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Operation Regimes and Slower-is-Faster-Effect in the Control of Traffic Intersections

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Modelling and Optimisation of Flows on Networks

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 2062))

Abstract

The efficiency of traffic flows in urban areas is known to crucially depend on signal operation. Here, elements of signal control are discussed, based on the minimization of overall travel times or vehicle queues. Interestingly, we find different operation regimes, some of which involve a “slower-is-faster effect”, where a delayed switching reduces the average travel times. These operation regimes characterize different ways of organizing traffic flows in urban road networks. Besides the optimize-one-phase approach, we discuss the procedure and advantages of optimizing multiple phases as well. To improve the service of vehicle platoons and support the self-organization of “green waves”, it is proposed to consider the price of stopping newly arriving vehicles.

First published in: The European Physical Journal B 70(2), 257–274, DOI: 10.1140/epjb/e2009-00213-5 (2009), © EDP Sciences, Societa Italiana di Fisica, Springer-Verlag 2009, reproduction with kind permission of The European Physical Journal (EPJ).

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Notes

  1. 1.

    For formulas to estimate these quantities as a function of the utilization of the service capacity of roads see [20].

  2. 2.

    If the cycle time \({T}_{\mathrm{cyc}}\) is limited to a certain maximum value \({T}_{\mathrm{cyc}}^{\mathrm{max}}\), one must replace the constraint \({x}_{1} + {x}_{2} \leq 1\) by \({x}_{1} + {x}_{2} \leq 1 - ({\tau }_{1} + {\tau }_{2})/{T}_{\mathrm{cyc}}^{\mathrm{max}}\) and 1 − u 2 by \(1 - {u}_{2} - ({\tau }_{1} + {\tau }_{2})/{T}_{\mathrm{cyc}}^{\mathrm{max}}\).

  3. 3.

    In this case, we do not expect a periodic signal control anymore, as the growing vehicle queue in one of the road sections, see [20], has to be considered in the signal optimization procedure. Our formulas for one-phase optimization can handle this case due to the dependence on \(\Delta {N}_{j}(0)\). In the two-phase optimization procedure, we would have to add \(\sum\limits_{j}{I}_{j}\,\Delta {N}_{j}(0)\) to formula (72), where \(\Delta {N}_{j}(0) = {A}_{j}{T}_{\mathrm{cyc}}^{k} -\widehat{ {Q}}_{j}\,\Delta {T}_{j}^{k}\) denotes the number of vehicles that was not served during the kth cycle \({T}_{\mathrm{cyc}}^{k} = {\tau }_{1} + \Delta {T}_{1}^{k} + {\tau }_{2} + \Delta {T}_{2}^{k}\). This gives an additional term \(\sum\limits_{j}{u}_{j}{I}_{j}\widehat{{Q}}_{j}({\tau }_{1} + {\tau }_{2})\sum\limits_{k}(1 + {\sigma }_{1}^{k} + {\sigma }_{2}^{k} - {\sigma }_{j}^{k}/{u}_{j})\) in (72).

  4. 4.

    The finite deceleration only matters slightly, when the exact moment must be determined when a road section becomes fully congested.

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Acknowledgements

Author contributions: DH set up the model, performed the analytical calculations, and wrote the manuscript. AM produced the numerical results and figures, and derived the separating lines given by (94) and (95).

Acknowledgements: The authors would like to thank for partial support by the ETH Competence Center “Coping with Crises in Complex Socio-Economic Systems” (CCSS) through ETH Research Grant CH1-01 08-2, the VW Foundation Project I/82 697 on “Complex Self-Organizing Networks of Interacting Machines: Principles of Design, Control, and Functional Optimization”, the Daimler-Benz Foundation Project 25-01.1/07 on “BioLogistics”, and the “Cooperative Center for Communication Networks Data Analysis”, a NAP project sponsored by the Hungarian National Office of Research and Technology under Grant No. KCKHA005.

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    Dirk Helbing & Amin Mazloumian

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Helbing, D., Mazloumian, A. (2013). Operation Regimes and Slower-is-Faster-Effect in the Control of Traffic Intersections. In: Modelling and Optimisation of Flows on Networks. Lecture Notes in Mathematics(), vol 2062. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32160-3_7

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