Stabilizing a Queue Subject to Activity-Dependent Server Performance
We consider a discrete-time system, comprising a first-come-first-served queue, a nonpreemptive server, and a scheduler that governs the assignment of tasks in the queue to the server. The server has an availability state that indicates, at each instant, whether the server is busy working on a task...
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| Vydané v: | IEEE transactions on control of network systems Ročník 8; číslo 4; s. 1579 - 1591 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Piscataway
IEEE
01.12.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 2325-5870, 2372-2533 |
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| Abstract | We consider a discrete-time system, comprising a first-come-first-served queue, a nonpreemptive server, and a scheduler that governs the assignment of tasks in the queue to the server. The server has an availability state that indicates, at each instant, whether the server is busy working on a task or is available. In the latter case, if the queue is nonempty, then a task-assignment control policy implemented by the scheduler either assigns a new task to the server or allows it to rest. The server also has an integer-valued activity state that is nonincreasing during rest periods, and is nondecreasing otherwise. An instantaneous service rate function ascribes to each possible value of the activity state a probability that the server can complete a task in one time step. For a typical instantaneous service rate function, the completion probability decreases (server performance worsens) as the activity state increases. The scheduler policy has access to the queue size and the entire state of the server.
In this article, we study the problem of designing scheduler policies that stabilize the queue. We show that stability, whenever viable, can be achieved by a simple policy that bases its decisions on the availability state, a threshold applied to the activity state, and a flag that indicates when the queue is empty. The supremum of the service rates achievable by stabilizing policies can be determined by a finite search. Our results remain valid even when the instantaneous service rate function is not monotonic. |
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| AbstractList | We consider a discrete-time system, comprising a first-come-first-served queue, a nonpreemptive server, and a scheduler that governs the assignment of tasks in the queue to the server. The server has an availability state that indicates, at each instant, whether the server is busy working on a task or is available. In the latter case, if the queue is nonempty, then a task-assignment control policy implemented by the scheduler either assigns a new task to the server or allows it to rest. The server also has an integer-valued activity state that is nonincreasing during rest periods, and is nondecreasing otherwise. An instantaneous service rate function ascribes to each possible value of the activity state a probability that the server can complete a task in one time step. For a typical instantaneous service rate function, the completion probability decreases (server performance worsens) as the activity state increases. The scheduler policy has access to the queue size and the entire state of the server.
In this article, we study the problem of designing scheduler policies that stabilize the queue. We show that stability, whenever viable, can be achieved by a simple policy that bases its decisions on the availability state, a threshold applied to the activity state, and a flag that indicates when the queue is empty. The supremum of the service rates achievable by stabilizing policies can be determined by a finite search. Our results remain valid even when the instantaneous service rate function is not monotonic. We consider a discrete-time system, comprising a first-come-first-served queue, a nonpreemptive server, and a scheduler that governs the assignment of tasks in the queue to the server. The server has an availability state that indicates, at each instant, whether the server is busy working on a task or is available. In the latter case, if the queue is nonempty, then a task-assignment control policy implemented by the scheduler either assigns a new task to the server or allows it to rest. The server also has an integer-valued activity state that is nonincreasing during rest periods, and is nondecreasing otherwise. An instantaneous service rate function ascribes to each possible value of the activity state a probability that the server can complete a task in one time step. For a typical instantaneous service rate function, the completion probability decreases (server performance worsens) as the activity state increases. The scheduler policy has access to the queue size and the entire state of the server. In this article, we study the problem of designing scheduler policies that stabilize the queue. We show that stability, whenever viable, can be achieved by a simple policy that bases its decisions on the availability state, a threshold applied to the activity state, and a flag that indicates when the queue is empty. The supremum of the service rates achievable by stabilizing policies can be determined by a finite search. Our results remain valid even when the instantaneous service rate function is not monotonic. |
| Author | Lin, Michael La, Richard J. Martins, Nuno C. |
| Author_xml | – sequence: 1 givenname: Michael orcidid: 0000-0002-9611-5288 surname: Lin fullname: Lin, Michael email: mlin1025@terpmail.umd.edu organization: Department of Electrical and Computer Engineering and the Institute for Systems Research, University of Maryland, College Park, MD, USA – sequence: 2 givenname: Richard J. orcidid: 0000-0002-4836-8475 surname: La fullname: La, Richard J. email: hyongla@umd.edu organization: Department of Electrical and Computer Engineering and the Institute for Systems Research, University of Maryland, College Park, MD, USA – sequence: 3 givenname: Nuno C. orcidid: 0000-0003-2083-8102 surname: Martins fullname: Martins, Nuno C. email: nmartins@umd.edu organization: Department of Electrical and Computer Engineering and the Institute for Systems Research, University of Maryland, College Park, MD, USA |
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| References_xml | – ident: ref18 doi: 10.1109/9.182479 – volume: 9 start-page: 69 year: 1967 ident: ref8 article-title: On bulk queues with state dependent parameters publication-title: J Oper Res Soc Jpn – start-page: 1295 year: 1997 ident: ref24 article-title: Supervisory control publication-title: Handbook of Human Factors and Ergonomics – ident: ref20 doi: 10.1287/opre.2.2.107 – year: 1968 ident: ref42 publication-title: Real Analysis Meerut India Krishna Prakashan Media – ident: ref39 doi: 10.1145/2489253.2489270 – start-page: 1684 year: 2004 ident: ref17 article-title: Optimal transmission scheduling with base station antenna array in cellular networks publication-title: Proc IEEE Int Conf Comput Commun – ident: ref4 doi: 10.1017/CBO9780511626630 – volume: 12 start-page: 132 year: 1962 ident: ref6 article-title: A queueing model with state dependent service rates publication-title: J Ind Eng – ident: ref16 doi: 10.1109/TNET.2005.850215 – start-page: 1533 year: 2002 ident: ref14 article-title: Optimality of certain channel aware scheduling policies publication-title: Proc Allerton Conf Commun Control Comput – ident: ref27 doi: 10.1109/TAC.2010.2069590 – ident: ref5 doi: 10.1017/9781108772662 – ident: ref38 doi: 10.1109/TWC.2018.2861874 – ident: ref35 doi: 10.1007/978-3-319-65614-4 – ident: ref31 doi: 10.1109/SURV.2011.060710.00094 – start-page: 132 year: 1997 ident: ref10 article-title: Queueing systems with state dependent parameters publication-title: Frontiers in Queueing Models and Applications in Science and Engineering (Probability and Stochastics Series) – year: 1999 ident: ref3 article-title: Analysis of queueing systems – ident: ref29 doi: 10.1007/BF01158688 – ident: ref33 doi: 10.1007/978-0-387-76464-1 – ident: ref11 doi: 10.1109/INFCOM.1996.497876 – ident: ref23 doi: 10.1109/MCS.2015.2471056 – ident: ref15 doi: 10.1017/S0269964804182041 – ident: ref7 doi: 10.1287/mnsc.10.1.131 – year: 2021 ident: ref36 article-title: Channels, remote estimation and queueing systems with a utilization-dependent component: A unifying survey of recent results – ident: ref13 doi: 10.1017/S0269964806060335 – ident: ref9 doi: 10.1287/opre.15.1.117 – ident: ref32 doi: 10.1145/1274858.1274870 – year: 2001 ident: ref41 publication-title: Probability and Random Processes doi: 10.1093/oso/9780198572237.001.0001 – year: 2002 ident: ref2 publication-title: Elements of Queueing Theory Palm Martingale Calculus and Stochastic Recurrences – ident: ref26 doi: 10.1287/mnsc.1090.1037 – ident: ref19 doi: 10.1016/j.neubiorev.2012.10.003 – year: 2021 ident: ref1 article-title: Stability of a single queue subject to action-dependent server performance – ident: ref34 doi: 10.1109/JSAC.2015.2391531 – volume: 64 start-page: 57 year: 2017 ident: ref21 article-title: Humans are not machines: The behavioral impact of queueing design on service time publication-title: Manage Sci – ident: ref37 doi: 10.1109/TIT.2009.2023753 – ident: ref22 doi: 10.1002/cne.920180503 – ident: ref30 doi: 10.1017/S0305004100027638 – ident: ref25 doi: 10.1197/j.aem.2006.10.104 – ident: ref12 doi: 10.1109/25.994812 – year: 2005 ident: ref40 publication-title: Markov Decision Processes Discrete Stochastic Dynamic Programming – ident: ref28 doi: 10.1109/JPROC.2011.2173264 |
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| SubjectTerms | Availability Discrete time systems Policies Queueing analysis Queues Scheduling algorithms Servers Stability Task scheduling |
| Title | Stabilizing a Queue Subject to Activity-Dependent Server Performance |
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