{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T02:55:54Z","timestamp":1777517754914,"version":"3.51.4"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2017,11,16]],"date-time":"2017-11-16T00:00:00Z","timestamp":1510790400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Queueing Syst"],"published-print":{"date-parts":[[2018,2]]},"DOI":"10.1007\/s11134-017-9553-y","type":"journal-article","created":{"date-parts":[[2017,11,16]],"date-time":"2017-11-16T11:27:35Z","timestamp":1510831655000},"page":"167-203","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Stability of linear EDF networks with resource sharing"],"prefix":"10.1007","volume":"88","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3073-959X","authenticated-orcid":false,"given":"\u0141ukasz","family":"Kruk","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,11,16]]},"reference":[{"key":"9553_CR1","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1287\/moor.2014.0690","volume":"40","author":"R Atar","year":"2015","unstructured":"Atar, R., Biswas, A., Kaspi, H.: Fluid limits of G\/G\/1+G queues under the non-preemptive earliest-deadline-first discipline. Math. Oper. Res. 40, 683\u2013702 (2015)","journal-title":"Math. Oper. Res."},{"key":"9553_CR2","unstructured":"Atar, R., Biswas, A., Kaspi, H.: Law of large numbers for the many-server earliest-deadline-first queue. arXiv:1610.03218v1"},{"key":"9553_CR3","unstructured":"Atar, R., Biswas, A., Kaspi, H., Ramanan, K.: A Skorokhod map on measure-valued paths with applications to priority queues. arXiv:1604.04874v1"},{"key":"9553_CR4","doi-asserted-by":"crossref","unstructured":"Baruah, S.K.: Resource sharing in EDF-scheduled systems: a closer look. In: Proceedings of the 27th IEEE International Real-Time Systems Symposium (RTSS\u201906). IEEE Computer Society, Los Alamos, CA (2006)","DOI":"10.1109\/RTSS.2006.41"},{"key":"9553_CR5","unstructured":"Bender, M., Chakrabarti, S., Muthukrishnan, S.: Flow and stretch metrics for scheduling continuous job streams. In: Proceedings of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms (1998)"},{"issue":"1","key":"9553_CR6","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1109\/TNET.2011.2157831","volume":"20","author":"B Birand","year":"2012","unstructured":"Birand, B., Chudnovsky, M., Ries, B., Seymour, P., Zussman, G., Zwols, Y.: Analyzing the performance of greedy maximal scheduling via local pooling and graphy theory. IEEE\/ACM Trans. Netw. 20(1), 163\u2013176 (2012)","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"9553_CR7","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1145\/384268.378438","volume":"2001","author":"T Bonald","year":"2001","unstructured":"Bonald, T., Massouli\u00e9, L.: Impact of fairness on Internet performance. Proc. ACM Sigmetrics 2001, 82\u201391 (2001)","journal-title":"Proc. ACM Sigmetrics"},{"key":"9553_CR8","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1023\/A:1017987600517","volume":"39","author":"M Bramson","year":"2001","unstructured":"Bramson, M.: Stability of earliest-due-date, first-served queueing networks. Queueing Syst. Theory Appl. 39, 79\u2013102 (2001)","journal-title":"Queueing Syst. Theory Appl."},{"key":"9553_CR9","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1214\/aoap\/1177004828","volume":"5","author":"JG Dai","year":"1995","unstructured":"Dai, J.G.: On positive Harris recurrence of multiclass queueing networks: a unified approach via fluid limit models. Ann. Appl. Probab. 5, 49\u201377 (1995)","journal-title":"Ann. Appl. Probab."},{"key":"9553_CR10","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1111\/j.2517-6161.1984.tb01308.x","volume":"46","author":"MHA Davis","year":"1984","unstructured":"Davis, M.H.A.: Piecewise-deterministic Markov processes: a general class of non-diffusion stochastic models. J. R. Stat. Soc. Ser. B 46, 353\u2013388 (1984)","journal-title":"J. R. Stat. Soc. Ser. B"},{"key":"9553_CR11","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1109\/90.909020","volume":"9","author":"G Veciana de","year":"2001","unstructured":"de Veciana, G., Lee, T.J., Konstantopoulos, T.: Stability and performance analysis of networks supporting elastic services. IEEE\/ACM Trans. Netw. 9, 2\u201314 (2001)","journal-title":"IEEE\/ACM Trans. Netw."},{"issue":"1","key":"9553_CR12","first-page":"131","volume":"14","author":"L Decreusefond","year":"2008","unstructured":"Decreusefond, L., Moyal, P.: Fluid limit of a heavily loaded EDF queue with impatient customers. Markov Process Relat. Fields 14(1), 131\u2013158 (2008)","journal-title":"Markov Process Relat. Fields"},{"issue":"2","key":"9553_CR13","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1017\/S0001867800001075","volume":"38","author":"A Dimakis","year":"2006","unstructured":"Dimakis, A., Walrand, J.: Sufficient conditions for stability of longest-queue-first scheduling: second order properties using fluid limits. Adv. Appl. Prob. 38(2), 505\u2013521 (2006)","journal-title":"Adv. Appl. Prob."},{"key":"9553_CR14","doi-asserted-by":"crossref","first-page":"880","DOI":"10.1287\/moor.1090.0409","volume":"34","author":"DG Down","year":"2009","unstructured":"Down, D.G., Gromoll, H.C., Puha, A.L.: Fluid limits for shortest remaining processing time queues. Math. Oper. Res. 34, 880\u2013911 (2009)","journal-title":"Math. Oper. Res."},{"key":"9553_CR15","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1214\/aoap\/1015345295","volume":"11","author":"B Doytchinov","year":"2001","unstructured":"Doytchinov, B., Lehoczky, J.P., Shreve, S.E.: Real-time queues in heavy traffic with earliest-deadline-first queue discipline. Ann. Appl. Probab. 11, 332\u2013378 (2001)","journal-title":"Ann. Appl. Probab."},{"key":"9553_CR16","doi-asserted-by":"crossref","unstructured":"Getoor, R.K.: Transience and recurrence of Markov processes. In: S\u00e9minaire de Probabilit\u00e9s XIV 284, 397-409, Springer, New York (1979)","DOI":"10.1007\/BFb0089505"},{"key":"9553_CR17","unstructured":"Gromoll, H.C., Williams, R.J.: Fluid model for a data network with $$\\alpha $$ \u03b1 -fair bandwidth sharing and general document size distributions: two examples of stability. In: IMS Collections, Markov Processes and Related Topics: A Festschrift for Thomas G. Kurtz, 4, 253\u2013265 (2008)"},{"key":"9553_CR18","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1214\/08-AAP541","volume":"19","author":"HC Gromoll","year":"2009","unstructured":"Gromoll, H.C., Williams, R.J.: Fluid limits for networks with bandwidth sharing and general document size distribution. Ann. Appl. Probab. 19, 243\u2013280 (2009)","journal-title":"Ann. Appl. Probab."},{"issue":"1","key":"9553_CR19","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1287\/msom.2014.0498","volume":"17","author":"I Gurvich","year":"2015","unstructured":"Gurvich, I., Van Mieghem, J.A.: Collaboration and multitasking in networks: architectures, bottlenecks and capacity. MSOM 17(1), 16\u201333 (2015)","journal-title":"MSOM"},{"key":"9553_CR20","doi-asserted-by":"crossref","unstructured":"Gurvich, I., Van Mieghem, J.A.: Collaboration and multitasking in networks: priorization and achievable capacity. Mgmt. Sc. to appear (2017)","DOI":"10.1287\/mnsc.2017.2722"},{"key":"9553_CR21","doi-asserted-by":"crossref","first-page":"524","DOI":"10.1287\/13-SSY130","volume":"4","author":"JM Harrison","year":"2014","unstructured":"Harrison, J.M., Mandayam, C., Shah, D., Yang, Y.: Resource sharing networks: overview and an open problem. Stoch. Syst. 4, 524\u2013555 (2014)","journal-title":"Stoch. Syst."},{"key":"9553_CR22","doi-asserted-by":"crossref","first-page":"1169","DOI":"10.1017\/S0021900200100567","volume":"33","author":"O Kella","year":"1996","unstructured":"Kella, O., Whitt, W.: Stability and structural properties of stochastic storage networks. J. Appl. Prob. 33, 1169\u20131180 (1996)","journal-title":"J. Appl. Prob."},{"key":"9553_CR23","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1002\/ett.4460080106","volume":"8","author":"FP Kelly","year":"1997","unstructured":"Kelly, F.P.: Charging and rate control for elastic traffic. Eur. Trans. Telecommun. 8, 33\u201337 (1997)","journal-title":"Eur. Trans. Telecommun."},{"key":"9553_CR24","first-page":"179","volume":"28","author":"\u0141 Kruk","year":"2008","unstructured":"Kruk, \u0141.: Stability of two families of real-time queueing networks. Probab. Math. Stat. 28, 179\u2013202 (2008)","journal-title":"Probab. Math. Stat."},{"key":"9553_CR25","doi-asserted-by":"crossref","first-page":"538","DOI":"10.1287\/moor.1110.0495","volume":"36","author":"\u0141 Kruk","year":"2011","unstructured":"Kruk, \u0141.: An open queueing network with asymptotically stable fluid model and unconventional heavy traffic behavior. Math. Oper. Res. 36, 538\u2013551 (2011)","journal-title":"Math. Oper. Res."},{"key":"9553_CR26","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1007\/s00186-016-0543-3","volume":"84","author":"\u0141 Kruk","year":"2016","unstructured":"Kruk, \u0141.: Minimality of EDF networks with resource sharing. Math. Meth. Oper. Res. 84, 259\u2013283 (2016)","journal-title":"Math. Meth. Oper. Res."},{"key":"9553_CR27","first-page":"37","volume":"1","author":"\u0141 Kruk","year":"2003","unstructured":"Kruk, \u0141., Lehoczky, J.P., Shreve, S.E.: Second order approximation for the customer time in queue distribution under the FIFO service discipline. Ann. UMCS Inf. AI 1, 37\u201348 (2003)","journal-title":"Ann. UMCS Inf. AI"},{"key":"9553_CR28","doi-asserted-by":"crossref","first-page":"516","DOI":"10.1214\/105051605000000809","volume":"16","author":"\u0141 Kruk","year":"2006","unstructured":"Kruk, \u0141., Lehoczky, J.P., Shreve, S.E.: Accuracy of state space collapse for earliest-deadline-first queues. Ann. Appl. Probab. 16, 516\u2013561 (2006)","journal-title":"Ann. Appl. Probab."},{"key":"9553_CR29","doi-asserted-by":"crossref","first-page":"1306","DOI":"10.1214\/105051604000000314","volume":"14","author":"\u0141 Kruk","year":"2004","unstructured":"Kruk, \u0141., Lehoczky, J.P., Shreve, S.E., Yeung, S.N.: Earliest-deadline-first service in heavy traffic acyclic networks. Ann. Appl. Probab. 14, 1306\u20131352 (2004)","journal-title":"Ann. Appl. Probab."},{"key":"9553_CR30","doi-asserted-by":"crossref","first-page":"1740","DOI":"10.1214\/009117906000000890","volume":"35","author":"\u0141 Kruk","year":"2007","unstructured":"Kruk, \u0141., Lehoczky, J.P., Ramanan, K., Shreve, S.E.: An explicit formula for the Skorokhod map on $$[0, a]$$ [ 0 , a ] . Ann. Probab. 35, 1740\u20131768 (2007)","journal-title":"Ann. Probab."},{"key":"9553_CR31","doi-asserted-by":"crossref","first-page":"484","DOI":"10.1214\/10-AAP681","volume":"21","author":"\u0141 Kruk","year":"2011","unstructured":"Kruk, \u0141., Lehoczky, J.P., Ramanan, K., Shreve, S.E.: Heavy traffic analysis for EDF queues with reneging. Ann. Appl. Probab. 21, 484\u2013545 (2011)","journal-title":"Ann. Appl. Probab."},{"issue":"1","key":"9553_CR32","first-page":"40","volume":"20","author":"CL Liu","year":"1973","unstructured":"Liu, C.L., Layland, J.W.: Scheduling algorithms for multiprogramming in a hard real-time environment. J. Assoc. Comput. Mach. 20(1), 40\u201361 (1973)","journal-title":"J. Assoc. Comput. Mach."},{"key":"9553_CR33","doi-asserted-by":"crossref","first-page":"809","DOI":"10.1214\/105051606000000907","volume":"17","author":"L Massouli\u00e9","year":"2007","unstructured":"Massouli\u00e9, L.: Structural properties of proportional fairness: stability and insensitivity. Ann. Appl. Probab. 17, 809\u2013839 (2007)","journal-title":"Ann. Appl. Probab."},{"key":"9553_CR34","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1023\/A:1019138827659","volume":"15","author":"L Massouli\u00e9","year":"2000","unstructured":"Massouli\u00e9, L., Roberts, J.: Bandwidth sharing and admission control for elastic traffic. Telecommun. Syst. 15, 185\u2013201 (2000)","journal-title":"Telecommun. Syst."},{"key":"9553_CR35","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1214\/aoap\/1177005204","volume":"4","author":"SP Meyn","year":"1994","unstructured":"Meyn, S.P., Tweedie, R.J.: State-dependent criteria for convergence of Markov chains. Ann. Appl. Probab. 4, 149\u2013168 (1994)","journal-title":"Ann. Appl. Probab."},{"key":"9553_CR36","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1109\/90.879343","volume":"8","author":"J Mo","year":"2000","unstructured":"Mo, J., Walrand, J.: Fair end-to-end window-based congestion control. IEEE\/ACM Trans. Netw. 8, 556\u2013567 (2000)","journal-title":"IEEE\/ACM Trans. Netw."},{"issue":"4","key":"9553_CR37","doi-asserted-by":"crossref","first-page":"496","DOI":"10.1016\/j.orl.2008.01.001","volume":"36","author":"P Moyal","year":"2008","unstructured":"Moyal, P.: Convex comparison of service disciplines in real time queues. Oper. Res. Lett. 36(4), 496\u2013499 (2008)","journal-title":"Oper. Res. Lett."},{"key":"9553_CR38","unstructured":"Panwar, S.S., Towsley, D.: On the optimality of the STE rule for multiple server queues that serve customers with deadlines. Technical Report 88-81, Department of Computer and Information Science, University Massachusetts, Amherst (1988)"},{"key":"9553_CR39","unstructured":"Panwar, S.S., Towsley, D.: Optimality of the stochastic earliest deadline policy for the G\/M\/c queue serving customers with deadlines. In: Second ORSA Telecommunications Conference. ORSA (Operations Research Society of America), Baltimore, MD (1992)"},{"key":"9553_CR40","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.peva.2005.07.008","volume":"62","author":"M Verloop","year":"2005","unstructured":"Verloop, M., Borst, S., N\u00fa\u00f1ez-Queija, R.: Stability of size-based scheduling disciplines in resource-sharing networks. Perform. Eval. 62, 247\u2013262 (2005)","journal-title":"Perform. Eval."},{"key":"9553_CR41","doi-asserted-by":"crossref","DOI":"10.1007\/b97479","volume-title":"Stochastic-Process Limits","author":"W Whitt","year":"2002","unstructured":"Whitt, W.: Stochastic-Process Limits. Springer, New York (2002)"},{"key":"9553_CR42","unstructured":"Yeung, S.N., Lehoczky, J.P.: Real-time queueing networks in heavy traffic with EDF and FIFO queue discipline. Preprint, Department of Statistics, Carnegie Mellon University (2001)"}],"container-title":["Queueing Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11134-017-9553-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11134-017-9553-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11134-017-9553-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,28]],"date-time":"2024-06-28T18:05:26Z","timestamp":1719597926000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11134-017-9553-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,11,16]]},"references-count":42,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2018,2]]}},"alternative-id":["9553"],"URL":"https:\/\/doi.org\/10.1007\/s11134-017-9553-y","relation":{},"ISSN":["0257-0130","1572-9443"],"issn-type":[{"value":"0257-0130","type":"print"},{"value":"1572-9443","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,11,16]]}}}