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Two Coupled Queues with Vastly Different Arrival Rates : Critical Loading Case
Joint Authors
Knessl, Charles
Morrison, John A.
Source
Advances in Operations Research
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-26, 26 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-03-15
Country of Publication
Egypt
No. of Pages
26
Main Subjects
Information Technology and Computer Science
Abstract EN
We consider two coupled queues with a generalized processor sharing service discipline.
The second queue has a much smaller Poisson arrival rate than the first queue, while the customer service times are of comparable magnitude.
The processor sharing server devotes most of its resources to the first queue, except when it is empty.
The fraction of resources devoted to the second queue is small, of the same order as the ratio of the arrival rates.
We assume that the primary queue is heavily loaded and that the secondary queue is critically loaded.
If we let the small arrival rate to the secondary queue be O(ε), where 0≤ε≪1, then in this asymptotic limit the number of customers in the first queue will be large, of order O(ε-1), while that in the second queue will be somewhat smaller, of order O(ε-1/2).
We obtain a two-dimensional diffusion approximation for this model and explicitly solve for the joint steady state probability distribution of the numbers of customers in the two queues.
This work complements that in (Morrison, 2010), which the second queue was assumed to be heavily or lightly loaded, leading to mean queue lengths that were O(ε-1) or O(1), respectively.
American Psychological Association (APA)
Knessl, Charles& Morrison, John A.. 2011. Two Coupled Queues with Vastly Different Arrival Rates : Critical Loading Case. Advances in Operations Research،Vol. 2011, no. 2011, pp.1-26.
https://search.emarefa.net/detail/BIM-455341
Modern Language Association (MLA)
Knessl, Charles& Morrison, John A.. Two Coupled Queues with Vastly Different Arrival Rates : Critical Loading Case. Advances in Operations Research No. 2011 (2011), pp.1-26.
https://search.emarefa.net/detail/BIM-455341
American Medical Association (AMA)
Knessl, Charles& Morrison, John A.. Two Coupled Queues with Vastly Different Arrival Rates : Critical Loading Case. Advances in Operations Research. 2011. Vol. 2011, no. 2011, pp.1-26.
https://search.emarefa.net/detail/BIM-455341
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-455341