Abstract
Software-Defined Networks (SDN) dynamically modify the paths of Internet flows in response to the quality of service or security needs, and hence frequently modify traffic levels at network routers. Thus network routers often operate in the transient regime, rather than at steady-state, with significant impact on packet loss probabilities and delay. We, therefore, investigate the time-dependent performance of a small network of routers, modelled as G/G/1/N queueing stations. A diffusion approximation is developed to predict the quality of service of the routers in the transient regime. Numerical examples show that the results in the transient regime can differ very significantly from the steady-state results, and therefore that the transient analysis must be taken into account in evaluating the performance of routers in a SDN network.
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References
Kleinrock, L.: Queueing Systems, Vol. 1: Theory. Wiley, Hoboken (1975)
Kleinrock, L.: Queueing Systems, Vol. 2: Computer Applications. Wiley, Hoboken (1976)
Toral-Cruz, H., Pathan, A.S.K., Pacheco, J.C.R.: Accurate modeling of VoIP traffic QoS parameters in current and future networks with multifractal and Markov models. Math. Comput. Model. 57(11–12), 2832–2845 (2013)
Buyya, R., et al.: A manifesto for future generation cloud computing: research directions for the next decade. ACM Comput. Surv. (CSUR) 51(5), 1–38 (2019)
McKeown, N., et al.: Openflow: enabling innovation in campus networks. ACM SIGCOMM Comput. Commun. Rev. 38(2), 69–74 (2008)
Tuncer, D., Charalambides, M., Clayman, S., Pavlou, G.: Adaptive resource management and control in software defined networks. IEEE Trans. Netw. Serv. Manag. 12(1), 18–33 (2015)
Xia, W., Wen, Y., Foh, C.H., Niyato, D., Xie, H.: A survey on software-defined networking. IEEE Commun. Surv. Tutor. 17(1), 27–51 (2015)
Gelenbe, E.: On approximate computer systems models. J. ACM 22(2), 261–269 (1975)
Kurtz, T.G.: Limit theorems for sequences of jump Markov processes approximating ordinary differential processes. J. Appl. Probab. 8(2), 344–356 (1971)
Fidler, M.: Survey of deterministic and stochastic service curve models in the network calculus. IEEE Commun. Surv. Tutor. 12(1), 59–86 (2010)
Fidler, M., Rizk, A.: A guide to the stochastic network calculus. IEEE Commun. Surv. Tutor. 17(1), 92–105 (2015)
Mahmood, K., Chilwan, A., Osterbo, O., Jarschel, M.: Modelling of OpenFlow-based software-defined networks: the multiple node case. Inst. Eng. Technol. J. 4(5), 278–284 (2015)
Ansell, J., Seah, W.K.G., Ng, B., Marshall, S.: Making queueing theory more palatable to SDN/OpenFlow-based network practitioners. In: Proceeding of the 2016 IEEE/IFIP Network Operations and Management Symposium, Istanbul, Turkey, pp. 1119–1124. IEEE (2016)
Singh, D., Ng, B., Lai, Y.-C., Lin, Y.-D., Seah, W.K.G.: Modelling software-defined networking: software and hardware switches. J. Comput. Netw. Comput. Appl. 122, 24–36 (2018)
Lai, Y.-C., Ali, A., Hassan, M., Hossain, S., Lin, Y.-D.: Performance modeling and analysis of TCP connections over software defined networks. In: Proceeding of the 2017 IEEE Global Communications Conference, Singapore, pp. 1–6. IEEE (2017)
Fahmin, A., Lai, Y.-C., Hossain, S., Lin, Y.-D., Saha, D.: Performance modeling of SDN with NFV under or aside the controller. In: Proceeding of the 5th International Conference on Future Internet of Things and Cloud Workshops, Prague, pp. 211–216. IEEE (2017)
Miao, W., Min, G., Wu, Y., Wang, H., Hu, J.: Performance modelling and analysis of software defined networking under bursty multimedia traffic. ACM Trans. Multimedia Comput. Commun. Appl. 12(55), 24–36 (2018)
Azodolmolky, S., Wieder, P., Yahyapour, R.: Performance evaluation of a scalable software-defined networking deployment. In: Proceeding of the 2013 Second European Workshop on Software Defined Networks, Berlin, Germany, pp. 68–74. IEEE (2013)
Azodolmolky, S., Nejabati, R., Pazouki, M., Wieder, P., Yahyapour, R., Simeonidou, D.: An analytical model for software defined networking: a network calculus-based approach. In: Proceeding of the IEEE Global Communications Conference, Atlanta, USA, pp. 1397–1402. IEEE (2013)
Czachórski, T., Gelenbe, E., Kuaban, G.S., Marek, D.: Transient behaviour of a network router, accepted. In: Herencsár, N., Benedetto, F., Hosek, J. (eds.) Proceedings of International Conference on Telecommunications and Signal Processing TSP 2020, Milano. IEEE (2020)
Czachórski, T., Pekergin, F.: Diffusion approximation as a modelling tool. In: Kouvatsos, D.D. (ed.) Network Performance Engineering. LNCS, vol. 5233, pp. 447–476. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-02742-0_20
Lee, S.K., Bae, M., Kim, H.: Future of IoT networks: a survey. Appl. Sci. 7(10), 1072 (2017)
Gelenbe, E., Domanska, J., Frohlich, P., Nowak, M., Nowak, S.: Self-aware networks that optimize security, QoS and energy. Proc. IEEE 108(7) (2020, accepted for publication)
Gelenbe, E.: Energy packet networks: adaptive energy management for the cloud. In: CloudCP 2012: Proceedings of the 2nd International Workshop on Cloud Computing Platforms, pp. 1–5. ACM (2012). https://doi.org/10.1145/2168697.2168698
Dobson, S., et al.: A survey of autonomic communications. ACM Trans. Auton. Adapt. Syst. (TAAS) 1(2), 223–259 (2006)
Gelenbe, E., Liu, P., Lainé, J.: Genetic algorithms for route discovery. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 36(6), 1247–1254 (2006)
Francois, F., Gelenbe, E.: Towards a cognitive routing engine for software defined networks. In: Proceeding of the 2016 IEEE International Conference on Communications, Kuala Lumpur, pp. 1–6. IEEE (2016)
Goto, Y., Ng, B., Seah, W.K.G., Takahashi, Y.: Queueing analysis of software defined network with realistic openflow-based switch model. Comput. Netw. 164, 106892 (2019)
Sood, K., Yi, S., Xiang, Y.: Performance analysis of software-defined network router using M/Geo/1. IEEE Commun. Lett. 20(12), 27–51 (2016)
Bozakov, Z., Rizk, A.: Taming SDN controllers in heterogeneous hardware environments. In: Proceeding of the 2013 Second European Workshop on Software Defined Networks, Berlin, Germany, pp. 50–55. IEEE (2013)
Bisnik, N., Abouzeid, A.A.: Queuing network models for delay analysis of multihop wireless ad hoc networks. Ad Hoc Netw. 7(1), 79–97 (2009)
Gelenbe, E., Pujolle, G.: The behaviour of a single-queue in a general queueing network. Acta Informatica 7, 123–136 (1976). https://doi.org/10.1007/BF00265766
Gelenbe, E.: Probabilistic models of computer systems part ii: Diffusion approximations, waiting times and batch arrivals. Acta Informatica 12, 285–303 (1979). https://doi.org/10.1007/BF00268317
Marin, G.A., Mang, X., Gelenbe, E., Önvural, R.O.: Statistical call admission control. US Patent 6,222,824 (2001)
Domański, A., Domańska, J., Czachórski, T., Klamka, J., Szygula, J., Marek, D.: Diffusion approximation model of TCP NewReno congestion control mechanism. SN Comput. Sci. 1, 43 (2020)
Czachórski, T.: A method to solve diffusion equation with instantaneous return processes acting as boundary conditions. Bull. Polish Acad. Sci. Tech. Sci. 41(4), 417–451 (1993)
Cox, R.P., Miller, H.D.: The Theory of Stochastic Processes. Chapman and Hall, London (1965)
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This research was supported by the SerIoT Research and Innovation Action, funded by the European Commission (EC) under the H2020-IOT-2017 Program, Grant Agreement 780139. The EC’s support does not constitute an endorsement of this paper, which reflects the views only of the authors.
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Czachórski, T., Gelenbe, E., Marek, D. (2021). Software Defined Network Dynamics via Diffusions. In: Calzarossa, M.C., Gelenbe, E., Grochla, K., Lent, R., Czachórski, T. (eds) Modelling, Analysis, and Simulation of Computer and Telecommunication Systems. MASCOTS 2020. Lecture Notes in Computer Science(), vol 12527. Springer, Cham. https://doi.org/10.1007/978-3-030-68110-4_2
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