An analysis of some continuous time queueing systems with feedback

Abstract

The entire work in this thesis is divided into six chapters. The first chapter is introductory in nature and contains fundamental concepts of queueing theory, its origin, stochastic processes, Markov processes, Description and representation of queues, Poisson process and exponential distribution, Markovian property of exponential distribution, different types of queues and work done in this thesis. The second chapter deals with the transient state probabilities for number of units in the / /1 M M feedback queueing system with intermittently available server for the two types of models. In the first model, units are served singly but in the second model these are served in batches of variable size. Steady state solution for the first model is also obtained. Special cases of interest are derived. Busy period distribution is also obtained for both the models. Numerical solutions are found for both models and thereafter various probabilities are plotted graphically. In the third chapter, we study feedback queueing system with two parallel servers having unequal service rates. Transient-state as well as steady-state probabilities of number of units in the system are obtained. Some special cases of interest are derived. Numerical solutions are also found and thereafter various probabilities are plotted graphically. The fourth chapter derives the probabilities of number of units in the system by a given time for a feedback queueing system with two special servers. Steady-state probabilities are also obtained. Some special cases of interest are discussed. Numerical solutions are also found and thereafter various probabilities are plotted graphically. Fifth chapter considers a multi-channel feedback queueing system and time dependent probabilities are found for the number of units in the system. Steady-state solution is also obtained. Special cases of interest are derived. Numerical solutions are also found and thereafter various probabilities are plotted graphically.