Waiting and Service Time of a Unique Customer in an M/M/m Preemptive LCFS Queue with Impatient Customers
We study an M/M/m preemptive last-come,first-served queue with impatient customers without priority classes.We focus on the probability of service completion and abandonment as well as the waiting and service times of a unique customer who has the mean service and patience times that are different from those of all other customers in the steady state.The problem is formulated as the first passage times in a combination of two one-dimensional birth-and-death processes each with two absorbing states.We provide explicit expressions in terms of Laplace-Stieltjes transform of the distribution function for the time to service completion or abandonment,which is decomposed into the waiting and service times of the unique customer.A numerical example is presented in order to demonstrate the computation of theoretical formulas.
M/M/m preemptive LCFS queue Impatient customers First passage time
Hideaki Takagi
University of Tsukuba,Tsukuba Science City 305-8573,Japan
国际会议
河北秦皇岛
英文
19-35
2017-08-21（万方平台首次上网日期，不代表论文的发表时间）