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1.12. Acknowledgment

      This work is partially supported by RFBR grant 17-01-00468.

1.13. References

      Afanaseva, L. (2019). Asymptotic analysis of queueing models based on synchronization method. Methodology and Computing in Applied Probability, 1–22, https://doi.org/10.1007/s11009-019-09694-9.

      Afanasyeva, L.G., Bashtova E.E. (2014). Coupling method for asymptotic analysis of queues with regenerative input and unreliable server. Queueing Systems, 76(2), 125–147.

      Afanasyeva, L., Bashtova, E., Bulinskaya, E. (2012). Limit theorems for semi-Markov queues and their applications. Communications in Statistics Part B: Simulation and Computation, 41(6), 688–709.

      Afanasyeva, L.G., Bulinskaya, E.V. (2009). Some problems for the flow of interacting particles. Modern Problems of Mathematics and Mechanics, 2, 55–68.

      Afanasyeva, L.G., Bulinskaya, E.V. (2010). Mathematical models of transport systems based on queueing systems methods. Proceedings of Moscow Institute of Physics and Technology, 2(4), 6–21.

      Afanasyeva, L.G., Bulinskaya, E.V. (2011). Stochastic models of transport flows. Commun. Stat. Theory Methods, 40(16), 2830–2846.

      Afanasyeva, L.G., Bulinskaya, E.V. (2013). Asymptotic analysis of traffic lights performance under heavy-traffic assumption. Methodology and Computing in Applied Probability, 15(4), 935–950.

      Afanasyeva, L.G., Mihaylova, I.V. (2015). Two models of the highway intersected by a crosswalk. Survey of Applied and Industrial Mathematics, 22(5), 520–532.

      Afanasyeva, L.G., Rudenko, I.V. (2012). GI|G|∞ queueing systems and their applications to the analysis of traffic models. Theory of Probability. Applications, 57(3), 427–452.

      Afanasyeva, L., Tkachenko, A. (2014). Multichannel queueing systems with regenerative input flow. Theory of Probability and Its Applications, 58(2), 174–192.

Afanasyeva, L., Tkachenko, A. (2016). Stability analysis of multi-server discrete-time queueing systems with interruptions and regenerative input flow. In New Trends in Stochastic Modeling and Data Analysis, Manca, R., McClean, S., Skiadas, C.H. (eds). ISAST: International Society for the Advancement of Science and Technology, Athens, 13–26.

      Afanasyeva, L., Tkachenko, A. (2018). Stability of discrete multi-server queueing systems with heterogeneous servers, interruptions and regenerative input flow. Reliability: Theory and Applications, 13(1), 63–75.

      Asmussen, S. (2003). Applied Probability and Queues. Springer-Verlag, New York.

      Avi-Itzhak, B., Naor, P. (1963). Some queueing problems with the service station subject to breakdown. Operations Research, 11(3), 303–320.

      Baycal-Gursoy, M., Xiao, W. (2004). Stochastic decomposition in M|M|∞ queues with Markov-modulated service rates. Queueing Systems, 48, 75–88.

      Baycal-Gursoy, M., Xiao, W., Ozbay, K. (2009). Modeling traffic flow interrupted by incidents. Eur. J. Oper. Res., 195, 127–138.

      Belorusov, T. (2012). Ergodicity of a multichannel queueing system with balking. Theory of Probability and Its Applications, 56(1), 120–126.

      Blank, M. (2003). Ergodic properties of a simple deterministic traffic flow model. J. Stat. Phys., 111, 903–930.

      Borovkov, A.A. (1976). Stochastic Processes in Queueing Theory. Springer-Verlag, New York.

      Caceres, F.C., Ferrari, P.A., Pechersky, E. (2007). A slow to start traffic model related to a M|M|1 queue. J. Stat. Mech. arXiv:cond-mat/0703709 v2 [cond-mat.statmech].

      Chen, H. (1995). Fluid approximation and stability of multiclass queueing networks: Work-conserving disciplines. Annals of Applied Probability, 5, 637–665.

      Chen, H., Yao, D. (2001). Fundamentals of Queueing Networks. Springer, New York.

      Chowdhury, D. (1999). Vehicular traffic: A system of interacting particles driven far from equilibrium. arXiv:arXiv:cond-mat/9910173 v1 [cond-mat.stat-mech].

      Dai, J. (1995). On positive Harris recurrence of multiclass queueing networks: A unified approach via fluid limit models. Annals of Applied Probability, 5, 49–77.

      Feller, W. (1971). An Introduction to Probability Theory and Its Applications, 2nd ed. John Wiley & Sons, New York.

      Fiems, D., Bruneel, H. (2013). Discrete-time queueing systems with Markovian preemptive vacations. Mathematical and Computer Modeling, 57(3-4), 782–792.

      Foss, S., Konstantopoulos, T. (2004). An overview on some stochastic stability methods. Journal of the Operations Research Society of Japan, 47(4), 275–303.

      Fuks, H., Boccara, N. (2001). Convergence to equilibrium in a class of interacting particle system evolving in discrete time. Phys. Rev. E., 64, 016117.

Gaver Jr., D. (1962). A waiting line with interrupted service, including priorities. Journal of the Royal Statistical Society. Series B (Methodological), 24, 73–90.

      Georgiadis, L., Szpankowski, W. (1992). Stability of token passing rings. Queueing Systems, 11, 7–33.

      Gideon, R., Pyke, R. (1999). Markov renewal modeling of Poisson traffic at intersections having separate turn lanes. In Semi-Markov Models and Applications, Janssen, J., Limneos, N. (eds). Springer, New York, NY, 285–310.

      Gillent, F., Latouche, G. (1983). Semi-explicit solution for M|PH|1 – like queueing systems. European Journal of Operational Research, 13(2), 151–160.

      Grandell, J. (1976). Double Stochastic Poisson Process, Lecture Notes in Mathematics, 529, Springer, Berlin.

      Greenshields, B.D. (1935). A study of highway capacity. Proc. Highway Res., 14, 448–477.

      Grinbeerg, H. (1959). An analysis of traffic flows. Oper. Res., 7, 79–85.

      Helbing, D. (2001). Traffic and related self-driven many-particle systems. Rev. Mod. Phys., 73, 1067–1141.

      Inose, H., Hamada, T. (1975). Road Traffic Control. University of Tokyo Press, Tokyo.

      Kiefer, J., Wolfowitz, J. (1955). On the theory of queues with many servers. Trans. Amer. Math. Soc., 78, 1–18.

      Krishnamoorthy, A., Pramod, P., Chakravarthy, S. (2012). Queues with interruptions: A survey. TOP, 1-31 doi:10.1007/s11750-012-0256-6.

      Loynes, R.M. (1962). The stability of a queue with non-independent inter-arrival and service times. Proc. Cambr. Phil. Soc., 58(3), 497–520.

      Maerivoet, S., de Moor, B. (2005). Cellular automata models of road traffic. Phys. Rep., 419, 1–64.

      Malyshev, V.A., Menshikov, M.V. (1982). Ergodicity continuity and analyticity of countable Markov chains. Trans Moscow Math, 1, 1–48.

      Meyn, S.P., Tweedie, R.L. (2009). Markov Chains and Stochastic Stability. Cambridge University Press, New York.

      Morozov, E. (2004). Weak regeneration in modeling of queueing processes. Queueing Systems, 46, 295–315.

      Morozov, E. (2007). A multiserver retrial queue: Regenerative stability analysis. Queueing Systems, 56(3-4), 157–168.

      Morozov, E., Dimitriou, I. (2017). Stability analysis of a multiclass retrial system with coupled orbit queues. In Computer Performance Engineering. EPEW 2017, Reinecke, P., Di Marco, A. (eds). Lecture Notes in Computer Science. Springer, Cham, 85–98.

Morozov, E., Fiems, D., Bruneel, H. (2011). Stability analysis of multiserver discrete-time queueing

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