{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,6,27]],"date-time":"2022-06-27T23:53:34Z","timestamp":1656374014546},"reference-count":21,"publisher":"Association for Computing Machinery (ACM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. ACM"],"published-print":{"date-parts":[[2005,9]]},"abstract":"\n In a wireless network, a basestation transmits data to mobiles at\n time-varying, mobile-dependent<\/jats:italic>\n rates due to the ever changing nature of the communication channels. In this article, we consider a wireless system in which the channel conditions and data arrival processes are governed by an\n adversary<\/jats:italic>\n . We first consider a single server and a set of users. At each time step\n t<\/jats:italic>\n , the server can only transmit data to one user. If user\n i<\/jats:italic>\n is chosen, the transmission rate is\n \n r\n i<\/jats:sub>\n <\/jats:italic>\n (\n t<\/jats:italic>\n ). We say that the system is (\n w<\/jats:italic>\n , \u03b5)-\n admissible<\/jats:italic>\n if in any window of\n w<\/jats:italic>\n time steps the adversary can schedule the users so that the total data arriving to each user is at most 1\u2212\u03b5 times the total service it receives.Our objective is to design online scheduling algorithms to ensure stability in an admissible system. We first show, somewhat surprisingly, that the admissibility condition alone does not guarantee the existence of a stable online algorithm, even in a subcritical system (i.e., \u03b5 > 0). For example, if the nonzero rates in an infinite rate set can be arbitrarily small, then a subcritical system can be unstable for any deterministic online algorithm.On a positive note, we present a tracking algorithm that attempts to mimic the behavior of the adversary. This algorithm ensures stability for all (\n w<\/jats:italic>\n , \u03b5)-admissible systems that are not excluded by our instability results. As a special case, if the rate set is finite, then the tracking algorithm is stable even for a critical system (i.e., \u03b5 = 0). Moreover, the queue sizes are independent of \u03b5. For subcritical systems, we also show that a simpler max weight algorithm is stable as long as the user rates are bounded away from zero.The offline version of our problem resembles the problem of scheduling unrelated machines and can be modeled by an integer program. We present a rounding algorithm for its linear relaxation and prove that the rounding technique cannot be substantially improved.\n <\/jats:p>","DOI":"10.1145\/1089023.1089028","type":"journal-article","created":{"date-parts":[[2005,11,7]],"date-time":"2005-11-07T16:00:45Z","timestamp":1131379245000},"page":"809-834","source":"Crossref","is-referenced-by-count":21,"title":["Scheduling over a time-varying user-dependent channel with applications to high-speed wireless data"],"prefix":"10.1145","volume":"52","author":[{"given":"Matthew","family":"Andrews","sequence":"first","affiliation":[{"name":"Bell Laboratories, Murrray Hill, New Jersey"}]},{"given":"Lisa","family":"Zhang","sequence":"additional","affiliation":[{"name":"Bell Laboratories, Murrray Hill, New Jersey"}]}],"member":"320","reference":[{"key":"e_1_2_1_1_1","first-page":"359","volume-title":"Proceedings of the 30th Annual ACM Symposium on Theory of Computing","author":"Aiello W."},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/TWC.2004.833419"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/363647.363677"},{"key":"e_1_2_1_4_1","unstructured":"Andrews M. Kumaran K. Ramanan K. Stolyar A. Vijayakumar R. and Whiting P. 2000. CDMA data QoS scheduling on the forward link with variable channel conditions. Bell Labs Tech. Memo. (Apr.). Andrews M. Kumaran K. Ramanan K. Stolyar A. Vijayakumar R. and Whiting P. 2000. CDMA data QoS scheduling on the forward link with variable channel conditions. Bell Labs Tech. Memo. (Apr.)."},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1109\/35.900644"},{"key":"e_1_2_1_6_1","volume-title":"Proceedings of the 34th Annual ACM Symposium on Theory of Computing (Montreal, Ont., Canada, May). ACM","author":"Anshelevich E."},{"key":"e_1_2_1_7_1","first-page":"158","volume-title":"Proceedings of the 42nd Annual Symposium on Foundations of Computer Science","author":"Awerbuch B."},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/363647.363659"},{"key":"e_1_2_1_9_1","volume-title":"Proceedings of IEEE INFOCOM '01","author":"Borst S."},{"key":"e_1_2_1_10_1","unstructured":"Garey M. R. and Johnson D. S. 1979. Computers and Intractability---A Guide to the Theory of NP-Completeness. W. H. Freeman and Company New York. Garey M. R. and Johnson D. S. 1979. Computers and Intractability---A Guide to the Theory of NP-Completeness. W. H. Freeman and Company New York."},{"key":"e_1_2_1_11_1","volume-title":"Proceedings of the IEEE Semiannual Vehicular Technology Conference, VTC2000-Spring","author":"Jalali A."},{"key":"e_1_2_1_12_1","volume-title":"Proceedings of the 40th Annual Allerton Conference on Communication, Control, and Computing.","author":"Kushner H."},{"key":"e_1_2_1_13_1","volume-title":"Proceedings of IEEE INFOCOM '02","author":"Neely M."},{"key":"e_1_2_1_14_1","volume-title":"Proceedings of the IEEE Semiannual Vehicular Technology Conference, VTC2001-Fall (Atlantic City, N.J., Oct.). IEEE Computer Society Press","author":"Rhee J."},{"key":"e_1_2_1_15_1","volume-title":"Proceedings of ACM Workshop on Wireless and Mobile Multimedia Seattle, WA (Aug.). ACM","author":"Shakkottai S."},{"key":"e_1_2_1_16_1","volume-title":"Proceedings of 17th International Teletraffic Congress (ITC-17)","author":"Shakkottai S."},{"key":"e_1_2_1_17_1","doi-asserted-by":"crossref","unstructured":"Shakkottai S. and Stolyar A. L. 2002. Scheduling for multiple flows sharing a time-varying channel: The exponential rule. In Analytic Methods in Applied Probability in Memory of Fridrih karpelevich. Yu. M. Shov Ed. American Mathematical Society Translations Series 2. American Mathematical Society Providence RI vol. 207 pp. 185--202. Shakkottai S. and Stolyar A. L. 2002. Scheduling for multiple flows sharing a time-varying channel: The exponential rule. In Analytic Methods in Applied Probability in Memory of Fridrih karpelevich. Yu. M. Shov Ed. American Mathematical Society Translations Series 2. American Mathematical Society Providence RI vol. 207 pp. 185--202.","DOI":"10.1090\/trans2\/207\/12"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01585178"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1040.0156"},{"key":"e_1_2_1_20_1","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1109\/9.182479","article-title":"Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks","volume":"37","author":"Tassiulas L.","year":"1992","journal-title":"IEEE Trans. Automat. Cont."},{"key":"e_1_2_1_21_1","unstructured":"Tse D. 200X. Multiuser diversity in wireless networks. http:\/\/www.eecs.berkeley.edu\/~dtse\/stanford416.ps. Tse D. 200X. Multiuser diversity in wireless networks. http:\/\/www.eecs.berkeley.edu\/~dtse\/stanford416.ps."}],"container-title":["Journal of the ACM"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1089023.1089028","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,18]],"date-time":"2021-02-18T00:56:45Z","timestamp":1613609805000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1089023.1089028"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,9]]},"references-count":21,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2005,9]]}},"alternative-id":["10.1145\/1089023.1089028"],"URL":"http:\/\/dx.doi.org\/10.1145\/1089023.1089028","relation":{},"ISSN":["0004-5411","1557-735X"],"issn-type":[{"value":"0004-5411","type":"print"},{"value":"1557-735X","type":"electronic"}],"subject":["Artificial Intelligence","Hardware and Architecture","Information Systems","Control and Systems Engineering","Software"],"published":{"date-parts":[[2005,9]]}}}