STOCHASTIC MODELING OF QUEUEING SYSTEMS WITH WORKING VACATION

Abstract

Queues with working vacation (WV) encounters in many congestion problems including communication systems, manufacturing systems, computer networks, etc. The research investigations on the modeling and analysis of queueing systems with working vacation in several frameworks depict various real-life settings. The main focus of our study in this thesis is to model and analyze some Markovian and non-Markovian queueing systems with working vacation by incorporating realistic features such as unreliable server, delay due to repair, hybrid vacation policy, retrial, imperfect service, bulk arrival, balking, feedback, etc. In order to study the concerned queueing models, various system metrics such as mean queue length, mean waiting time, throughput, long run probabilities, etc. have been established by using suitable analytical/numerical techniques. The cost optimization and evaluation of optimal system parameters of the concerned queueing models have been done via numerical optimization method namely, steepest descent search method and metaheuristic approaches such as genetic algorithm, particle swarm optimization, artificial bee colony optimization, etc. The fuzzy logic and parametric non-linear programming are also employed for the prediction of performance indices of queueing models with fuzzified parameters. The sensitivity analysis is also presented so as to validate the analytical results derived for the concerned queueing model developed in different set up. The investigations done on the modeling and performance analysis of queueing models with WV are organized into ten chapters. The brief of the investigations done are described as follows. Chapter 1 is dedicated to the general introduction which supports the motivation and objectives for studying the queueing models with WV. It presents the preliminaries related to stochastic analysis of queueing models with different aspects of WV models. This Chapter includes the overview and literature review related to the work done. The organization of the thesis and future research scope of the research work done are briefly discussed. Chapter 2 is concerned with Markovian queueing system with WV and imperfect service in crisp and fuzzy environment. The PGF method is used to derive the performance metrics of the proposed model. The parametric non-linear programming approach (P-NLP) is employed for the assessment of some performance metrics in fuzzified environment. Chapter 3 presents the study on Markovian queueing system subject to service interruption and operating under hybrid vacation policy. Using PGF methodology, various performance metrics are derived. By framing the cost function, two metaheuristic optimization techniques viz. PSO and ABC for cost optimization purpose have been used. Chapter 4 is devoted to the performance analysis of single server Markovian queue with bi-level network process and bi-level vacation process with balking. MGM is used to analyze the proposed model. MEP has been employed to derive the steady state probabilities of the queue size distributions. The steepest descent search method has been used to obtain the cost optimization results. Chapter 5 studies an unreliable server Markovian queueing model with two stage service process under hybrid vacation policy. To evaluate the steady state probability distribution of the queue size, MGM is employed. Two soft computing approaches viz. PSO and ABC optimization techniques are employed to compute the optimal decision variables along with optimum cost. Chapter 6 presents the performance analysis of multi-server queue with imperfect service and WV. The hybrid vacation policy is used to study Markovian queueing model in which second optional service is considered. MGM is used to investigate the queue length distribution and other performance indices. The sensitivity analysis has been performed to validate the model by taking suitable example. Chapter 7 is concerned with the fluid queueing model driven by the features of WV, disaster, and balking. The continued fractions and generating function methodologies are used to present the steady state results. Chapter 8 and Chapter 9 are concerned with an unreliable server bulk arrival general service queueing model with WV. In Chapter 8, the realistic features of balking and vacation interruption have been incorporated. The supplementary variable technique (SVT) is used to analyze the concerned model. The non-Markovian model studied in Chapter 9 deals with the noble concepts of multi-phase repair and delay in verification. The steady state analysis of the concerned models have been done using supplementary variable technique (SVT). The sensitivity and numerical results are provided in the form of graphs and tables to validate the analytical results of the key performance indices. In Chapter 10, the conclusions and future scope of the research work done have been given. The contributions and significance of the investigations presented in the thesis are mentioned. At the end of this thesis, the list of relevant references has been given in a lexicographic order. The system organizers and decision makers may be able to maintain a balance between operating expenses and service quality based on the suggested cost optimization done for different queueing models with WV. It is hoped that the performance analysis of queueing systems with working vacation presented will contribute in improving the quality of service provided by many existing systems and offer valuable guidance to the system designers, practitioners, and developers in order to design better service systems in a variety of real-life congestion problems.