The Library
Insensitivity of the mean field limit of loss systems under SQ(d) routeing
Tools
Tools
Tools
Vasantam, Thirupathaiah, Mukhopadhyay, Arpan and Mazumdar, Ravi R. (2019) Insensitivity of the mean field limit of loss systems under SQ(d) routeing. Advances in Applied Probability, 51 (4). pp. 1027-1066. doi:10.1017/apr.2019.41 ISSN 0001-8678.
|
PDF
WRAP-insensitivity-mean-field-limit-loss-systems-under-SQ(d)-routeing-Mukhopadhyay-2020.pdf - Accepted Version - Requires a PDF viewer. Download (1038Kb) | Preview |
Official URL: http://dx.doi.org/10.1017/apr.2019.41
Abstract
In this paper, we study a large multi-server loss model under the SQ(d) routeing scheme when the service time distributions are general with finite mean. Previous works have addressed the exponential service time case when the number of servers goes to infinity, giving rise to a mean field model. The fixed point of the limiting mean field equations (MFEs) was seen to be insensitive to the service time distribution in simulations, but no proof was available. While insensitivity is well known for loss systems, the models, even with state-dependent inputs, belong to the class of linear Markov models. In the context of SQ(d) routeing, the resulting model belongs to the class of nonlinear Markov processes (processes whose generator itself depends on the distribution) for which traditional arguments do not directly apply. Showing insensitivity to the general service time distributions has thus remained an open problem. Obtaining the MFEs in this case poses a challenge due to the resulting Markov description of the system being in positive orthant as opposed to a finite chain in the exponential case. In this paper, we first obtain the MFEs and then show that the MFEs have a unique fixed point that coincides with the fixed point in the exponential case, thus establishing insensitivity. The approach is via a measure-valued Markov process representation and the martingale problem to establish the mean field limit.
| Item Type: | Journal Article | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics T Technology > T Technology (General) |
||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||||||
| Library of Congress Subject Headings (LCSH): | Erlang's loss formula, Queuing theory, Markov processes, Queuing networks (Data transmission) | ||||||||
| Journal or Publication Title: | Advances in Applied Probability | ||||||||
| Publisher: | Applied Probability Trust | ||||||||
| ISSN: | 0001-8678 | ||||||||
| Official Date: | December 2019 | ||||||||
| Dates: |
|
||||||||
| Volume: | 51 | ||||||||
| Number: | 4 | ||||||||
| Page Range: | pp. 1027-1066 | ||||||||
| DOI: | 10.1017/apr.2019.41 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Reuse Statement (publisher, data, author rights): | This article has been published in a revised form in Advances in Applied Probability http://dx.doi.org/10.1017/apr.2019.41. This version is published under a Creative Commons CC-BY-NC-ND. No commercial re-distribution or re-use allowed. Derivative works cannot be distributed. © Applied Probability Trust 2019 | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 7 August 2020 | ||||||||
| Date of first compliant Open Access: | 7 August 2020 |
Request changes or add full text files to a record
Repository staff actions (login required)
 |
View Item |
Downloads
Downloads per month over past year
