NDLI: Additive functionals with application to sojourn times in infinite-server and processor sharing systems

Content Provider	Springer Nature Link
Author	Brandt, Manfred Brandt, Andreas
Copyright Year	2012
Abstract	We deal with additive functionals of stationary processes. It is shown that under some assumptions a stationary model of the time-changed process exists. Further, bounds for the expectation of functions of additive functionals are derived. As an application we analyze virtual sojourn times in an infinite-server system where the service speed is governed by a stationary process. It turns out that the sojourn time of some kind of virtual requests equals in distribution an additive functional of a stationary time-changed process, which provides bounds for the expectation of functions of virtual sojourn times, in particular bounds for fractional moments and the distribution function. Interpreting the GI(n)/GI(n)/∞ system or equivalently the GI(n)/GI system under state-dependent processor sharing as an infinite-server system where the service speed is governed by the number n of requests in the system provides results for sojourn times of virtual requests. In the case of M(n)/GI(n)/∞, the sojourn times of arriving and added requests equal in distribution sojourn times of virtual requests in modified systems, which yields several results for the sojourn times of arriving and added requests. In case of positive integer moments, the bounds generalize earlier results for M/GI(n)/∞. In particular, the mean sojourn times of arriving and added requests in M(n)/GI(n)/∞ are proportional to the required service time, generalizing Cohen’s famous result for M/GI(n)/∞.
Ending Page	409
Page Count	41
Starting Page	369
File Format	PDF
ISSN	02570130
e-ISSN	15729443
Journal	Queueing Systems
Issue Number	4
Volume Number	70
Language	English
Publisher	Springer US
Publisher Date	2012-03-06
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Sojourn times Queues and service Systems Theory, Control Bounds Stationary processes Probability Theory and Stochastic Processes Virtual requests Moments GI(n)/GI(n)/∞ Time transformation State-dependent processor sharing M(n)/GI(n)/∞ Random environment Performance evaluation; queueing; scheduling Operations Research/Decision Theory Distribution Production/Logistics/Supply Chain Infinite-server Additive functionals Queueing theory Inequalities; stochastic orderings Computer Communication Networks
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Management Science and Operations Research Computational Theory and Mathematics Computer Science Applications

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