Skip to main content
SpringerLink
Log in

Complex Dynamics of Bus, Tram, and Elevator Delays in Transportation Systems

  • Reference work entry
  • First Online:
Complex Dynamics of Traffic Management

Part of the book series: Encyclopedia of Complexity and Systems Science Series ((ECSSS))

  • Originally published in
  • R. A. Meyers (ed.), Encyclopedia of Complexity and Systems Science, © Springer Science+Business Media LLC 2017

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 279.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 379.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Bibliography

Primary Literature

  • Chowdhury D, Desai RC (2000) Steady-states and kinetics of ordering in bus-route models: connection with the Nagel-Schreckenberg model. Eur Phys J B 15:375–384

    Article  Google Scholar 

  • Dong C, Ma X, Wang B, Sun X (2010) Effects of prediction feedback in multi-route intelligent traffic systems. Phys A 389:3274–3281

    Article  Google Scholar 

  • Gupta AK, Sharma S, Redhu P (2015) Effect of multi-phase optimal velocity function on jamming transition in a lattice hydrodynamic model with passing. Nonlinear Dyn 80:1091–1108

    Article  Google Scholar 

  • He DR, Yeh WJ, Kao YH (1985) Studies of return maps, chaos, and phase-locked states in a current-driven Josephson-junction simulator. Phys Rev B 31:1359–1373

    Article  Google Scholar 

  • Hino Y, Nagatani T (2014) Effect of bottleneck on route choice in two-route traffic system with real-time information. Phys A 395:425–433

    Article  Google Scholar 

  • Hino Y, Nagatani T (2015) Asymmetric effect of route-length difference and bottleneck on route choice in two-route traffic system. Phys A 428:416–425

    Article  Google Scholar 

  • Huijberts HJC (2002) Analysis of a continuous car-following model for a bus route: existence, stability and bifurcations of synchronous motions. Phys A 308:489–517

    Article  MathSciNet  Google Scholar 

  • Kerner BS (2004) Three-phase traffic theory and highway capacity. Phys A 333:379–440

    Article  MathSciNet  Google Scholar 

  • Kerner BS (2016a) The maximization of the network throughput ensuring free flow conditions in traffic and transportation networks: breakdown minimization (BM) principle versus Wardrop’s equilibria. Eur Phys J B 89:199

    Article  Google Scholar 

  • Kerner BS (2016b) Failure of classical traffic flow theories: stochastic highway capacity and automatic driving. Phys A 450:700–747

    Article  MathSciNet  Google Scholar 

  • Kerner BS (2017) Breakdown minimization principle versus Wardrop’s equilibria for dynamic traffic assignment and control in traffic and transportation networks: a critical mini-review. Phys A 466:626–662

    Article  MathSciNet  Google Scholar 

  • Komada K, Kojima K, Nagatani T (2011) Vehicular motion in 2D city traffic network with signals controlled by phase shift. Phys A 390:914–928

    Article  Google Scholar 

  • Lämmer S, Gehlsen B, Helbing D (2006) Scaling laws in the spatial structure of urban road networks. Phys A 363:89–95

    Article  Google Scholar 

  • Li X, Fang K, Peng G (2017) A new lattice model of traffic flow with the consideration of the drivers’ aggressive characteristics. Phys A 468:315–321

    Article  MathSciNet  Google Scholar 

  • Masoller C, Rosso OA (2011) Quantifying the complexity of the delayed logistic map. Philos Trans R Soc A 369:425–438

    Article  MathSciNet  Google Scholar 

  • Nagatani T (2000) Kinetic clustering and jamming transitions in a car following model of bus route. Phys A 287:302–312

    Article  Google Scholar 

  • Nagatani T (2001a) Bunching transition in a time-headway model of bus route. Phys Rev E 63:036115-1-7

    Article  Google Scholar 

  • Nagatani T (2001b) Interaction between buses and passengers on a bus route. Phys A 296:320–330

    Article  MathSciNet  Google Scholar 

  • Nagatani T (2001c) Delay transition of a recurrent bus on a circular route. Phys A 297:260–268

    Article  MathSciNet  Google Scholar 

  • Nagatani T (2002a) Bunching and delay in bus-route system with a couple of recurrent buses. Phys A 305:629–639

    Article  MathSciNet  Google Scholar 

  • Nagatani T (2002b) Dynamical transition to periodic motions of a recurrent bus induced by nonstops. Phys A 312:251–259

    Article  MathSciNet  Google Scholar 

  • Nagatani T (2002c) Transition to chaotic motion of a cyclic bus induced by nonstops. Phys A 316:637–648

    Article  MathSciNet  Google Scholar 

  • Nagatani T (2002d) Dynamical behavior in the nonlinear-map model of an elevator. Phys A 310:67–77

    Article  MathSciNet  Google Scholar 

  • Nagatani T (2002e) Chaotic and periodic motions of a cyclic bus induced by speedup. Phys Rev E 66:046103-1-7

    Article  Google Scholar 

  • Nagatani T (2003a) Chaotic motion of shuttle buses in two-dimensional map model. Chaos Solitons Fractals 18:731–738

    Article  Google Scholar 

  • Nagatani T (2003b) Complex behavior of elevators in peak traffic. Phys A 326:556–566

    Article  MathSciNet  Google Scholar 

  • Nagatani T (2003c) Fluctuation of tour time induced by interactions between cyclic trams. Phys A 331:279–290

    Article  MathSciNet  Google Scholar 

  • Nagatani T (2003d) Transitions to chaos of a shuttle bus induced by continuous speedup. Phys A 321:641–652

    Article  MathSciNet  Google Scholar 

  • Nagatani T (2003e) Complex motions of shuttle buses by speed control. Phys A 322:685–697

    Article  MathSciNet  Google Scholar 

  • Nagatani T (2003f) Dynamical transitions to chaotic and periodic motions of two shuttle buses. Phys A 319:568–578

    Article  MathSciNet  Google Scholar 

  • Nagatani T (2003g) Chaos and headway distribution of shuttle buses that pass each other freely. Phys A 323:686–694

    Article  MathSciNet  Google Scholar 

  • Nagatani T (2003h) Fluctuation of riding passengers induced by chaotic motions of shuttle buses. Phys Rev E 68:036107-1-8

    Article  Google Scholar 

  • Nagatani T (2003i) Dynamical behavior of N shuttle buses not passing each other: chaotic and periodic motions. Phys A 327:570–582

    Article  MathSciNet  Google Scholar 

  • Nagatani T (2004) Dynamical transitions in peak elevator traffic. Phys A 333:441–452

    Article  MathSciNet  Google Scholar 

  • Nagatani T (2005a) Self-similar behavior of a single vehicle through periodic traffic lights. Phys A 347:673–682

    Article  Google Scholar 

  • Nagatani T (2005b) Chaos and dynamics of cyclic trucking of size two. Int J Bifurcat Chaos 15:4065–4073

    Article  Google Scholar 

  • Nagatani T (2006a) Control of vehicular traffic through a sequence of traffic lights positioned with disordered interval. Phys A 368:560–566

    Article  Google Scholar 

  • Nagatani T (2006b) Chaos control and schedule of shuttle buses. Phys A 371:683–691

    Article  Google Scholar 

  • Nagatani T (2007a) Clustering and maximal flow in vehicular traffic through a sequence of traffic lights. Phys A 377:651–660

    Article  Google Scholar 

  • Nagatani T (2007b) Dynamical model for retrieval of tram schedule. Phys A 377:661–671

    Article  MathSciNet  Google Scholar 

  • Nagatani T (2007c) Passenger’s fluctuation and chaos on ferryboats. Phys A 383:613–623

    Article  Google Scholar 

  • Nagatani T (2008) Dynamics and schedule of shuttle bus controlled by traffic signal. Phys A 387:5892–5900

    Article  Google Scholar 

  • Nagatani T (2011a) Complex motion of shuttle buses in the transportation reducing energy consumption. Phys A 390:4494–4501

    Article  MathSciNet  Google Scholar 

  • Nagatani T (2011b) Complex motion in nonlinear-map model of elevators in energy-saving traffic. Phys Lett A 375:2047–2050

    Article  Google Scholar 

  • Nagatani T (2012) Delay effect on schedule in shuttle bus transportation controlled by capacity. Phys A 391:3266–3276

    Article  Google Scholar 

  • Nagatani T (2013a) Dynamics in two-elevator traffic system with real-time information. Phys Lett A 377:3296–3299

    Article  Google Scholar 

  • Nagatani T (2013b) Nonlinear-map model for control of airplane. Phys A 392:6545–6553

    Article  MathSciNet  Google Scholar 

  • Nagatani T (2013c) Modified circle map model for complex motion induced by a change of shuttle buses. Phys A 392:3392–3401

    Article  MathSciNet  Google Scholar 

  • Nagatani T (2013d) Complex motion of elevators in piecewise map model combined with circle map. Phys Lett A 377:2047–2051

    Article  MathSciNet  Google Scholar 

  • Nagatani T (2013e) Nonlinear-map model for bus schedule in capacity-controlled transportation. App Math Model 37:1823–1835

    Article  MathSciNet  Google Scholar 

  • Nagatani T (2014) Dynamic behavior in two-route bus system with real-time information. Phys A 413:352–360

    Article  Google Scholar 

  • Nagatani T (2015) Complex motion induced by elevator choice in peak traffic. Phys A 436:159–169

    Article  Google Scholar 

  • Nagatani T (2016a) Effect of stopover on motion of two competing elevators in peak traffic. Phys A 444:613–621

    Article  Google Scholar 

  • Nagatani T (2016b) Effect of speedup delay on shuttle bus schedule. Phys A 460:121–130

    Article  Google Scholar 

  • Nagatani T (2016c) Complex motion of a shuttle bus between two terminals with periodic inflows. Phys A 449:254–264

    Article  MathSciNet  Google Scholar 

  • Nagatani T (2017) Effect of periodic inflow on speed-controlled shuttle bus. Phys A 469:224–231

    Article  Google Scholar 

  • Nagatani T, Naito Y (2011) Schedule and complex motion of shuttle bus induced by periodic inflow of passengers. Phys Lett A 375:3579–3582

    Article  Google Scholar 

  • Nagatani T, Tobita K (2012) Effect of periodic inflow on elevator traffic. Phys A 391:4397–4405

    Article  Google Scholar 

  • Nagatani T, Yoshimura J (2002) Dynamical transition in a coupled-map lattice model of a recurrent bus. Phys A 316:625–636

    Article  Google Scholar 

  • Naito Y, Nagatani T (2012) Effect of headway and velocity on safety-collision transition induced by lane changing in traffic flow. Phys A 391:1626–1635

    Article  Google Scholar 

  • O’loan OJ, Evans MR, Cates ME (1998) Jamming transition in a homogeneous one-dimensional system: the bus route model. Phys Rev E 58:1404–1421

    Article  Google Scholar 

  • Redhu P, Gupta AK (2016) The role of passing in a two-dimensional network. Nonlinear Dyn 86:389–399

    Article  MathSciNet  Google Scholar 

  • Sugiyama Y, Nagatani T (2012) Multiple-vehicle collision induced by a sudden stop. Phys Lett A 376:1803–1806

    Article  Google Scholar 

  • Sugiyama Y, Nagatani T (2013) Multiple-vehicle collision in traffic flow by a sudden slowdown. Phys A 392:1848–1857

    Article  Google Scholar 

  • Tobita K, Nagatani T (2012) Effect of signals on two-route traffic system with real-time information. Phys A 391:6137–6145

    Article  Google Scholar 

  • Tobita K, Nagatani T (2013) Green-wave control of unbalanced two-route traffic system with signals. Phys A 392:5422–5430

    Article  Google Scholar 

  • Toledo BA, Munoz V, Rogan J, Tenreiro C, Valdivia JA (2004) Modeling traffic through a sequence of traffic lights. Phys Rev E 70:016107

    Article  Google Scholar 

  • Toledo BA, Cerda E, Rogan J, Munoz V, Tenreiro C, Zarama R, Valdivia JA (2007) Universal and nonuniversal feature in a model of city traffic. Phys Rev E 75:026108

    Article  Google Scholar 

  • Treiber M, Hennecke A, Helbing D (2000) Congested traffic states in empirical observations and microscopic simulations. Phys Rev E 62:1805

    Article  Google Scholar 

  • Treiber M, Kesting A, Helbing D (2006) Delays, inaccuracies and anticipation in microscopic traffic models. Phys A 360:71–88

    Article  Google Scholar 

  • Villalobos J, Toledo BA, Pasten D, Nunoz V, Rogan J, Zarma R, Valdivia JA (2010) Characterization of the nontrivial and chaotic behavior that occurs in a simple city traffic model. Chaos 20:013109

    Article  MathSciNet  Google Scholar 

  • Wahle J, Lucia A, Bazzan C, Klugl F, Schreckenberg M (2000) Decision dynamics in a traffic scenario. Phys A 287:669–681

    Article  Google Scholar 

  • Wastavino LA, Toledo BA, Rogan J, Zarama R, Muñoz V, Valdivia JA (2008) Modeling traffic on crossroads. Phys A 381:411–419

    Article  Google Scholar 

Books and Reviews

  • Chowdohury D, Santen L, Schadschneider A (2000) Statistical physics of vehicular traffic and some related systems. Phys Rep 329:199–329

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Kerner BS (2004) The physics of traffic. Springer, Heidelberg

    Google Scholar 

  • Nagatani T (2002) The physics of traffic jams. Rep Prog Phys 63:1331–1386

    Google Scholar 

  • Paterson SE, Allan LK (2009) Road traffic: safety, modeling, and impacts. Nova Science Publishers, New York

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Shizuoka University, Hamamatsu, Japan

    Takashi Nagatani

Authors
  1. Takashi Nagatani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Takashi Nagatani .

Editor information

Editors and Affiliations

  1. Physics of Transport and Traffic, University Duisburg-Essen, Duisburg, Germany

    Boris S. Kerner

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Science+Business Media, LLC, part of Springer Nature

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Nagatani, T. (2019). Complex Dynamics of Bus, Tram, and Elevator Delays in Transportation Systems. In: Kerner, B. (eds) Complex Dynamics of Traffic Management. Encyclopedia of Complexity and Systems Science Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-8763-4_656

Download citation

Publish with us

Policies and ethics

Search

Navigation