Analytical and Scalable Analysis of Transient Tandem Markovian Finite Capacity Queueing Networks

References

• Balsamo S, de Nitto Personé V, Onvural R (2001) Analysis of Queueing Networks with Blocking, Internat. Series Oper. Res. Management Sci., Vol. 31 (Kluwer Academic Publishers, Boston).Crossref, Google Scholar
• Barceló J (2010) Fundamentals of Traffic Simulation, Internat. Series Oper. Res. Management Sci., Vol. 145 (Springer-Verlag, New York).Crossref, Google Scholar
• Brandwajn A, Jow Y (1988) An approximation method for tandem queues with blocking. Oper. Res. 36(1):73–83.Link, Google Scholar
• Chong L, Osorio C (2017) A simulation-based optimization algorithm for dynamic large-scale urban transportation problems. Transportation Sci.. ePub ahead of print July 19, http://dx.doi.org/10.1287/trsc.2016.0717.Link, Google Scholar
• Cohen JW (1982) Some variants of the single server queue. Cohen JW, ed. The Single Server Queue, Applied Math. Mechanics, Vol. 8 (North-Holland, Amsterdam).Google Scholar
• Coleman TF, Li Y (1994) On the convergence of reflective Newton methods for large-scale nonlinear minimization subject to bounds. Math. Programming 67(2):189–224.Crossref, Google Scholar
• Coleman TF, Li Y (1996) An interior, trust region approach for nonlinear minimization subject to bounds. SIAM J. Optim. 6(2):418–445.Crossref, Google Scholar
• Department of Transportation (2008) Transportation vision for 2030. Technical report, U.S. Department of Transportation (DOT), Research and Innovative Technology Administration, Washington, DC.Google Scholar
• Durrett R (1999) Essentials of Stochastic Processes, Springer Texts Statistics (Springer-Verlag, New York).Google Scholar
• Flötteröd G, Osorio C (2013) Approximation of time-dependent multi-dimensional queue-length distributions. Proc. Triennial Symp. Transportation Anal. (TRISTAN).Google Scholar
• Gayah VV, Gao XS, Nagle AS (2014) On the impacts of locally adaptive signal control on urban network stability and the macroscopic fundamental diagram. Transportation Res. Part B 70:255–268.Crossref, Google Scholar
• Gregoire J, Qian X, Frazzoli E, de La Fortelle A, Wongpiromsarn T (2015) Capacity-aware back-pressure traffic signal control. IEEE Trans. Control Networked Systems 2(2):164–173.Crossref, Google Scholar
• Griffiths JD, Leonenko GM, Williams JE (2008) Approximation to the transient solution of the M/Ek/1 queue. INFORMS J. Comput. 20(4):510–515.Link, Google Scholar
• Gupta S (2011) A framework to span airport delay estimates using transient queuing models. Technical report, Massachusetts Institute of Technology, Cambridge.Google Scholar
• He Q, Head KL, Ding J (2014) Multi-modal traffic signal control with priority, signal actuation and coordination. Transportation Res. Part C 46:65–82.Crossref, Google Scholar
• Heidemann D (1996) A queueing theory approach to speed-flow-density relationships. Proc. 13th Internat. Sympos. Transportation Traffic Theory, 103–118.Google Scholar
• Heidemann D (2001) A queueing theory model of nonstationary traffic flow. Transportation Sci. 35(4):405–412.Link, Google Scholar
• Hogg R, Tanis E (2006) Probability and Statistical Inference, 7th ed. (Pearson Education, Upper Saddle River, NJ).Google Scholar
• Kaczynski WH, Leemis LM, Drew JH (2012) Transient queueing analysis. INFORMS J. Comput. 24(1):10–28.Link, Google Scholar
• Larson R, Odoni A (1981) Urban Operations Research (Prentice-Hall, Englewood Cliffs, NJ).Google Scholar
• Li J (2005) Overlapping decomposition: A system-theoretic method for modeling and analysis of complex manufacturing systems. IEEE Trans. Automation Sci. Engrg. 2(1):40–53.Crossref, Google Scholar
• Lighthill M, Witham J (1955) On kinematic waves II. A theory of traffic flow on long crowded roads. Proc. Roy. Soc. London Series A 229:317–345.Crossref, Google Scholar
• Lin S (2011) Efficient model predictive control for large-scale urban traffic networks. Unpublished doctoral thesis, Delft University of Technology, Delft, Netherlands.Google Scholar
• Little JDC (1961) A proof for the queuing formula: L = λW. Oper. Res. 9(3):383–387.Link, Google Scholar
• Little JDC (2011) Little’s law as viewed on its 50th anniversary. Oper. Res. 59(3):536–549.Link, Google Scholar
• Mathworks (2011) Global optimization toolbox: User’s guide. User’s Guide Matlab version 2011b.Google Scholar
• McCalla C, Whitt W (2002) A time-dependent queueing-network model to describe the life-cycle dynamics of private-line telecommunication services. Telecommun. Systems 19(1):9–38.Crossref, Google Scholar
• Meier P (2007) Simulation d’un réseau de files d’attente à capacités finies. Technical report, ROSO Chair of Operations Research SO, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland.Google Scholar
• Morse P (1958) Queues, Inventories and Maintenance: The Analysis of Operational Systems with Variable Demand and Supply (Wiley, New York).Google Scholar
• Odoni AR, Roth E (1983) An empirical investigation of the transient behavior of stationary queueing systems. Oper. Res. 31(3): 432–455.Link, Google Scholar
• Osorio C (2010) Mitigating network congestion: Analytical models, optimization methods and their applications. Unpublished doctoral thesis, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland.Google Scholar
• Osorio C, Bierlaire M (2009) An analytic finite capacity queueing network model capturing the propagation of congestion and blocking. Eur. J. Oper. Res. 196(3):996–1007.Crossref, Google Scholar
• Osorio C, Bierlaire M (2013) A simulation-based optimization framework for urban transportation problems. Oper. Res. 61(6): 1333–1345.Link, Google Scholar
• Osorio C, Chong L (2015) A computationally efficient simulation-based optimization algorithm for large-scale urban transportation problems. Transportation Sci. 49(3):623–636.Link, Google Scholar
• Osorio C, Flötteröd G (2015) Capturing dependency among link boundaries in a stochastic network loading model. Transportation Sci. 49(2):420–431.Link, Google Scholar
• Osorio C, Nanduri K (2015) Energy-efficient urban traffic management: A microscopic simulation-based approach. Transportation Sci. 49(3):637–651.Link, Google Scholar
• Osorio C, Selvam K (2017) Simulation-based optimization: Achieving computational efficiency through the use of multiple simulators. Transportation Sci. 51(2):395–411.Link, Google Scholar
• Osorio C, Wang C (2017) On the analytical approximation of joint aggregate queue-length distributions for traffic networks: A stationary finite capacity Markovian network approach. Transportation Res. Part B 95:305–339.Crossref, Google Scholar
• Osorio C, Flötteröd G, Bierlaire M (2011) Dynamic network loading: A stochastic differentiable model that derives link state distributions. Transportation Res. Part B 45(9):1410–1423.Crossref, Google Scholar
• Osorio C, Chen X, Marsico M, Talas M, Gao J, Zhang S (2015) Reducing gridlock probabilities via simulation-based signal control. Transportation Res. Procedia, 4th Internat. Sympos. Transport Simulation (ISTS), Vol. 6, 101–110.Crossref, Google Scholar
• Peterson MD, Bertsimas DJ, Odoni AR (1995a) Decomposition algorithms for analyzing transient phenomena in multiclass queueing networks in air transportation. Oper. Res. 43(6):995–1011.Link, Google Scholar
• Peterson MD, Bertsimas DJ, Odoni AR (1995b) Models and algorithms for transient queueing congestion at airports. Management Sci. 41(8):1279–1295.Link, Google Scholar
• Reibman A (1991) A splitting technique for Markov chain transient solution. Stewart WJ, ed. Numerical Solution of Markov Chains (Marcel Dekker, New York), 373–400.Google Scholar
• Rice JA (1994) Mathematical Statistics and Data Analysis (Duxbury Press, Belmont, CA).Google Scholar
• Richards PI (1956) Shock waves on highways. Oper. Res. 4(1):42–51.Link, Google Scholar
• Schmidt LC, Jackman J (2000) Modeling recirculating conveyors with blocking. Eur. J. Oper. Res. 124(2):422–436.Crossref, Google Scholar
• Schweitzer P (1991) A survey of aggregation-disaggregation in large Markov chains. Stewart W, ed. Numerical Solutions of Markov Chains (Marcel Dekker, New York), 63–88.Google Scholar
• Schweitzer PJ (1984) Aggregation methods for large Markov chains. Iazeolla G, Courtois PJ, Hordijk A, eds. Mathematical Computer Performance and Reliability (North-Holland, Amsterdam), 275–286.Google Scholar
• Sharma OP, Gupta UC (1982) Transient behavior of an M/M/1/N queue. Stochastic Processes Their Appl. 13(3):327–331.Crossref, Google Scholar
• Sharma OP, Shobha B (1988) Transient behaviour of a double-channel Markovian queue with limited waiting space. Queueing Systems 3(1):89–96.Crossref, Google Scholar
• Stewart WJ (1994) Introduction to the Numerical Solution of Markov Chains (Princeton University Press, Princeton, NJ).Google Scholar
• Stewart WJ (2009) Probability, Markov Chains, Queues, and Simulation (Princeton University Press, Princeton, NJ).Google Scholar
• Texas Transportation Institute (2012) 2012 Urban mobility report. Technical report, Texas Transportation Institute (TTI), Texas A&M University System, College Station.Google Scholar
• Transport for London (2010) Traffic modelling guidelines. Version 3.0. Technical report, Transport for London (TfL), London.Google Scholar
• TSS (2011) AIMSUN 6.1 Microsimulator Users Manual. Transport Simulation Systems.Google Scholar
• Van Woensel T, Vandaele N (2007) Modelling traffic flows with queueing models: A review. Asia-Pacific J. Oper. Res. 24(4):1–27.Crossref, Google Scholar
• Varaiya P (2013) Max pressure control of a network of signalized intersections. Transportation Res. Part C 36:177–195.Crossref, Google Scholar
• VSS (1992) Norme Suisse SN 640837 Installations de feux de circulation; temps transitoires et temps minimaux. Union des professionnels suisses de la route, VSS, Zurich.Google Scholar
• Whitt W (1999) Decomposition approximations for time-dependent Markovian queueing networks. Oper. Res. Lett. 24(3):97–103.Crossref, Google Scholar
• Yamani JH (2013) Approximation of the transient joint queue-length distribution in tandem networks. Unpublished Master’s thesis, Massachusetts Institute of Technology, Cambridge.Google Scholar
• Zhang L, Wang C, Arinez J, Biller S (2013) Transient analysis of Bernoulli serial lines: Performance evaluation and system-theoretic properties. IIE Trans. 45(5):528–543.Crossref, Google Scholar