SOJOURN TIME IN A SINGLE-SERVER QUEUE WITH THRESHOLD SERVICE RATE CONTROL

被引：1

作者：

Adan, Ivo ^{[1
]}

D'Auria, Bernardo ^{[2
]}

机构：

[1] Eindhoven Univ Technol, Dept Mech Engn, Postbus 513, NL-5600 MB Eindhoven, Netherlands

[2] Univ Carlos III Madrid, Dept Stat, Avda Univ 30, Leganes 28911, Madrid, Spain

来源：

SIAM JOURNAL ON APPLIED MATHEMATICS | 2016年 / 76卷 / 01期

关键词：

sojourn time distribution; matrix generating function; adaptable service speed; SPEED;

D O I：

10.1137/14097046X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the sojourn time in a queueing system with a single exponential server, serving a Poisson stream of customers in order of arrival. Service is provided at a low or high rate, which can be adapted at exponential inspection times. When the number of customers in the system is above a given threshold, the service rate is upgraded to the high rate, otherwise, it is downgraded to the low rate. The state dependent changes in the service rate make the analysis of the sojourn time a challenging problem, since the sojourn time now also depends on future arrivals. We determine the Laplace transform of the stationary sojourn time and describe a procedure to compute all moments as well. First we analyze the special case of continuous inspection, where the service rate immediately changes once the threshold is crossed. Then we extend the analysis to random inspection times. This extension requires the development of a new methodological tool, that is, matrix generating functions. The power of this tool is that it can also be used to analyze generalizations to phase-type services and inspection times.

引用

页码：197 / 216

页数：20

共 16 条

[1]

[Anonymous], 2003, Applied probability and queues

[2]

[Anonymous], 1999, Introduction to matrix analytic methods in stochastic modeling, DOI DOI 10.1137/1.9780898719734

[3] Queues with service speed adaptations [J].