PERFORMANCE ANALYSIS OF STATE DEPENDENT MARKOVIAN QUEUES WITH RETRIAL ORBIT

Abstract

The retrial queueing systems can be encountered in many congestion scenarios, including telecommunication and cellular radio networks, production and manufacturing systems, computing and call centres, etc. Markov retrial queueing models with state dependent rates in different frameworks facilitate to resolve various real-life delay and blocking challenges. The primary focus of our study in this thesis is the modeling and analysis of state-dependent Markovian retrial queueing systems with realistic features such as double orbits, impatient customers, feedback of the customers, unreliable server, imperfect/additional repair, imperfect/additional service, a variant of server’s vacationing, F-policy, etc. To evaluate the performance metrics of the retrial queueing models, various analytical techniques including the probability generating function (PGF) approach, matrix geometric method (MGM), maximum entropy principle (MEP), recursive techniques, Runge-Kutta Method (RKM) etc. have been utilized. To investigate Markovian retrial queueing systems, various performance metrics such as expected queue length, expected system lengths, expected waiting times, long run probabilities, throughput, etc. have been established by implementing suitable analytical/numerical techniques. The sensitivity analysis has been conducted to validate the derived analytical findings of the concerned retrial queueing model. For some retrial queueing systems, numerical simulation has also been done and validated in some models via ANFIS results. To find the optimal parameters and joining probability for the concerned retrial queueing models, metaheuristic approaches such as particle swarm optimization (PSO), grey wolf optimizer (GWO), etc. are employed. The numerical techniques viz. golden section method (GSM) has also been employed for the optimization purpose. The investigation carried out on Markov analysis of state dependent retrial queueing systems is organized into ten chapters. Chapter 1 is concerned with the introduction of the thesis which highlights the motivation and the objective behind the study of state dependent retrial queueing systems. It provides the preliminaries on the techniques employed for the analysis of various state-dependent retrial queueing models. This chapter includes the comprehensive overview and literature review related to the work done. The organization of the thesis and the scope for the future research are also outlined. Chapter 2 presents unreliable single server retrial queueing system with balking, reneging and differentiated vacation policy. Using MGM, various performance indices of the retrial queueing system are established. Chapter 3 is devoted to the unreliable single server retrial queueing system with two-way communication. Using PGF approach, various performance metrics of the system have been derived. The cost optimization has been done using GWO. In both chapters 2 and 3, the ANFIS computing has been performed and ANFIS results have been compared with numerical results obtained using analytical approach.