A Probabilistic Framework for the Design of Queueing Models using Mixed Distributions

Abstract

The main objectives of this research work are to study the proposed model newline treating two like jobs as a single entity by deriving the relative measures using newlinedifferent techniques and then validating them against the standard models. The main newlineaim is to optimize the total cost involved by reducing the waiting time and newlineincreasing the server utility. The proposed work relates to the design of a queuing newlinemodel which takes mixed random variables for its arrival rate and studies the newlinerelative measures using various techniques by categorizing a job as a paired job or newlinenot. newlineIn this thesis different queueing models having the property of treating two newlinelike jobs that have very small inter-arrival time as one single job is studied. The newlinemodels analysed in this study are obtained by considering a linear combination of newlinedistributions such as exponential and geometric distributions which possess memory newlineless property for their service distribution. Their relative measures are derived and newlinecompared with the existing queuing models such as the M/M/2 queueing model. The newlinemodel consists of a single server which takes two like jobs that arrive with very newlinesmall interarrival time as a single job. The thesis comprises of six chapters. The first newlinechapter is introduction to the model studied in this thesis newline