An LIL Version of L = λW

An LIL Version of L = λW

This paper establishes a law-of-the-iterated-logarithm (LIL) version of the fundamental queueing formula L = λW: Under regularity conditions, the continuous-time arrival counting process and queue-length process jointly obey an LIL when the discrete-time sequence of interarrival times and waiting ti...

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Veröffentlicht in:Mathematics of Operations Research. - Institute for Operations Research and the Management Sciences. - 13(1988), 4, Seite 693-710
1. Verfasser: Glynn, Peter W. (VerfasserIn)
Weitere Verfasser: Whitt, Ward
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 1988
Zugriff auf das übergeordnete Werk:Mathematics of Operations Research
Schlagworte:Queueing theory Little's law Conservation laws Law of the iterated logarithm Limit theorems Inverse stochastic processes Random sums Mathematics Philosophy Behavioral sciences
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245 1 3 |a An LIL Version of L = λW 
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520 |a This paper establishes a law-of-the-iterated-logarithm (LIL) version of the fundamental queueing formula L = λW: Under regularity conditions, the continuous-time arrival counting process and queue-length process jointly obey an LIL when the discrete-time sequence of interarrival times and waiting times jointly obey an LIL, and the limit sets are related. The standard relation L = λW appears as a corollary. LILs for inverse processes and random sums are also established, which are of general probabilistic interest because the usual independence, identical-distribution and moment assumptions are not made. Moreover, an LIL for regenerative processes is established, which can be used to obtain the other LILs. 
540 |a Copyright 1988 The Institute of Management Sciences/Operations Research Society of America 
650 4 |a Queueing theory 
650 4 |a Little's law 
650 4 |a Conservation laws 
650 4 |a Law of the iterated logarithm 
650 4 |a Limit theorems 
650 4 |a Inverse stochastic processes 
650 4 |a Random sums 
650 4 |a Mathematics  |x Mathematical procedures  |x Approximation 
650 4 |a Mathematics  |x Mathematical expressions  |x Mathematical theorems 
650 4 |a Mathematics  |x Mathematical expressions  |x Mathematical functions  |x Transcendental functions  |x Logarithms 
650 4 |a Mathematics  |x Pure mathematics  |x Arithmetic  |x Addition  |x Partial sums 
650 4 |a Mathematics  |x Pure mathematics  |x Probability theory  |x Random variables 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Statistical theories 
650 4 |a Philosophy  |x Logic  |x Metalogic  |x Logical truth  |x Sufficient conditions 
650 4 |a Mathematics  |x Pure mathematics  |x Probability theory  |x Random variables  |x Stochastic processes 
650 4 |a Behavioral sciences  |x Psychology  |x Cognitive psychology  |x Cognitive processes  |x Thought processes  |x Reasoning 
655 4 |a research-article 
700 1 |a Whitt, Ward  |e verfasserin  |4 aut 
773 0 8 |i Enthalten in  |t Mathematics of Operations Research  |d Institute for Operations Research and the Management Sciences  |g 13(1988), 4, Seite 693-710  |w (DE-627)320435318  |w (DE-600)2004273-5  |x 15265471  |7 nnns 
773 1 8 |g volume:13  |g year:1988  |g number:4  |g pages:693-710 
856 4 0 |u https://www.jstor.org/stable/3689952  |3 Volltext 
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