Distribution of the maximum buffer content during a busy period for state-dependent M/G/L queues

作     者：Knessl, C. Matkowsky, B.J. 

作者机构：Department of Engineering Sciences and Applied Mathematics The Technological Institute Northwestern University Evanston Il 60201 United States Department of Mathematics Tel Aviv University Tel Aviv Israel Dept. of Mathematics Statistics and Computer Science University of Illinois At Chicago Chicago Il 60680 United States 

出 版 物：《Communications in Statistics. Stochastic Models》 (Communications in Statistics, Stochastic Models)

年 卷 期：1987年第3卷第2期

页      面：191-226页

基　　金：U.S. Israel National Foundation National Science Foundation, NSF, (D MS-85-01535, DMS-84-06110, DMS-86-20267) National Science Foundation, NSF Israel Academy of Sciences and Humanities 

摘      要：We consider M/G/l queues characterized by the total unfinished work (buffer content) U(t) in the system at time t. We allow the rate of the Poisson arrivals as well as the rate at which the server works, to depend on the instantaneous value of U(t). in addition, the service density depends on the value of U(t) at the instant that the customer enters the system. We consider systems with a large arrival rate and small mean service times. We then construct asymptotic approximations to the probability that U(t) reaches the level K before completing the current busy period and we also compute the distribution of the maximum of U(t) during a busy period. © 1987, Taylor & Francis Group, LLC. All rights reserved.