An analytical model of a system with priorities servicing a mixture of different elastic traffic streams

• Autorzy: Nowak B. , Piechowiak M. , Stasiak M. , Zwierzykowski P.

Identyfikatory

DOI

10.24425/bpasts.2020.133111

• Języki publikacji: EN

Abstrakty

EN

This article proposes an analytical model of a system with priorities servicing a mixture of different elastic traffic streams. The model presented in the article was developed as the extension of earlier works published by the authors. It utilizes the concept of equivalent bandwidth and then, following bandwidth discretization, uses the dependencies introduced on the basis of the assumptions adopted for the generalized Kaufman-Roberts formula and for the model of a full-availability group with traffic compression. The article presents a possibility of using the proposed model to model the radio interface in a multi-service mobile network and provides an example of the above with the interface of an LTE network. Since the proposed model is an approximate one, the results of the calculations are compared with the results of simulations. A comparison of the results confirms an acceptable level of accuracy of the model. The model can be successfully used in the analysis and design of links and nodes of telecommunication and computer networks.

Słowa kluczowe

EN

teletraffic engineering; analytical model; priorities

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2020
• Tom: Vol. 68, nr 2
• Strony: 263--270
• Opis fizyczny: Bibliogr. 58 poz., rys., tab.

Twórcy

autor

Nowak B.

• Poznań University of Technology, ul. Polanka 3, Poland

autor

Piechowiak M.

• Kazimierz Wielki University, ul. Kopernika 1, 85-074 Bydgoszcz, Poland

autor

Stasiak M.

• Poznań University of Technology, ul. Polanka 3, Poland

autor

Zwierzykowski P.

• Poznań University of Technology, ul. Polanka 3, Poland

Bibliografia

• [1] K. Wesołowski, Mobile Communication Systems, John Wiley & Sons, 2002.
• [2] P. Zwierzykowski, Traffic menagement mechanisms in multiservice cellular networks, Poznan University of Technology, Poznań, 2014.
• [3] D. Parmenter, Key Performance Indicators: Developing, Implementing, and Using Winning KPIs, John Wiley & Sons, 2007.
• [4] M. Pióro, J. Lubacz, and U. Korner, “Traffic engineering problems in multiservice circuit switched networks”, in Proc. Traffic Theories for Telecommun. Services, 1990, 127–136.
• [5] H. Akimuru and K. Kawashima, Teletraffic: Theory and Application, Berlin-Heidelberg-New York, 1999.
• [6] J. Roberts, V. Mocci, and I. Virtamo, Broadband Network Teletraffic, Commission of the European Communities, Springer, Berlin, 1996.
• [7] K. Ross, Multiservice Loss Models for Broadband Telecommunication Network, Springer, London, 1995.
• [8] W. Bziuk, “Approximate state probabilities in large shared multirate loss systems with an application to trunk reservation”, Eur. Trans. Telecommun. 16(3), 145–152 (2002).
• [9] I. Moscholios, M. Logothetis and G. Kokkinakis, “Connection-dependent threshold model: a generalization of the Erlang multiple rate loss model”, Perform. Eval. 48(1-4), 177–200 (2002).
• [10] M. Janaszka and J. Lubacz, “Multirate traffic in dynamic synchronous transfer mode networks”, in Proc. 2nd Polish-German Teletraffic Symp. 2002, 133–146.
• [11] V. Iversen, Teletraffic Engineering Handbook, ITU-D, Study Group 2, Question 16/2, Geneva, 2005.
• [12] H.L. Hartmann and M. Knoke, “The one-level functional equation of multirate loss systems”, Eur. Trans. Telecommun. 14(2), 107–118 (2003).
• [13] V.G. Vassilakis, I.D. Moscholios, and M.D. Logothetis, “Call-level performance modelling of elastic and adaptive service-classes with finite population”, IEICE Trans. Commun. E91-B(1), 151–163 (2008).
• [14] Z. Dziong and J.W. Roberts, “Congestion probabilities in a circuit-switched integrated services network”, Perform. Eval. 7(4), 267–284 (1987).
• [15] D. Staehle and A. Mäder, “An analytic approximation of the up-link capacity in a UMTS network with heterogeneous traffic”, in Proc. 18th Int. Teletraffic Cong. 2003, 81–91.
• [16] V. Iversen, V. Bentis, N. Ha, and S. Stepanov, “Evaluation of multi-service CDMA networks with soft blocking”, in Proc. 16th. ITC Specialist Sem. on Perform. Eval. of Wireless and Mobile Syst. Antwerp, 2004.
• [17] A. Viterbi and A. Viterbi, “Erlang capacity of a power controlled CDMA system”, IEEE J. Sel. Areas Commun. 11(6), 892–900 (1993).
• [18] M. Głąbowski, M. Stasiak, A. Wiśniewski and P. Zwierzykowski, “Blocking probability calculation for cellular systems with WCDMA radio interface servicing PCT1 and PCT2 multirate traffic”, IEICE Trans. Commun. 92-B(4), 1156–1165 (2009).
• [19] G.A. Kallos, V.G. Vassilakis, I.D. Moscholios, and M.D. Logothetis, “Performance modelling of W-CDMA networks supporting elastic and adaptive traffic”, in Proc. 4th Int. Working Conf. on Perform. Modell. and Eval. of Heterogen. Net., Ilkley, 2006.
• [20] J. Juarez, R. Paulo, E. San Jose, and F. Velez, “Modelling and simulation of multi-rate multi-service traffic in the presence of mobility”, in Proc. Veh. Technol. Conf., 2006, 1–6.
• [21] V.G. Vassilakis, G.A. Kallos, I.D. Moscholios, and M.D. Logothetis, “The wireless engset multi-rate loss model for the call-level analysis of W-CDMS networks”, in Proc. 18th IEEE Ann. Int. Symp. on Pers. Indoor and Mobile Radio Commun., Athens, 2007, 1–5.
• [22] M. Sobieraj, M. Stasiak, J. Weissenberg, and P. Zwierzykowski, “Analytical model of the single threshold mechanism with hysteresis for multi-service networks”, IEICE Trans. Commun. 95-B(1), 120–132 (2012).
• [23] I. Moscholios and M. Logothetis, Efficient Multirate Teletraffic Loss Models Beyond Erlang, Wiley and IEEE Press, 2019.
• [24] J. Roberts, “Teletraffic models for the Telcom 1 integrated services network”, in Int. Teletraffic Cong. 1983, Session 1.1, paper 2, 1–7.
• [25] J. Roberts, Performance Evaluation and Design of Multiservice Networks, Commission of the European Communities, Brussels, 1992.
• [26] F. Kelly, “Effective bandwith at multi-class queues”, Queueing Syst. 9(1), 5–15 (1991).
• [27] D. Staehle, Analytic Methods for UMTS Radio Network Planning, PhD thesis, Bayerische Julius-Maximilians-Universitat Wurzburg, 2004.
• [28] M. Stasiak, M. Głąbowski, A. Wiśniewski, and P. Zwierzykowski, Modeling and dimensioning of mobile networks: from GSM to LTE, John Wiley & Sons, Chichester, West Sussex, 2011.
• [29] H. Holma and A. Toskala, WCDMA for UMTS. Radio Access For Third Generation Mobile Communications, John Wiley & Sons, Chichester, West Sussex, 2004.
• [30] M. Stasiak, P. Zwierzykowski, and M. Głąbowski, “High-Speed Downlink Packet Access (HSDPA) and High-Speed Uplink Packet Access (HSUPA) Cells: Teletraffic Engineering”, in Encyclopedia of Wireless and Mobile Commun., Taylor & Francis, London–New York, 2012, 552–568.
• [31] H. Holma and A. Toskala, LTE for UMTS: Evolution to LTE-Advanced, John Wiley & Sons, Chichester, West Sussex, 2011.
• [32] E. Dahlman, S. Parkvall and J. Skold, 4G, LTE-Advanced Pro and The Road to 5G, Academic Press, Inc., Orlando, FL, USA, 2016.
• [33] H. Holma and A. Toskala, HSDPA/HSUPA for UMTS: High Speed Radio Access for Mobile Communications, John Wiley & Sons, Chichester, West Sussex, 2006.
• [34] S. Hanczewski, M. Stasiak, and P. Zwierzykowski, “Modelling of the access part of a multi-service mobile network with service priorities”, J. Wireless Com. Network. 194 (2015).
• [35] M. Stasiak, P. Zwierzykowski, J. Wiewióra, and D. Parniewicz, “An Approximate Model of the WCDMA Interface Servicing a Mixture of Multi-rate Traffic Streams with Priorities”, in Comp. Perform. Eng., Vol. 5261, Springer, Spain, 2008, 168–180.
• [36] M. Stasiak, J. Wiewióra, and P. Zwierzykowski, “The analytical model of the WCDMA interface with priorities in the UMTS network”, in Proc. Int. Symp. Inf. Theory and its App., Auckland, New Zealand, 2008.
• [37] M. Stasiak, J. Wiewióra, and P. Zwierzykowski, “WCDMA interface in UMTS network carrying a mixture of multi-rate traffic with different priorities”, in Proc. Int. Conf. Telecomun., Marrakech, Maroco, 2009, 265–270.
• [38] M. Stasiak, J. Wiewióra, and P. Zwierzykowski, “Analytical model of the WCDMA radio interface in UMTS network with user differentiation”, in Proc. of 5th Adv. Int. Conf. Telecomun., Venice, Italy, 2009, 83–88.
• [39] J. Kołakowski and J. Cichocki, UMTS System telefonii komórkowej trzeciej generacji, Wydawnictwo Komunikacji i Łączności, Warszawa, 2003.
• [40] H. Holma and A. Toskala, WCDMA for UMTS: HSPA Evolution and LTE, John Wiley & Sons, New York, London, 2010.
• [41] M.S. Taqqu, W. Willinger, and R. Sherman, “Proof of a fundamental result in self-similar traffic modeling”, ACM Comp. Commun. Rev. 27(2), 5–23 (1997).
• [42] W. Willinger, V. Paxson, R.H. Riedi, and M.S. Taqqu, “Long-Range Dependence and Data Network Traffic”, in Theory and applications of long-range dependence, Brikhauser Boston and Springer Vertlag, Boston, USA, 2003, 373–406.
• [43] A. Chydzinski, “Transient analysis of the MMPP/G/1/K queue”, Telecommun. Syst. 32(4), 247–262 (2006).
• [44] B. Filipowicz and J. Kwiecień, “Queueing systems and networks. Models and applications”, Bull. Pol. Ac.: Tech. 56(4), 379–390 (2008).
• [45] W. Oniszczuk, “Loss tandem networks with blocking – a semi-markov approach”, Bull. Pol. Ac.: Tech. 58(4), 673–681 (2010).
• [46] O. Tikhonenko and M. Ziółkowski, “Single-server queueing system with external and internal customers”, Bull. Pol. Ac.: Tech. 66(4), 539–551 (2018).
• [47] O. Tikhonenko, M. Ziółkowski, and M. Kurkowski, “M/G/N/(0,V) Erlang queueing system with non-homogeneous customers non-identical servers and limited memory space", Bull. Pol. Ac.: Tech. 67(3), 489–500 (2019).
• [48] B. Ryu and S. Lowen, “Fractal traffic models for internet simulation”, in Proc. of the 5th IEEE Symp.Comp.Commun., Washington, DC, USA, IEEE Computer Society, 2000, 200–206.
• [49] T. Bonald and J. Virtamo, “A recursive formula for multirate systems with elastic traffic”, IEEE Commun. Lett. 9(8), 753–755 (2005).
• [50] T. Bonald and J. Roberts, “Internet and the Erlang formula”, SIGCOMM Comput. Commun. Rev. 42(1), 23–30 (2012).
• [51] F. Kelly, Notes on effective bandwidth, Technical report, University of Cambridge, 1996.
• [52] A.K. Erlang, “Løsning af nogle Problemer fra Sandsynlighedsregningen af Betydning for de automatiske Telefoncentraler”, Elektroteknikeren 13, 138-–155 (1917).
• [53] J. Kaufman, “Blocking in a shared resource environment”, IEEE Trans. Commun. 29(10), 1474–1481 (1981).
• [54] J. Roberts, “A service system with heterogeneous user requirements – application to multi-service telecommunications systems”, in Proc. of Perform. of Data Commun. Syst. and their App., Amsterdam, Elsevier Science Ltd., 1981, 423–431.
• [55] G. Stamatelos and V. Koukoulidis, “Reservation-based bandwidth allocation in a radio ATM network”, IEEE/ACM Trans. Netw. 5(3), 420–428 (1997).
• [56] M. Stasiak, “Queuing systems for the Internet”, IEICE Trans. Commun. 99-B(6), 1234–1242 (2016).
• [57] S. Hanczewski, M. Stasiak, and J. Weissenberg, “A queueing model of a multi-service system with state-dependent distribution of resources for each class of calls”, IEICE Trans. Commun. 97-B(8), 1592–1605 (2014).
• [58] L. Katzschner, “Loss sytstems with displacing priorities”, in Proc. 6th Int. Teletraffic Cong., Munchen, Germany (1970), paper 224II–224.

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).