Steady-state Analysis Of Customers' Impatience In An M~X/M/c Queue With Working Vacation

Queuing system with impatient customers is widely applied in many fields such as in-ventory management,communication network,computer system and so on.The working vacation strategy can effectively solve the inefficient problem of the queuing system,so the research on queuing system with work vacation is a hot topic in the field of queuing sys-tem.With the continuous development of science and technology,it is very common for customers to arrive in a service system in batch such as the arrival of the port cargo and the arrival of the tour group.Therefore,it is necessary to study the batch arrival queuing system with impatient customers and working vacation strategy.This paper mainly studies the batch arrival queuing system with impatient customers and working vacation.The specific contents are as follows:Firstly,this paper studies the M~X/M/1 queue with impatient customers and-working vacation policy.Some analytical expressions of the steady-state performance measures are obtained.When the special value ofis taken,the performance measures under the sin-gle vacation strategy and the multiple vacation strategy are obtained.Numerical results are presented to demonstrate effects of some parameters and the maximum numberon the performance measures of the system.Secondly,this paper considers the M~X/M/c queue with impatient customers and asyn-chronous single working vacation policy.A two-dimensional Markov process is established and the matrix solution of steady state probability is obtained by using recursive matrix method.In addition,the expressions of other performance measures are derived such as the mean queue and the reneging rate.Finally,a numerical example is given to illustrate the influence of system parameters on the performance measures of the system.