A mathematical study of markovian queues with vacations and working vacations

Abstract

In queueing theory, the phenomenon that customers leave the system newlinewithout getting their required service when the waiting time exceeds their newlinetolerance is called customer impatience and return back to the system after newlinereceiving their service when the customer has unsatisfactory due to some newlinereasons is called feedback. In the modern design of service systems, the newlineimpact of customer abandonments and feedback on the system performance newlineand queueing dynamics has been realized. Meanwhile, the server decides to newlinego for a vacation after waiting for a random period of time for new newlinecustomers is classified as vacation queues with a waiting server. This is newlinecrucial to avoid customer loss. newlineThe subject matter of this thesis is to study the stationary properties newlinefor queuing systems with both customer abandonments, a waiting server and newlinefeedbacks with working vacation queues and differentiated vacations. The newlinematrix geometric methods and probability generating function methods are newlineapplied to reach the objectives. First, we study a queuing system with newlineworking vacations, vacation interruptions with a waiting server and newlinefeedbacks. newlineThe necessary and sufficient condition for the existence of steady state newlinesolution of all the models related to working vacation queues are obtained. newlineBy probability generating function, we characterize the stationary properties newlineof such a queueing system with differentiated vacations with a waiting newlineserver and feedbacks. newlineTo justify our findings some schematic figures are included to newlinevisualize the relevant arguments. newline