COST OPTIMIZATION AND JOINING STRATEGIES FOR MARKOVIAN QUEUES

Abstract

The implementation of cost optimization for Markovian queues is commonly encountered in various congestion scenarios, such as airport boarding systems, railway ticket counters, shopping malls, communication networks, coffee shops, and many more. The arriving customers, before joining the system/queue, may decide whether to join the system or not, based on linear reward cost factors. Therefore, the joining strategy of a queueing system is the key concern regarding the organizer and customer’s point of view. The noble features of the investigations carried out on the analysis of Markovian queueing systems are the design of joining policies for various queueing models. By considering several features such as social profit/individual profit, cooperative/non-cooperative strategy, observable/unobservable strategy, etc., the main focus of this thesis is to model and implement the cost optimization and optimal joining policies for the queueing system. By incorporating realistic features such as retrial orbit, imperfect service, vacation policy, discouragement, feedback, unreliable server, delay due to repair, etc., the investigation done portrays the real-life congestion situations. To study the concerned queueing models, various performance indices, such as long-run probabilities, average queue length, average waiting time, throughput, etc., along with cost analysis and equilibrium joining strategies have been established by using suitable analytical /computational techniques. The cost optimization and evaluation of optimal decision values of the concerned queueing models have also been done via numerical techniques, namely golden section search, quasi-Newton method, parametric non-linear programming, and metaheuristic techniques such as genetic algorithm, particle swarm optimization, differential evaluation, harmony search, firefly algorithm, grey wolf optimization, etc. Soft computing techniques, namely fuzzy logic, adaptive neuro-fuzzy inference system, are also employed to quantity the performance metrics of the concerned queueing systems. The investigation, focusing on the modeling and performance analysis of queueing models with joining strategy policy and cost optimization, is organized into ten chapters. Chapter 1 is devoted to motivation, basic concepts, methodological aspects, and outlines of the research investigation presented in the thesis. Chapters 2-9 are concerned with the joining strategies and social profit function for Markovian queueing models with different features. The chapter-wise organization of the thesis is as follows.