Queues with Server Vacations as a Model for Pretimed Signalized Urban Traffic

References

• Akçelik R (1980) Time-dependent expressions for delay, stop rate and queue length at traffic signals. Internal Report AIR 367-1, Australian Road Research Board, Melbourne, Australia.Google Scholar
• Akçelik R (2002) aaSIDRA users’ manual. ARRB Transport Research Ltd., Victoria, Australia.Google Scholar
• Alfa AS, Neuts MF (1995) Modelling vehicular traffic using the discrete time Markovian arrival process. Transportation Sci. 29(2):109–117.Link, Google Scholar
• Brockfeld E, Wagner P (2006) Validating microscopic traffic flow models. Proc. 9th IEEE Intelligent Transportation Systems Conf. (IEEE, Piscataway, NJ), 1604–1608.Crossref, Google Scholar
• Cheng C, Du Y, Sun L, Ji Y (2016) Review on theoretical delay estimation model for signalized intersections. Transport Rev. 36(4):479–499.Crossref, Google Scholar
• Daganzo C (1995) The cell transmission model, part II: Network traffic. Transportation Res. Part B 29(2):79–93.Crossref, Google Scholar
• Dion F, Rakha H, Kang YS (2004) Comparison of delay estimates at under-saturated and over-saturated pre-timed signalized intersections. Transportation Res. Part B 38(2):99–122.Crossref, Google Scholar
• Doshi BT (1986) Queueing systems with vacations—A survey. Queueing Systems 1(1):29–66.Crossref, Google Scholar
• El-Taha M, Stidham S Jr (1999) Sample-Path Analysis of Queueing Systems (Kluwer Academic Publishers, Norwell, MA).Crossref, Google Scholar
• Fu L, Hellinga B (2000) Delay variability at signalized intersections. Transportation Res. Record 1710:215–221.Crossref, Google Scholar
• Heidemann D (1994) Queue length and delay distributions at traffic signals. Transportation Res. Part B 28(5):377–389.Crossref, Google Scholar
• Hu XN, Tang LC, Ong HL (1997) A M/DX/1 vacation queue model for signalized intersection. Comput. Indust. Engrg. 33(3–4):801–804.Crossref, Google Scholar
• Kulkarni VG (1995) Modeling and Analysis of Stochastic Systems (Chapman & Hall, London).Google Scholar
• Kwiatkowska M, Norman G, Pacheco A (2006) Model checking expected time and expected reward formulae with random time bounds. Comput. Math. Appl. 51(2):305–316.Crossref, Google Scholar
• Latouche G (1994) Newton’s iteration for non-linear equations in Markov chains. IMA J. Numer. Anal. 14:583–598.Crossref, Google Scholar
• McNeil DR, Weiss GH (1974) Delay problems for isolated intersections. Gazis DC, ed. Traffic Science (Wiley, New York), 109–174.Google Scholar
• Miller AJ (1968) Australian road capacity guide; provisional introduction and signalized intersections. Bulletin 4, Australian Road Research Board, Sydney, Australia.Google Scholar
• Neuts MF (1989) Structured Stochastic Matrices of M/G/1 Type and Their Applications (Marcel Dekker, New York).Google Scholar
• Newell GF (1965) Approximation methods for queues with applications to the fixed-cycle traffic light. SIAM Rev. 7:223–240.Crossref, Google Scholar
• Ohno K (1978) Computational algorithm for a fixed-cycle traffic light problem for compound Poisson arrivals. Transportation Sci. 12(1):29–47.Link, Google Scholar
• Olszewski PS (1994) Modeling probability distribution of delay at signalized intersections. J. Advanced Transportation 28(3):253–274.Crossref, Google Scholar
• Osorio C, Flotterod G (2015) Capturing dependency among link boundaries in a stochastic dynamic network loading model. Transportation Sci. 49(2):420–431.Link, Google Scholar
• Osorio C, Flotterod G, Bierlaire M (2011) Dynamic network loading: A stochastic differentiable model that derives link state distributions. Transportation Res. Part B 45:1410–1423.Crossref, Google Scholar
• Pandwai S, Dia H (2005) Comparative evaluation of microscopic car-following behavior. IEEE Trans. Intelligent Transportation System 6(3):314–325.Crossref, Google Scholar
• Ramaswami V (1988) A stable recursion for the steady state vector in Markov chains of M/G/1 type. Comm. Statist.—Stochastic Models 4(1):183–188.Crossref, Google Scholar
• Rorbech J (1968) Determining the length of the approach lanes required at signal-controlled intersections on through highways. Transportation Res. 2(3):283–291.Crossref, Google Scholar
• Rouphail N, Tarko A, Li J (1996) Traffic flow at signalized intersections. Traffic Flow Theory (U.S. Department of Transportation, Washington, DC), 9-1–9-32.Google Scholar
• Schellhaas H (1990) On Ramaswami’s algorithm for the computation of the steady state vector in Markov chains of M/G/1-type. Comm. Statist.—Stochastic Models 6(3):541–550.Crossref, Google Scholar
• Simões L, Milheiro-Oliveira P, Pires da Costa A (2010) Modeling and simulation of traffic movements at semi-actuated signalized intersections. J. Transportation Engrg. 136(6):554–564.Crossref, Google Scholar
• Stephanopoulos G, Michalopoulos PG (1979) Modelling and analysis of traffic queue dynamics at signalized intersections. Transportation Res. Part A 13:295–307.Crossref, Google Scholar
• Sumalee A, Zhong RX, Pan TL, Szeto WY (2011) Stochastic cell transmission model (SCTM): A stochastic dynamic traffic model for traffic state surveillance and assignment. Transportation Res. Part B 45(3):507–533.Crossref, Google Scholar
• Sun B, Wu N, Ge YE, Kim T, Zhang HM (2016) A new car-following model considering acceleration of lead vehicle. Transport 31(1):1–10.Crossref, Google Scholar
• Transportation Research Board (2010) Highway Capacity Manual (Transportation Research Board, National Research Council, Washington, DC).Google Scholar
• van den Broek MS, van Leeuwaarden JSH, Adan IJBF, Boxma OJ (2006) Bounds and approximations for the fixed-cycle traffic-light queue. Transportation Sci. 40(4):484–496.Link, Google Scholar
• van Leeuwaarden JSH (2006) Delay analysis for the fixed-cycle traffic-light queue. Transportation Sci. 40(2):189–199.Link, 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
• Viti F (2006) The dynamics and the uncertainty of delays at signals. Doctoral thesis, TRAIL thesis series, Delft University of Technology, Delft, Netherlands.Google Scholar
• Viti F, van Zuylen HJ (2010) Probabilistic models for queues at fixed control signals. Transportation Res. Part B 44(1):120–135.Crossref, Google Scholar
• Webster FV (1958) Traffic signal settings. Road Research Technical Papers, Number 39, Road Research Laboratory, H.M. Stationery Office, London.Google Scholar
• Zhong RX, Sumalee A, Pan TL, Lam WHK (2013) Stochastic cell transmission model for traffic network with demand and supply uncertainties. Transportmetrica A: Transport Sci. 9(7):567–602.Crossref, Google Scholar