Waiting times when service times are stable laws
Subtitle: tamed and wild
By: by Donald P. Gaver, Patricia A. Jacobs
Contributors: Jacobs, Patricia A.; Naval Postgraduate School (U.S.). Dept. of Operations Research
Publisher: Naval Postgraduate School; Available from National Technical Information Service
Published: 1996
Place of publication: Monterey, Calif; Springfield, Va
Language: eng
Number of pages: 28
Subjects: STOCHASTIC PROCESSES; TIME INTERVALS; TELECOMMUNICATIONS; QUEUEING THEORY
Other titles: NPS-OR-96-009.
Description: Modern telecommunication systems must accommodate tasks or messages of extremely      variable time duration. Understanding of that variability, and appropriate stochastic      models are needed to describe the resulting queues or buffer contents. To this end,      consider an M/G/1 queue with service times having a positive stable law distribution.      Such service times are extremely long (and short) tailed, and thus do not have finite first      and second moments; classical queue-theoretic results do not apply directly. Here we      suggest two procedures for initially taming stable laws, i.e. so that they possess finite      mean and variance. We apply the tamed laws to calculate certain familiar queuing      properties, such as the transform of the stationary distribution of the long-run virtual      waiting time and mean thereof. We show that, by norming or scaling traffic intensity,      waiting times, and other measures of congestion, we can obtain bona fide limiting      distributions as the underlying service times become untamed, i.e. return to the wild.      Simulations support the theory.
Notes: Cover title.

"NPS-OR-96-009."

"August 1996."

AD A315 665.

Includes bibliographical references (p. 14).

aq/aq cc:9116 01/22/97.