Diffusion limits for the queue length of jobs in multi-server open queueing networks
Author
Abstract
Suggested Citation
DOI: 10.5277/ord170404
Download full text from publisher
References listed on IDEAS
- Avishai Mandelbaum & Alexander L. Stolyar, 2004. "Scheduling Flexible Servers with Convex Delay Costs: Heavy-Traffic Optimality of the Generalized cμ-Rule," Operations Research, INFORMS, vol. 52(6), pages 836-855, December.
- Martin I. Reiman, 1984. "Open Queueing Networks in Heavy Traffic," Mathematics of Operations Research, INFORMS, vol. 9(3), pages 441-458, August.
- Hong Chen & Hanqin Zhang, 2000. "Stability of Multiclass Queueing Networks Under Priority Service Disciplines," Operations Research, INFORMS, vol. 48(1), pages 26-37, February.
- Sakalauskas, L. L. & Minkevicius, S., 2000. "On the law of the iterated logarithm in open queueing networks," European Journal of Operational Research, Elsevier, vol. 120(3), pages 632-640, February.
- Austin J. Lemoine, 1978. "State of the Art--Networks of Queues: A Survey of Weak Convergence Results," Management Science, INFORMS, vol. 24(11), pages 1175-1193, July.
Most related items
These are the items that most often cite the same works as this one and are cited by the same works as this one.- Itai Gurvich, 2014. "Validity of Heavy-Traffic Steady-State Approximations in Multiclass Queueing Networks: The Case of Queue-Ratio Disciplines," Mathematics of Operations Research, INFORMS, vol. 39(1), pages 121-162, February.
- Saulius Minkevičius & Edvinas Greičius, 2019. "Heavy Traffic Limits for the Extreme Waiting Time in Multi-phase Queueing Systems," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 109-124, March.
- Saulius MinkeviÄ ius, 2020. "On the law of the iterated logarithm in hybrid multiphase queueing systems," Operations Research and Decisions, Wroclaw University of Science Technology, Faculty of Management, vol. 30(4), pages 57-64.
- Yongjiang Guo & Yunan Liu & Renhu Pei, 2018. "Functional law of the iterated logarithm for multi-server queues with batch arrivals and customer feedback," Annals of Operations Research, Springer, vol. 264(1), pages 157-191, May.
- Minkevicius, Saulius & Steisunas, Stasys, 2003. "A law of the iterated logarithm for global values of waiting time in multiphase queues," Statistics & Probability Letters, Elsevier, vol. 61(4), pages 359-371, February.
- Heng-Qing Ye & David D. Yao, 2008. "Heavy-Traffic Optimality of a Stochastic Network Under Utility-Maximizing Resource Allocation," Operations Research, INFORMS, vol. 56(2), pages 453-470, April.
- Junfei Huang & Boaz Carmeli & Avishai Mandelbaum, 2015. "Control of Patient Flow in Emergency Departments, or Multiclass Queues with Deadlines and Feedback," Operations Research, INFORMS, vol. 63(4), pages 892-908, August.
- Saulius Minkevičius & Vladimiras Dolgopolovas & Leonidas L. Sakalauskas, 2016. "A Law of the Iterated Logarithm for the Sojourn Time Process in Queues in Series," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 37-57, March.
- Amy R. Ward & Mor Armony, 2013. "Blind Fair Routing in Large-Scale Service Systems with Heterogeneous Customers and Servers," Operations Research, INFORMS, vol. 61(1), pages 228-243, February.
- Achal Bassamboo & J. Michael Harrison & Assaf Zeevi, 2006. "Design and Control of a Large Call Center: Asymptotic Analysis of an LP-Based Method," Operations Research, INFORMS, vol. 54(3), pages 419-435, June.
- Josh Reed & Yair Shaki, 2015. "A Fair Policy for the G / GI / N Queue with Multiple Server Pools," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 558-595, March.
- Saulius Minkevičius & Igor Katin & Joana Katina & Irina Vinogradova-Zinkevič, 2021. "On Little’s Formula in Multiphase Queues," Mathematics, MDPI, vol. 9(18), pages 1-15, September.
- Amarjit Budhiraja & Chihoon Lee, 2009. "Stationary Distribution Convergence for Generalized Jackson Networks in Heavy Traffic," Mathematics of Operations Research, INFORMS, vol. 34(1), pages 45-56, February.
- Rosario Delgado, 2010. "State space collapse and stability of queueing networks," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(3), pages 477-499, December.
- Gabriel Zayas‐Cabán & Emmett J. Lodree & David L. Kaufman, 2020. "Optimal Control of Parallel Queues for Managing Volunteer Convergence," Production and Operations Management, Production and Operations Management Society, vol. 29(10), pages 2268-2288, October.
- Budhiraja, Amarjit & Lee, Chihoon, 2007. "Long time asymptotics for constrained diffusions in polyhedral domains," Stochastic Processes and their Applications, Elsevier, vol. 117(8), pages 1014-1036, August.
- Kuang Xu & Yuan Zhong, 2020. "Information and Memory in Dynamic Resource Allocation," Operations Research, INFORMS, vol. 68(6), pages 1698-1715, November.
- Wanyang Dai, 2013. "Optimal Rate Scheduling via Utility-Maximization for J -User MIMO Markov Fading Wireless Channels with Cooperation," Operations Research, INFORMS, vol. 61(6), pages 1450-1462, December.
- Zhen Xu & Jiheng Zhang & Rachel Q. Zhang, 2019. "Instantaneous Control of Brownian Motion with a Positive Lead Time," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 943-965, August.
- Rami Atar & Subhamay Saha, 2017. "Optimality of the generalized $$\varvec{c\mu }$$ c μ rule in the moderate deviation regime," Queueing Systems: Theory and Applications, Springer, vol. 87(1), pages 113-130, October.
More about this item
Keywords
performance evaluation; multiserver open queueing network; limit theorem; queue length;All these keywords.
Statistics
Access and download statisticsCorrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wut:journl:v:4:y:2017:p:71-84:id:1303. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Adam Kasperski (email available below). General contact details of provider: https://edirc.repec.org/data/iopwrpl.html .
Please note that corrections may take a couple of weeks to filter through the various RePEc services.