Research On Performance And Cost Of Queuing Systems With Impatient Customers

At present, many large service centers have become an important part of businessstructure, especially the computing service center. Computing service center has containthousands of servers generally, which require large amounts of power to run. If we reduceservers, system appears a large number of customers, customers can produce impatientmood, which not only throw away customers’ time, but also affect profit of the servicecenter. If all the servers have been open, idle servers will waste a lot of power. For servicecenters who have a large number of servers, it is not desirable to micro-manage powerconsumption by turning isolated servers on and off, open or closed can cause waste ofpower. It is necessary to research service optimization problem for reducing the powerconsumption.Based on the background of the computing service center, we propose a dynamicoperation policy, we establish the model of queuing system.Firstly, we consider M/M/N queueing system with two group spare servers andimpatient customers. By applying the Markov process theory and transition diagram, weestablish the steady-state probability equations. By probability generating functions anditerative recursive methods, we obtain some performance measures of the system,including the average number of jobs that are lost per unit time because of defections andthe average number of servers that are consuming power. We establish a cost function ofserver consumes power and impatient customers’ lost, we obtain the calculation method ofcost function in theory. Finally we give two special cases of the model, reveal therelationship between the model and research actuality.Secondly, we consider multiple sets of spare servers which can optimize servicecenter, so we study M/M/N queueing system with more group spare servers and impatientcustomers. By applying the Markov process theory and transition diagram, we establishthe steady-state probability equations. By probability generating functions and iterativerecursive methods, we obtain some performance measures of the system, including theaverage number of jobs that are lost per unit time because of defections and the average number of servers that are consuming power. We establish a cost function of serverconsumes energy and impatient customers’ lost, we obtain the calculation method of costfunction in theory.Finally, we consider M/M/N vacation queueing system with one group spare serversand impatient customers. During the vacation, the servers don’t work. By applying theMarkov process theory and transition diagram, we establish the steady-state probabilityequations. By probability generating functions and iterative recursive methods, we obtainsome performance measures of the system, including the average number of jobs that arelost per unit time because of defections and the average number of servers that areconsuming power. We establish a cost function of server consumes energy and impatientcustomers’ lost, we obtain the calculation method of cost function in theory. In addition,we give a special case of the model, reveal the relationship between the model andresearch actuality.