Performance Analysis of impatient customer Queues with and without working vacations

Abstract

Abstract newlineQueueing theory is an intricate and highly practical and#64257;eld of mathematical study newlinethat has vast applications. Impatient customer queues frequently occur in many areas newlinesuch as impatient telephone switchboard customers, hospital emergency rooms newlinehandling critical patients, inventory systems that store perishable goods, etc. Various newlinequeueing models have been developed to analyze the congestion phenomena in newlinemany areas like the ones mentioned above. In this thesis, we study the performance newlineanalysis of and#64257;nite buand#64256;er impatient customer queues with and without working vaca- newlinetions. We consider two types of impatience, namely, balking and reneging. Balking newlinemeans the phenomenon of customers arriving for service into a non-empty queue newlineand leaving without joining the queue. On the other hand, a customer is said to newlinehave reneged if after joining the queue he gets impatient and leaves the system without newlinereceiving service. Under working vacation policy, whenever the system becomes newlineempty, the server leaves for a working vacation during which it renders service to newlinethe waiting customers at a diand#64256;erent rate. Steady-state system length distributions newlineare obtained using blocked matrix method, probability generating functions and newlinerecursive technique for Markovian models. For non-Markovian queues we have employed newlineembedded Markov chain, supplementary variable and recursive techniques. newlineCost optimization under a suitable cost structure is carried out through quadratic newlineand#64257;t search method and/or particle swarm optimization. newlineThis thesis consists of eleven chapters. Chapter 1 is introductory, justiand#64257;es the purpose newlineand reasons for our work. Chapter 2 analyzes a Markovian working vacations newlinequeue with balking and reneging. Chapter 3 deals with Markovian variant working newlinevacations queue with impatient customers. Chapters 4 and 5 present the study newlineof impatient customer queues with vacation interruption under Bernoulli-schedule newlineand N newlinepolicy, newlinerespectively. We analyze a Markovian two server queue with balking, newlinereneging and triadic policy in Chapter 6. C