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The planning of headways in urban public transit. (English) Zbl 0839.90030
Summary: A basic issue in the planning of urban public transport in the determination of headways or inter-dispatch times. During each season, i.e. distinct time-period whose demand characteristics are constant, the following tradeoff must be considered. Dispatching too many vehicles on a route causes high operating costs, while too few vehicles may result in unsatisfactory levels of service. An appropriate policy on headways will help to balance resources between lines (routes) in peak-demand hours and will influence the total number of buses acquired by a transit company.
Previous practice in industry usually bases the planning of headways upon satisfying service criteria on a “most-congested segment”. This approach reduces the problem from that of studying a route to that of a single segment (stop), but thereby fails to account for other important information about the line’s characteristics. In this article, we develop two new service criteria which consider the line as a whole: (1) “crowding-overdistance” takes into account discomfort resulting from a vehicle carrying too many passengers, and the corresponding distance travelled; and (2) “probability-of-failure”, the frequency with which a waiting passenger fails to board due to lack of space. COD will be analyzed using simulation. POF will be related to a finite-dependent Markov chain that is “inhomogeneous” in terms of distance along the route. Optimal headways are those which dispatch the smallest number of buses while meeting the particular service criterion. Models based on each of the two criteria are illustrated and applied to a number of routes of the Israeli transit company, DAN.

90B06 Transportation, logistics and supply chain management
Full Text: DOI
[1] A. Adamski, Probabilistic models of passenger service processes at bus stops, Transp. Res. 26B(1992)253–259.
[2] O. Adebisi, A mathematical model for headway variance of fixed-route buses, Transp. Res. 20B(1986)59–70.
[3] P.A. Andersson and G.P. Scalia-Tomba, Statistical analysis of an urban bus route, Report LiTHMAT-R-78-11, Department of Mathematics, Linköping Institute of Technology (1978).
[4] A. Ceder, Computer application for determining buses and timetables, in:Advances in Bus Service Planning Practices, Record 1011 (Transportation Research Board, Washington, DC, 1985) pp. 76–87.
[5] A. Ceder, Bus frequency determination using passenger count data, Transp. Res. 18A(1987)439–453.
[6] S.K. Chang and P.M. Schonfeld, Multiple period optimization of bus transit systems, Transp. Res. 25B(1991)453–478.
[7] R.A.Chapman, H.E. Gault and I.A. Jenkins, Factors affecting the operation of urban bus routes, Research Report No. 23, TORG University, Newcastle-upon-Tyne (1976).
[8] E. Çinlar,Introduction to Stochastic Processes (Prentice-Hall, 1975). · Zbl 0341.60019
[9] P.G. Furth and N.H.M. Wilson, Setting frequencies on bus routes: Theory and practice, Transp. Res. Record 818(1981)1–7.
[10] G. Kocur and C. Henderson, Design of local bus service with demand equilibrium, Transp. Sci. 16(1982)149–170.
[11] G.K. Kuah and J. Perl, Optimization of feeder bus routes and bus stop spacing, J. Transp. Eng. 114(1988)341–354.
[12] G.F. Newell, Dispatching policies for a transportation route, Transp. Sci. 5(1971)91–105.
[13] R.H. Oldfield and P.H. Bly, An analytic investigation of optimal bus size, Transp. Res. 22B(1988)319–337.
[14] W.B. Powell and Y. Sheffi, A probabilistic model of bus route performance, Transp. Sci. 17(1983)376–404.
[15] Y.J. Stephanedes, P.G. Michalopoulos and T. Bountis, Dynamic transit scheduling under efficiency constraints, Transp. Res. 19B(1985)95–111.
[16] L. Tam and P. Seneviratne, Computer simulation model for bus service analysis, presented atTransportation Research Board, 1989 annual meeting, Washington, DC.
[17] J. Woodhull, J. Simon and D.A. Shoemaker, Goals for bus transit scheduling, in:Advances in Bus Service Planning Practices, Record 1011 (Transportation Research Board, Washington, DC, 1985) pp. 72–76.
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