Tandem Queues with Dependent Service Times in Light Traffic

Ronald W. Wolff
Additional contact information
Ronald W. Wolff: University of California, Berkeley, California

Operations Research, 1982, vol. 30, issue 4, 619-635

Abstract: Light traffic results about delay in queue are obtained for r single-channel queues in tandem with Poisson arrivals where the r service times of the same customer at different stations have an arbitrary joint distribution. By light traffic, we mean asymptotic behavior as server utilization approaches zero. A detailed analysis of delay at the second station is presented for r = 2. An expression for expected delay is obtained for r = 3. Methods developed for these purposes may be used for arbitrary r > 3. For arbitrary r , an expression for expected delay is obtained in the special case where the r service times of the same customer are equal. For exponential service, a simple closed form expression is obtained. For r = 2, it is shown that when service times are positively quadrant dependent , expected delay is greater than when service times are independent. In some cases, the ratio between expected delays in the dependent and independent cases is very large, particularly when r is large. This agrees with and generalizes published results in several papers and conflicts with results in one paper. An explanation for this conflict is given.

Keywords: 683 approximate behavior in light traffic; 703 tandem queues with dependent service times (search for similar items in EconPapers)
Date: 1982
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://dx.doi.org/10.1287/opre.30.4.619 (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:30:y:1982:i:4:p:619-635

Access Statistics for this article

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