicability of the proposed models by evaluating the correlation effect of arrivals with varying service rates in network flow. Due to the variability in arrival rate it s essential to impose the effectiveness in the service mechanism based on the prioritized type of customer for better transmission without any delay. Numerical analysis of the parameters enhances the proposed study to support the conclusion and by continuously adapting such study to other complex models might provide a generalized solution to certain systems. newline