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Mean field and propagation of chaos in multi-class heterogeneous loss models
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Mukhopadhyay, Arpan, Karthik, A., Mazumdar, Ravi R. and Guillemin, Fabrice (2015) Mean field and propagation of chaos in multi-class heterogeneous loss models. Performance Evaluation, 91 . pp. 117-131. doi:10.1016/j.peva.2015.06.008
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WRAP-mean-field-propagation-chaos-multi-class-heterogeneous-loss-models-Mukhopadhyay-2015.pdf - Accepted Version - Requires a PDF viewer. Available under License Creative Commons Attribution Non-commercial No Derivatives 4.0. Download (668Kb) | Preview |
Official URL: https://doi.org/10.1016/j.peva.2015.06.008
Abstract
We consider a system consisting of parallel servers, where jobs with different resource requirements arrive and are assigned to the servers for processing. Each server has a finite resource capacity and therefore can serve only a finite number of jobs at a time. We assume that different servers have different resource capacities. A job is accepted for processing only if the resource requested by the job is available at the server to which it is assigned. Otherwise, the job is discarded or blocked. We consider randomized schemes to assign jobs to servers with the aim of reducing the average blocking probability of jobs in the system. In particular, we consider a scheme that assigns an incoming job to the server having maximum available vacancy or unused resource among randomly sampled servers. We consider the system in the limit where both the number of servers and the arrival rates of jobs are scaled by a large factor. This gives rise to a mean field analysis. We show that in the limiting system the servers behave independently—a property termed as propagation of chaos. Stationary tail probabilities of server occupancies are obtained from the stationary solution of the mean field which is shown to be unique and globally attractive. We further characterize the rate of decay of the stationary tail probabilities. Numerical results suggest that the proposed scheme significantly reduces the average blocking probability of jobs as compared to static schemes that probabilistically route jobs to servers independently of their states.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics > QA75 (Please use QA76 Electronic Computers. Computer Science) Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software |
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| Divisions: | Faculty of Science > Computer Science | ||||||||
| Journal or Publication Title: | Performance Evaluation | ||||||||
| Publisher: | Elsevier Science BV | ||||||||
| ISSN: | 0166-5316 | ||||||||
| Official Date: | September 2015 | ||||||||
| Dates: |
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| Volume: | 91 | ||||||||
| Page Range: | pp. 117-131 | ||||||||
| DOI: | 10.1016/j.peva.2015.06.008 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Title of Event: | IFIP Performance 2015 | ||||||||
| Type of Event: | Conference | ||||||||
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