An extremal property of the FIFO discipline via an ordinal version of L=λW.

An extremal property of the FIFO discipline via an ordinal version of L=λW.

0.00 Avg rating0 Votes
Article ID: iaor1989359
Country: United States
Volume: 5
Start Page Number: 515
End Page Number: 529
Publication Date: Jan 1989
Journal: Communications in Statistics - Stochastic Models
Authors: ,
Abstract:

The authors apply the relation L=λW to prove that in great generality the long-run average number of customers in a queueing system at an arrival epoch is equal to the long-run average number of arrivals during the period a customer spends in the system. This relation can be regarded as an ordinal version of L=λW, arising when they measure time solely in terms of the number of arrivals that occur. The authors apply the ordinal version of L=λW to obtain a conservation law for single-server queues. They use this conservation law to establish an extremal property for the FIFO service discipline: The authors show that in a G/GI/1 system the FIFO discipline minimizes (maximizes) the long-run average sojourn time per customer among all work-conserving disciplines that are non-anticipating with respect to the service times (may depend on completed service times, but not remaining service times) when the service-time distribution is NBUE (NWUE). Among the disciplines in this class are round robin, processor sharing and shortest expected remaining processing time.

Reviews

Required fields are marked *. Your email address will not be published.