Transportation Queueing

  • Randolph W. Hall
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 23)

Abstract

Since the time that humans first gathered into societies, there have been queues. They have existed whenever people have demanded more of a service than that service could provide. Though queueing is by no means new, the study of queues is relatively recent, dating only to the beginning of the twentieth century and the work of A.K. Erlang (Brockmeyer et al, 1948). Erlang’s investigations centered on determining capacity requirements for telephone systems, a then very new technology. Even to this day, much of the research in queueing has been directed at applications in communication. The first textbook on the subject, Queues, Inventories and Maintenance, was written in 1958 by Morse. The first textbook focusing on queueing applications in transportation (Applications of Queueing Theory) was written by Newell in 1971.

Keywords

Arrival Rate Transportation Research Batch Size Traffic Signal Demand Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Allsop, R.E. (1970). Optimisation techniques for reducing delay to traffic in signalised road networks. Ph.D. Thesis, University of London.Google Scholar
  2. Andreatta, G. and Romanin-Jacur, G. (1987). Aircraft flow management under congestion. Transportation Science, 21, 249–253.CrossRefGoogle Scholar
  3. Bailey, N.T.J. (1954). On queueing processes with bulk service, Journal of the Royal Stastical Society B, 16, 80–87.Google Scholar
  4. Barnett, A. (1974). On controlling randomness in transit operations. Transportation Science, 8, 102–116.CrossRefGoogle Scholar
  5. Beckmann, M.J., McGuire, C.B. and Winsten, B. (1956). Studies in the Economics of Transportation,. Yale University Press, New Haven, Connecticut.Google Scholar
  6. Beckmann, M.J. (1965). On optimal tolls for highways,tunnels and bridges, In: Vehicular Traffic Science (Edie, Herman and Rothery, eds.), 331–341. Elsevier, New York.Google Scholar
  7. Blumenfeld, D.E., Burns, L.D., Diltz, J.D. and Daganzo, C.F. (1985). Analyzing trade-offs between transportation, inventory and production costs on freight networks. Transportation Research, 19B, 361–380.Google Scholar
  8. Blumenfeld, D.E., Burns, L.D. and Daganzo, C.F. (1991). Synchronizing production and transportation schedules. Transportation Research, 25B:23–27.Google Scholar
  9. Burns, L.D., Hall, R.W., Blumenfeld, D.E. and Daganzo, C.F. (1985). Distribution strategies that minimize transportation and inventory cost. Operations Research, 33, 469–490.CrossRefGoogle Scholar
  10. Chaiken, J. and Larson, R. (1972). Methods for allocating urban emergency units: a survey. Management Science, 19, 110–130.CrossRefGoogle Scholar
  11. Cheng, T.E.C. and Allam, S. (1992). A review of stochastic modelling of delay and capacity at unsignalized interjections. European Journal of Operations Research, 60, 47–259.CrossRefGoogle Scholar
  12. Clayton, A.J.H. (1941). Road traffic calculations, Journal of Institute of Civil Engineers, 16, 247–284, 558-594.CrossRefGoogle Scholar
  13. Dafermos, S. C. and Sparrow, F.T. (1971). Optimal resource allocation and toll patterns in a user-optimized transportation network. Journal of Transportation Economic Policy, 5, 198–200.Google Scholar
  14. Daganzo, C.F. (1982). Supplying a single location from heterogeneous sources. Transportation Research, 19B: 409–420.Google Scholar
  15. Daganzo (1989). On the coordination of inbound and outbound schedules at transportation terminals, Institute of Transportation Studies Research Report, Berkeley, California.Google Scholar
  16. Daganzo, C.F., Dowling, R.G. and Hall, R.W. (1983). Railroad classification yard throughput: the case of multistage triangular sorting. Transportation Research, 17A, 95–106.Google Scholar
  17. Dessouky, M., Hall, R., Nowroozi, A. and Singh, A. (1997). Evaluation of ITS technology for bus timed transfers. PATH Research Report, Berkeley, California.Google Scholar
  18. Edie, L.C. (1956). Traffic delays at toll booths. Journal of Operations Research, 4, 107–138.CrossRefGoogle Scholar
  19. Edie, L.C. (1961). Car-following and steady-state theory for non-congested traffic. Operations Research, 9, 66–76.CrossRefGoogle Scholar
  20. Edie, L.C., and Foote, R.S. (1958). Traffic flow in tunnels, Proceedings of the Highway Research Board, 37, 334–344.Google Scholar
  21. Edie, L.C., and Foote, R.S. (1960). Effect of shock waves on tunnel traffic flow. Proceedings of the Highway Research Board, 39, 492–505.Google Scholar
  22. Frank, O. (1966). Two-way traffic in a single line of railway. Operations Research. 14, 801–811.CrossRefGoogle Scholar
  23. Gallagher, H.P. and Wheeler, R.C. (1958). Nonstationary queueing probabilities for landing congested aircraft. Operations Research, 6, 64–275.Google Scholar
  24. Ghobrial, A., Daganzo, C.F. and Kazimi, T. (1982). Baggage claim area congestion at airports: an empirical model of mechanized claim device performance. Transportation Science, 16, 246–260.CrossRefGoogle Scholar
  25. Grace, M.M. and Potts, R.B. (1964). A theory of diffusion of traffic platoons. Operations Research, 12, 255–275.CrossRefGoogle Scholar
  26. Green, L. and Kolesar, P. (1989). Testing the validity of a queueing model of police patrol. Management Science, 35, 127–148.CrossRefGoogle Scholar
  27. Greenshields, B.D. (1935). A study of traffic capacity. Poceedings of the Highway Research Board, 14, 448Google Scholar
  28. Hall, R.W. (1985). Determining vehicle dispatch frequency when shipping frequency differs among suppliers. Transportation Research, 19B: 421–431.Google Scholar
  29. Hall, R.W. (1996). On the integration of production and distribution: economic order and production quantity implications. Transportation Research, 30B, 387–403.Google Scholar
  30. Hall, R.W. (1996). On the integration of production and distribution: economic order and production quantity implications. Transportation Research, 30, 387–403.CrossRefGoogle Scholar
  31. Hall, R.W. (1991). Queueing Methods for Services and Manufacturing, Prentice Hall, Engelwood Cliffs, New Jersey.Google Scholar
  32. Hankin, J.D. and Wright, R.A. (1958). Passenger flow in subways. Operations Research Quarterly, 9, 81–88.CrossRefGoogle Scholar
  33. Herman, R., Montroll, E.W., Potts, R.B. and Rothery, R.W. (1959). Traffic dynamics: analysis of stability in car following, Operations Research, 7, 86–106.CrossRefGoogle Scholar
  34. Horonjeff, R. (1969). Analysis of passenger and baggage flows in airport terminal buildings. 6, 446–451.Google Scholar
  35. Ignall, E.J., Kolesar, P. and Walker, W.E. (1978). Using simulation to develop and validate analytic models: some case studies. Operations Research, 6, 37–253.Google Scholar
  36. Kolesar, P. (1975). A model for predicting average fire engine travel times. Operations Research, 23, 603–613.CrossRefGoogle Scholar
  37. Kolesar, P. and Blum, E.H. (1973). Square root laws for fire engine response distances. Management Science, 19, 1368–1378.CrossRefGoogle Scholar
  38. Kolesar, P.J., K.L. Rider, T.B. Crabill and Walker, W.E. (1975). A Queueing-linear programming approach to scheduling police patrol cars. Operations Research. 23, 1045–1062.CrossRefGoogle Scholar
  39. Koopman, B.O. (1972). Air-terminal queues under time-dependent conditions. Operations Research, 20, 1089–1114.CrossRefGoogle Scholar
  40. Larson, R.C. (1972). Urban Police Patrol Analysis. The MIT Press, Cambridge, Massachusetts.Google Scholar
  41. Lighthill, M.J. and Whitham, G.B. (1955). On kinematic waves, II, a theory of traffic flow on long straight crowded roads. Proceedings of the Royal Society, London, Series A 229, 317–345.CrossRefGoogle Scholar
  42. Little, J.D.C. (1961). A proof for the queueing formula L = λW. Operations Research, 9, 83–387.Google Scholar
  43. Little, J.D.C, Kelman, M.D. and Gartner, N.H. (1981). MAXBAND: a program for setting signals on arterials and triangular networks. Transportation Research Record, 795, 40–46.Google Scholar
  44. Lovas, G.G. (1994). Modeling and simulation of pedestrian traffic flow. Transportation Research, 28B, 429–443.Google Scholar
  45. May, A.D. and Keller, H.E. (1967). A deterministic queueing model. Transportation Research, 1, 117–128.CrossRefGoogle Scholar
  46. Makigami, Y., Newell, G.F. and Rother, R. (1971). Three-dimensional representations of traffic flow. Transportation Science, 5, 302–313.CrossRefGoogle Scholar
  47. Miller, A.J. (1963). Settings for fixed-cycle traffic signals. Operational Research Quarterly, 14, 373–386.CrossRefGoogle Scholar
  48. Morse, P. (1958). Queues, Inventories and Maintenance. New York: John-Wiley.Google Scholar
  49. Neuts, M.F. (1967). A general class of Poisson queues with Poisson input. Annals of Mathematical Statistics, 8, 759–770.CrossRefGoogle Scholar
  50. Newell, G.F. (1965). Approximation methods for queues with application to the fixed-cycle traffic light. SIAM Review, 2, 23–240.Google Scholar
  51. Newell, G.F. (1971, 1982). Applications of Queueing Theory, Chapman and Hall, London.CrossRefGoogle Scholar
  52. Newell, G.F. (1975). Control of pairing of vehicles on a public transportation route, two vehicles, one control point. Transportation Science, 9, 248–264.CrossRefGoogle Scholar
  53. Newell, G.F. (1979). Airport capacity and delays, Transportation Science, 13, 201–241.CrossRefGoogle Scholar
  54. Newell, G.F. (1993). A simplified theory of kinematic waves in highway traffic, Parts I-III. Transportation Research, 27B, 281–313.Google Scholar
  55. Newell, G.F. (1955). Mathematical models for freely-flowing highway traffic, Operations Research, 3, 176–186.CrossRefGoogle Scholar
  56. Odoni, A.R. (1987). The flow management problem in air traffic control. In A.R. Odoni, L. Bianco and G. Szego (Eds.), Flow Control of Congested Networks, 69–288. Springer Verlag, New York.CrossRefGoogle Scholar
  57. Older, S.J. (1968). Movement of pedestrians on footways in shopping streets. Traffic Engineering and Control, 13, 434–438.Google Scholar
  58. Oliver, R.M. and Samuel, A.H. (1967). Reducing letter delays in post offices. Operations Research, 10, 839–892.CrossRefGoogle Scholar
  59. Osuna, E.E. and Newell, G.F. (1972). Control strategies for an idealized public transportation system. Transportation Science, 6, 52–72.CrossRefGoogle Scholar
  60. Pacey, G.M. (1956). Progress of a bunch of vehicles released from a traffic signal. Report RN/2665, Dept. of Scientific and Industrial Research, Road Research Laboratory, England.Google Scholar
  61. Petersen, E.R. (1974). Over-the-road transit time for a single track railway. Transportation Science, 8, 65–74.CrossRefGoogle Scholar
  62. Petersen, E.R. (1977a). Railyard modeling, part I, prediction of put-through time. Transportation Science, 11, 37–49.CrossRefGoogle Scholar
  63. Petersen, E.R. (1977b). Railyard modeling, part II, the effect of yard facilities on congestion. Transportation Science, 11, 50–59.CrossRefGoogle Scholar
  64. Peterson, M.D., Bertsimas, D.J. and Odoni, A.R. (1995). Decomposition algorithms for analyzing transient phenomena in multiclass queueing networks in air transportation. Operations Research, 43, 995–1011.CrossRefGoogle Scholar
  65. Peterson, M.D., Bertsimas, D.J. and Odoni, A.R. (1995). Models and algorithms for transient queueing congestion at airports, ManagementScience, 41, 1279–1295.Google Scholar
  66. Powell, W.B. (1985) Analysis of vehicle holding and cancellation strategies in bulk arrival, bulk service queues, Transportation Science, 19, 352–377.CrossRefGoogle Scholar
  67. Powell, W.B. (1986) Approximate closed form moment formulas for bulk arrival, bulk service queues. Transportation Science, 20, 13–23.CrossRefGoogle Scholar
  68. Powell, W.B. and Humblet, P. (1984) The bulk service queue with a general control strategy, Operations Research, 19, 352–377.Google Scholar
  69. Richards, P.I. (1956). Shock waves on the highway. Operations Research, 4, 42–51.CrossRefGoogle Scholar
  70. Richetta, O. and A.R. Odoni (1994). Dynamic solution to the ground-holding problem in air traffic control. Transportation Research, 28A, 167–185.Google Scholar
  71. Rider, K.L. (1976). A parametric model for the allocation of fire companies in New York City, Management Science, 28, 146–158.CrossRefGoogle Scholar
  72. Robertson, D.I. (1969). TRANSYT: a traffic network study tool. Road Research Laboratory, LR 253, Crowthorne, England.Google Scholar
  73. Robuste, F. and Daganzo, C.F. (1992). Analysis of baggage sorting schemes for containerized aircraft. Transportation Research A, 26A, 75–92.Google Scholar
  74. Tanner, J.C. (1962). A theoretical analysis of delays at an uncontrolled intersection. Biometrica, 49, 163–170.Google Scholar
  75. Turnquist, M.A. and Daskin, M.S. (1982). Queueing models of classification and connection delay in railyards. Transportation Science, 16, 207–230.CrossRefGoogle Scholar
  76. Vickrey, W. (1963). Pricing in urban and suburban transportation. American Economic Review, 53, 452–465.Google Scholar
  77. Vickrey, W. (1969). Congestion theory and transport investment. American Economic Review, 59, 251–26Google Scholar
  78. Wardrop, J.G. (1952). Some theoretical aspects of road traffic research. Proceedings of the Institute of Civil Engineers II. 1, 325–364.Google Scholar
  79. Webster, F.V. (1958). Traffic signal settings, Road Research Laboratory Technical Paper, Her Majesty’s Stationery Office, London.Google Scholar
  80. Welch, N. and Gussow, J. (1986). Expansion of Canadian Nation Railway’s line capacity. Interfaces, 16:1, 51–64.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Randolph W. Hall
    • 1
  1. 1.University of SouthernCaliforniaUSA

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