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Cohen, \u201cThe multiple phase service network with generalized processor sharing,\u201d Acta Informatica, vol.12, no.3, pp.245-284, 1979.","DOI":"10.1007\/BF00264581"},{"key":"3","unstructured":"[3] K. Lindberger, \u201cBalancing quality of service, pricing and utilisation in multiservice networks with stream and elastic traffic,\u201d Proc. 16th International Teletraffic Congress, Edinburgh, pp.1127-1136, UK, 1999."},{"key":"4","doi-asserted-by":"crossref","unstructured":"[4] N. Dukkipati, M. Kobayashi, R. Zhang-Shen, and N. McKeown, \u201cProcessor sharing flows in the Internet,\u201d Quality of Service \u2014 IWQoS 2005, Lecture Notes in Computer Science, vol.3552, pp.271-285, Springer Berlin Heidelberg, Berlin, Heidelberg, 2005.","DOI":"10.1007\/11499169_22"},{"key":"5","unstructured":"[5] IETF, \u201cRFC 793: Transmission control protocol,\u201d 1981, edited by Jon Postel. [Online]. Available: https:\/\/tools.ietf.org\/html\/rfc793"},{"key":"6","doi-asserted-by":"crossref","unstructured":"[6] T. Bonald and J.W. Roberts, \u201cInternet and the Erlang formula,\u201d SIGCOMM Comput. Commun. Rev., vol.42, no.1, pp.23-30, Jan. 2012.","DOI":"10.1145\/2096149.2096153"},{"key":"7","unstructured":"[7] J. Bertsekas and R.G. Gallager, Data Networks, 2nd ed., Prentice Hall, 1992."},{"key":"8","doi-asserted-by":"crossref","unstructured":"[8] F. Kelly, \u201cMathematical modelling of the internet,\u201d in Mathematics Unlimited \u2014 2001 and Beyond, B. Engquist and W. Schmid, Eds., pp.685-702, Springer, 2001.","DOI":"10.1007\/978-3-642-56478-9_6"},{"key":"9","doi-asserted-by":"crossref","unstructured":"[9] T. Bonald, L. Massouli\u00e9, A. Prouti\u00e8re, and J. Virtamo, \u201cA queueing analysis of max-min fairness, proportional fairness and balanced fairness,\u201d Queueing Syst., vol.53, no.1-2, pp.65-84, 2006.","DOI":"10.1007\/s11134-006-7587-7"},{"key":"10","doi-asserted-by":"crossref","unstructured":"[10] J. Kaufman, \u201cBlocking in a shared resource environment,\u201d IEEE Trans. Commun., vol.29, no.10, pp.1474-1481, 1981.","DOI":"10.1109\/TCOM.1981.1094894"},{"key":"11","unstructured":"[11] J. Roberts, \u201cA service system with heterogeneous user requirements \u2014 Application to multi-service telecommunications systems,\u201d Proc. Performance of Data Communications Systems and their Applications, G. Pujolle, Ed., pp.423-431, 1981."},{"key":"12","doi-asserted-by":"crossref","unstructured":"[12] G.M. Stamatelos and V.N. Koukoulidis, \u201cReservation-based bandwidth allocation in a radio ATM network,\u201d IEEE\/ACM Trans. Netw., vol.5, no.3, pp.420-428, June 1997.","DOI":"10.1109\/90.611106"},{"key":"13","doi-asserted-by":"crossref","unstructured":"[13] T. Bonald and J. Virtamo, \u201cA recursive formula for multirate systems with elastic traffic,\u201d IEEE Commun. Lett., vol.9, no.8, pp.753-755, 2005.","DOI":"10.1109\/LCOMM.2005.1496605"},{"key":"14","doi-asserted-by":"crossref","unstructured":"[14] J.-P. Haddad and R.R. Mazumdar, \u201cCongestion in large balanced multirate networks,\u201d Queueing Syst., vol.74, no.2-3, pp.333-368, 2013.","DOI":"10.1007\/s11134-012-9322-x"},{"key":"15","doi-asserted-by":"crossref","unstructured":"[15] S. Hanczewski, M. Stasiak, and J. Weissenberg, \u201cThe queueing model of a multiservice system with dynamic resource sharing for each class of calls,\u201d Computer Networks, Communications in Computer and Information Science, vol.370, pp.436-445, Springer Berlin Heidelberg, Berlin, Heidelberg, 2013.","DOI":"10.1007\/978-3-642-38865-1_44"},{"key":"16","doi-asserted-by":"crossref","unstructured":"[16] S. Hanczewski, M. Stasiak, and J. Weissenberg, \u201cA queueing model of a multi-service system with state-dependent distribution of resources for each class of calls,\u201d IEICE Trans. Commun., vol.E97-B, no.8, pp.1592-1605, Aug. 2014.","DOI":"10.1587\/transcom.E97.B.1592"},{"key":"17","unstructured":"[17] S. Hanczewski, D. Kmiecik, M. Stasiak, and J. Weissenberg, \u201cMultiservice queuing system with elastic traffic,\u201d Proc. IEICE Gen. Conf., 2016, BS-3-18, March 2016."},{"key":"18","doi-asserted-by":"crossref","unstructured":"[18] V. Paxson and S. Floyd, \u201cWide area traffic: The failure of Poisson modeling,\u201d IEEE\/ACM Trans. Netw., vol.3, no.3, pp.226-244, June 1995.","DOI":"10.1109\/90.392383"},{"key":"19","doi-asserted-by":"crossref","unstructured":"[19] J.Y. Hui, \u201cResource allocation for broadband networks,\u201d IEEE J. Sel. Areas. Commun., vol.6, no.9, pp.1598-1608, Dec. 1988.","DOI":"10.1109\/49.12887"},{"key":"20","unstructured":"[20] F. Kelly, \u201cNotes on effective bandwidth,\u201d Tech. Rep., University of Cambridge, 1996."},{"key":"21","doi-asserted-by":"crossref","unstructured":"[21] J. Roberts, V. Mocci, and I. Virtamo, Eds., Broadband Network Teletraffic, Final Report of Action COST 242, Commission of the European Communities, Springer, Berlin, 1996.","DOI":"10.1007\/3-540-61815-5"},{"key":"22","doi-asserted-by":"crossref","unstructured":"[22] R. Guerin, H. Ahmadi, and M. Naghshineh, \u201cEquivalent capacity and its application to bandwidth allocation in high-speed networks,\u201d IEEE J. Sel. Areas. Commun., vol.9, no.7, pp.968-981, Sept. 1991.","DOI":"10.1109\/49.103545"},{"key":"23","doi-asserted-by":"crossref","unstructured":"[23] I. Norros, \u201cOn the use of fractional Brownian motion in the theory of connectionless networks,\u201d IEEE J. Sel. Areas. Commun., vol.13, no.6, pp.953-962, Aug. 1995.","DOI":"10.1109\/49.400651"},{"key":"24","doi-asserted-by":"crossref","unstructured":"[24] A. Pras, L. Nieuwenhuis, R. van de Meent, and M. Mandjes, \u201cDimensioning network links: A new look at equivalent bandwidth,\u201d IEEE Netw., vol.23, no.2, pp.5-10, March 2009.","DOI":"10.1109\/MNET.2009.4804330"},{"key":"25","unstructured":"[25] A. Erlang, \u201cSolution of some problems in the theory of probabilities of significance in automatic telephone exchanges,\u201d Elektrotechnikeren, vol.13, p.5, 1917."},{"key":"26","doi-asserted-by":"crossref","unstructured":"[26] L. Gimpelson, \u201cAnalysis of mixtures of wide- and narrow-band traffic,\u201d IEEE Trans. Commun., vol.13, no.3, pp.258-266, Sept. 1965.","DOI":"10.1109\/TCOM.1965.1089121"},{"key":"27","doi-asserted-by":"crossref","unstructured":"[27] J. Aein, \u201cA multi-user-class, blocked-calls-cleared, demand access model,\u201d IEEE Trans. Commun., vol.26, no.3, pp.378-385, March 1978.","DOI":"10.1109\/TCOM.1978.1094081"},{"key":"28","unstructured":"[28] H. Inose, An Introduction to Digital Integrated Communications Systems, University of Tokyo Press, Tokyo, 1979."},{"key":"29","unstructured":"[29] V. Iversen, \u201cThe exact evaluation of multi-service loss system with access control,\u201d Seventh Nordic Teletraffic Seminar, pp.56-61, Lund, Aug. 1987."},{"key":"30","unstructured":"[30] A. Nilson and M. Perry, \u201cProvisioning models for digital loop carriers,\u201d Proc. 13th International Teletraffic Congress, vol. Discussion Circle, pp.271-276, Copenhagen, 1991."},{"key":"31","doi-asserted-by":"crossref","unstructured":"[31] K.W. Ross, Multiservice Loss Models for Broadband Telecommunication Networks, Springer London, London, 1995.","DOI":"10.1007\/978-1-4471-2126-8"},{"key":"32","doi-asserted-by":"crossref","unstructured":"[32] L. Delbrouck, \u201cOn the steady-state distribution in a service facility carrying mixtures of traffic with different peakedness factors and capacity requirements,\u201d IEEE Trans. Commun., vol.31, no.11, pp.1209-1211, 1983.","DOI":"10.1109\/TCOM.1983.1095768"},{"key":"33","doi-asserted-by":"crossref","unstructured":"[33] E.A. van Doorn and F.J.M. Panken, \u201cBlocking probabilities in a loss system with arrivals in geometrically distributed batches and heterogeneous service requirements,\u201d IEEE\/ACM Trans. Netw., vol.1, no.6, pp.664-667, 1993.","DOI":"10.1109\/90.266054"},{"key":"34","doi-asserted-by":"crossref","unstructured":"[34] J.S. Kaufman and K.M. Rege, \u201cBlocking in a shared resource environment with batched Poisson arrival processes,\u201d Perform. Evaluation, vol.24, no.4, pp.249-263, 1996.","DOI":"10.1016\/0166-5316(94)00029-8"},{"key":"35","doi-asserted-by":"crossref","unstructured":"[35] M. G\u0142\u0105bowski, \u201cModelling of state-dependent multirate systems carrying BPP traffic,\u201d Ann. Telecommun., vol.63, no.7-8, pp.393-407, 2008.","DOI":"10.1007\/s12243-008-0034-5"},{"key":"36","doi-asserted-by":"crossref","unstructured":"[36] M. G\u0142\u0105bowski, M. Stasiak, and J. Weissenberg, \u201cProperties of recurrent equations for the full-availability group with BPP traffic,\u201d Math. Probl. Eng., vol.2012, pp.1-17, 2012.","DOI":"10.1155\/2012\/547909"},{"key":"37","doi-asserted-by":"crossref","unstructured":"[37] S. R\u00e1cz, B.P. Ger\u00f6, and G. Fodor, \u201cFlow level performance analysis of a multi-service system supporting elastic and adaptive services,\u201d Perform. Evaluation, vol.49, no.1-4, pp.451-469, 2002.","DOI":"10.1016\/S0166-5316(02)00115-3"},{"key":"38","doi-asserted-by":"crossref","unstructured":"[38] G. Fodor and M. Telek, \u201cBounding the blocking probabilities in multirate CDMA networks supporting elastic services,\u201d IEEE\/ACM Trans. Netw., vol.15, no.4, pp.944-956, Aug. 2007.","DOI":"10.1109\/TNET.2007.893880"},{"key":"39","doi-asserted-by":"crossref","unstructured":"[39] V.G. Vassilakis, I.D. Moscholios, and M.D. Logothetis, \u201cCall-level performance modelling of elastic and adaptive service-classes with finite population,\u201d IEICE Trans. Commun., vol.E91-B, no.1, pp.151-163, Jan. 2008.","DOI":"10.1093\/ietcom\/e91-b.1.151"},{"key":"40","doi-asserted-by":"crossref","unstructured":"[40] I. Moscholios, J. Vardakas, M. Logothetis, and A. Boucouvalas, \u201cCongestion probabilities in a batched Poisson multirate loss model supporting elastic and adaptive traffic,\u201d Ann. 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