Some Inequalities in Queuing

K. T. Marshall
Additional contact information
K. T. Marshall: Bell Telephone Laboratories, Inc., Holmdel, New Jersey

Operations Research, 1968, vol. 16, issue 3, 651-668

Abstract: Bounds are found for various measures of performance in certain classes of the GI / /G 1 queue. First, the mean wait in queue is found in terms of the mean and variance of the interarrival, service, and idle distributions. Bounds on the idle time moments lead to bounds on the mean wait and number in queue. The interarrival time distribution is then assumed to have mean residual life bounded above by 1/λ (λ = arrival rate); i.e., given a time t since the last arrival, the expected time to the next arrival is no more than 1/λ. With this assumption the mean number in queue (and hence system) is bounded to within (1 + p )/2 customers. Both upper and lower bounds are tight. The stronger assumption that, given time t since the last arrival, the probability an arrival occurs in the next ▵ t is nondecreasing in t , leads to bounds on the mean queue length to within ( c 2 a + p )/2, where c a is the coefficient of variation of the arrival distribution. Again the bounds are tight. Specializing to the D / G /1 queue the mean queue length is found to within p /2

Date: 1968
References: Add references at CitEc
Citations: View citations in EconPapers (11)

Downloads: (external link)
http://dx.doi.org/10.1287/opre.16.3.651 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:16:y:1968:i:3:p:651-668

Access Statistics for this article

More articles in Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().