A vehicle-to-infrastructure communication based algorithm for urban traffic control

We present in this paper a new algorithm for urban traffic light control with mixed traffic (communicating and non communicating vehicles) and mixed infrastructure (equipped and unequipped junctions). We call equipped junction here a junction with a traffic light signal (TLS) controlled by a road side unit (RSU). On such a junction, the RSU manifests its connectedness to equipped vehicles by broadcasting its communication address and geographical coordinates. The RSU builds a map of connected vehicles approaching and leaving the junction. The algorithm allows the RSU to select a traffic phase, based on the built map. The selected traffic phase is applied by the TLS; and both equipped and unequipped vehicles must respect it. The traffic management is in feedback on the traffic demand of communicating vehicles. We simulated the vehicular traffic as well as the communications. The two simulations are combined in a closed loop with visualization and monitoring interfaces. Several indicators on vehicular traffic (mean travel time, ended vehicles) and IEEE 802.11p communication performances (end-to-end delay, throughput) are derived and illustrated in three dimension maps. We then extended the traffic control to a urban road network where we also varied the number of equipped junctions. Other indicators are shown for road traffic performances in the road network case, where high gains are experienced in the simulation results.Comment: 6 page

Equicontinuous local dendrite maps

[EN] Let X be a local dendrite, and f : X → X be a map. Denote by E(X) the set of endpoints of X. We show that if E(X) is countable, then the following are equivalent:(1) f is equicontinuous;(2)  fn (X) = R(f);(3) f|  fn (X) is equicontinuous;(4) f| fn (X) is a pointwise periodic homeomorphism or is topologically conjugate to an irrational rotation of S 1 ;(5) ω(x, f) = Ω(x, f) for all x ∈ X.This result generalizes [17, Theorem 5.2], [24, Theorem 2] and [11, Theorem 2.8].Salem, AH.; Hattab, H.; Rejeiba, T. (2021). Equicontinuous local dendrite maps. Applied General Topology. 22(1):67-77. https://doi.org/10.4995/agt.2021.13446OJS6777221H. Abdelli, ω-limit sets for monotone local dendrite maps. Chaos, Solitons and Fractals, 71 (2015), 66-72. https://doi.org/10.1016/j.chaos.2014.12.003H. Abdelli and H. Marzougui, Invariant sets for monotone local dendrite maps, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 26, no. 9 (2016), 1650150 (10 pages). https://doi.org/10.1142/S0218127416501509E. Akin, J. Auslander and K. Berg, When is a transitive map chaotic?, in: Convergence in Ergodic Theory and Probability, Walter de Gruyter and Co., Berlin, 1996, pp. 25-40. https://doi.org/10.1515/9783110889383.25G. Askri and I. Naghmouchi, Pointwise recurrence on local dendrites, Qual. Theory Dyn Syst 19, 6 (2020). https://doi.org/10.1007/s12346-020-00347-8F. Balibrea, T. Downarowicz, R. Hric, L. Snoha and V. Spitalsky, Almost totally disconnected minimal systems, Ergodic Th. & Dynam Sys. 29, no. 3 (2009), 737-766. https://doi.org/10.1017/S0143385708000540F. Blanchard, B. Host and A. Maass, Topological complexity, Ergodic Th. & Dynam Sys. 20 (2000), 641-662. https://doi.org/10.1017/S0143385700000341A. M. Blokh, Pointwise-recurrent maps on uniquely arcwise connected locally arcwise connected spaces, Proc. Amer. Math. Soc. 143 (2015), 3985-4000. https://doi.org/10.1090/S0002-9939-2015-12589-0A. M. Blokh, The set of all iterates is nowhere dense in C([0,1],[0,1]), Trans. Amer. Math. Soc. 333, no. 2 (1992), 787-798. https://doi.org/10.1090/S0002-9947-1992-1153009-7W. Boyce, Γ-compact maps on an interval and fixed points, Trans. Amer. Math. Soc. 160 (1971), 87-102. https://doi.org/10.1090/S0002-9947-1971-0280655-1A. M. Bruckner and T. Hu, Equicontinuity of iterates of an interval map, Tamkang J. Math. 21, no. 3 (1990), 287-294.J. Camargo, M. Rincón and C. Uzcátegui, Equicontinuity of maps on dendrites, Chaos, Solitons and Fractals 126 (2019), 1-6. https://doi.org/10.1016/j.chaos.2019.05.033J. Cano, Common fixed points for a class of commuting mappings on an interval, Trans. Amer. Math. Soc. 86, no. 2 (1982), 336-338. https://doi.org/10.1090/S0002-9939-1982-0667301-2R. Gu and Z. Qiao, Equicontinuity of maps on figure-eight space, Southeast Asian Bull. Math. 25 (2001), 413-419. https://doi.org/10.1007/s100120100004A. Haj Salem and H. Hattab, Group action on local dendrites, Topology Appl. 247, no. 15 (2018), 91-99. https://doi.org/10.1016/j.topol.2018.08.002K. Kuratowski, Topology, vol. 2. New York: Academic Press; 1968.J. Mai, Pointwise-recurrent graph maps, Ergodic Th. & Dynam Sys. 25 (2005), 629-637. https://doi.org/10.1017/S0143385704000720J. Mai, The structure of equicontinuous maps, Trans. Amer. Math. Soc. 355, no. 10 (2003), 4125-4136. https://doi.org/10.1090/S0002-9947-03-03339-7C. A. Morales, Equicontinuity on semi-locally connected spaces, Topology Appl. 198 (2016), 101-106. https://doi.org/10.1016/j.topol.2015.11.011S. Nadler, Continuum Theory. Inc., New York: Marcel Dekker; 1992.G. Su and B. Qin, Equicontinuous dendrites flows, Journal of Difference Equations and Applications 25, no. 12 (2019), 1744-1754. https://doi.org/10.1080/10236198.2019.1694012T. Sun, Equicontinuity of σ-maps, Pure and Applied Math. 16, no. 3 (2000), 9-14.T. Sun, Z. Chen, X. Liu and H. G. Xi, Equicontinuity of dendrite maps, Chaos, Solitons and Fractals 69 (2014), 10-13. https://doi.org/10.1016/j.chaos.2014.08.010T. Sun, G. Wang and H. J. Xi, Equicontinuity of maps on a dendrite with finite branch points. Acta Mat. Sin. 33, no. 8 (2017), 1125-1130. https://doi.org/10.1007/s10114-017-6289-xT. Sun, Y. Zhang and X. Zhang, Equicontinuity of a graph map, Bull. Austral Math. Soc. 71 (2005), 61-67. https://doi.org/10.1017/S0004972700038016A. Valaristos, Equicontinuity of iterates of circle maps, Internat. J. Math. and Math. Sci. 21 (1998), 453-458. https://doi.org/10.1155/S016117129800062

A Data-driven Approach for Estimating the Fundamental Diagram

The fundamental diagram links average speed to density or traffic flow. An analytic form of this diagram, with its comprehensive and predictive power, is required in a number of problems. This paper argues, however, that, in some assessment studies, such a form is an unnecessary constraint resulting in a loss of accuracy. A non-analytical fundamental diagram which best fits the empirical data and respects the relationships between traffic variables is developed in this paper. In order to obtain an unbiased fundamental diagram, separating congested and non-congested observations is necessary. When defining congestion in parallel with a safety constraint, the density separating congestion and non-congestion appears as a decreasing function of the flow and not as a single critical density value. This function is here identified and used. Two calibration techniques - a shortest path algorithm and a quadratic optimization with linear constraints - are presented, tested, compared and validated

A semi-decentralized control strategy for urban traffic

We present in this article a semi-decentralized approach for urban traffic control, based on the TUC (Traffic responsive Urban Control) strategy. We assume that the control is centralized as in the TUC strategy, but we introduce a contention time window inside the cycle time, where antagonistic stages alternate a priority rule. The priority rule is set by applying green colours for given stages and yellow colours for antagonistic ones, in such a way that the stages with green colour have priority over the ones with yellow colour. The idea of introducing this time window is to reduce the red time inside the cycle, and by that, increase the capacity of the network junctions. In practice, the priority rule could be applied using vehicle-to-vehicle (v2v) or vehicle-to-infrastructure (v2i) communications. The vehicles having the priority pass almost normally through the junction, while the others reduce their speed and yield the way. We propose a model for the dynamics and the control of such a system. The model is still formulated as a linear quadratic problem, for which the feedback control law is calculated off-line, and applied in real time. The model is implemented using the Simulation of Urban MObility (SUMO) tool in a small regular (American-like) network configuration. The results are presented and compared to the classical TUC strategy.Comment: 16 page

Upper bounds for the travel time on traffic systems

A key measure of performance and comfort in a road traffic network is the travel time that the users of the network experience to complete their journeys. Travel times on road traffic networks are stochastic, highly variable, and dependent on several parameters. It is, therefore, necessary to have good indicators and measures of their variations. In this article, we extend a recent approach for the derivation of deterministic bounds on the travel time in a road traffic network (Farhi, Haj-Salem and Lebacque 2013). The approach consists in using an algebraic formulation of the cell-transmission traffic model on a ring road, where the car-dynamics is seen as a linear min-plus system. The impulse response of the system is derived analytically, and is interpreted as what is called a service curve in the network calculus theory (where the road is seen as a server). The basic results of the latter theory are then used to derive an upper bound for the travel time through the ring road. We consider in this article open systems rather than closed ones. We define a set of elementary traffic systems and an operator for the concatenation of such systems. We show that the traffic system of any road itinerary can be built by concatenating a number of elementary traffic systems. The concatenation of systems consists in giving a service guarantee of the resulting system in function of service guarantees of the composed systems. We illustrate this approach with a numerical example, where we compute an upper bound for the travel time on a given route in a urban network.Comment: 11 page