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...
| Veröffentlicht in: | Mathematics of Operations Research. - Institute for Operations Research and the Management Sciences. - 13(1988), 4, Seite 693-710 |
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| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
1988
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| 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 |
| Zusammenfassung: | 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. |
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| ISSN: | 15265471 |