Fluctuation Bounds for the Max-Weight Policy with Applications to State Space Collapse
© 2020 The Author(s). We consider a multihop switched network operating under a max-weight scheduling policy and show that the distance between the queue length process and a fluid solution remains bounded by a constant multiple of the deviation of the cumulative arrival process from its average. We...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Institute for Operations Research and the Management Sciences (INFORMS)
2021
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| Online Access: | https://hdl.handle.net/1721.1/134013 |
| _version_ | 1826199426760179712 |
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| author | Sharifnassab, Arsalan Tsitsiklis, John N Golestani, S Jamaloddin |
| author2 | Massachusetts Institute of Technology. Laboratory for Information and Decision Systems |
| author_facet | Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Sharifnassab, Arsalan Tsitsiklis, John N Golestani, S Jamaloddin |
| author_sort | Sharifnassab, Arsalan |
| collection | MIT |
| description | © 2020 The Author(s). We consider a multihop switched network operating under a max-weight scheduling policy and show that the distance between the queue length process and a fluid solution remains bounded by a constant multiple of the deviation of the cumulative arrival process from its average. We then exploit this result to prove matching upper and lower bounds for the time scale over which additive state space collapse (SSC) takes place. This implies, as two special cases, an additive SSC result in diffusion scaling under nonMarkovian arrivals and, for the case of independent and identically distributed arrivals, an additive SSC result over an exponential time scale. |
| first_indexed | 2024-09-23T11:20:02Z |
| format | Article |
| id | mit-1721.1/134013 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:20:02Z |
| publishDate | 2021 |
| publisher | Institute for Operations Research and the Management Sciences (INFORMS) |
| record_format | dspace |
| spelling | mit-1721.1/1340132023-12-12T19:54:25Z Fluctuation Bounds for the Max-Weight Policy with Applications to State Space Collapse Sharifnassab, Arsalan Tsitsiklis, John N Golestani, S Jamaloddin Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science © 2020 The Author(s). We consider a multihop switched network operating under a max-weight scheduling policy and show that the distance between the queue length process and a fluid solution remains bounded by a constant multiple of the deviation of the cumulative arrival process from its average. We then exploit this result to prove matching upper and lower bounds for the time scale over which additive state space collapse (SSC) takes place. This implies, as two special cases, an additive SSC result in diffusion scaling under nonMarkovian arrivals and, for the case of independent and identically distributed arrivals, an additive SSC result over an exponential time scale. 2021-10-27T19:57:38Z 2021-10-27T19:57:38Z 2020 2021-03-23T18:34:45Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/134013 en 10.1287/STSY.2019.0038 Stochastic Systems Creative Commons Attribution 4.0 International license https://creativecommons.org/licenses/by/4.0/ application/pdf Institute for Operations Research and the Management Sciences (INFORMS) INFORMS |
| spellingShingle | Sharifnassab, Arsalan Tsitsiklis, John N Golestani, S Jamaloddin Fluctuation Bounds for the Max-Weight Policy with Applications to State Space Collapse |
| title | Fluctuation Bounds for the Max-Weight Policy with Applications to State Space Collapse |
| title_full | Fluctuation Bounds for the Max-Weight Policy with Applications to State Space Collapse |
| title_fullStr | Fluctuation Bounds for the Max-Weight Policy with Applications to State Space Collapse |
| title_full_unstemmed | Fluctuation Bounds for the Max-Weight Policy with Applications to State Space Collapse |
| title_short | Fluctuation Bounds for the Max-Weight Policy with Applications to State Space Collapse |
| title_sort | fluctuation bounds for the max weight policy with applications to state space collapse |
| url | https://hdl.handle.net/1721.1/134013 |
| work_keys_str_mv | AT sharifnassabarsalan fluctuationboundsforthemaxweightpolicywithapplicationstostatespacecollapse AT tsitsiklisjohnn fluctuationboundsforthemaxweightpolicywithapplicationstostatespacecollapse AT golestanisjamaloddin fluctuationboundsforthemaxweightpolicywithapplicationstostatespacecollapse |