AN INTERMODAL TRAFFIC CONTROL STRATEGY FOR PRIVATE VEHICLE AND PUBLIC TRANSPORT

Transcription

1 dvanced OR and I Methods in Transportation N INTERMODL TRFFIC CONTROL STRTEGY FOR PRIVTE VEHICLE ND PUBLIC TRNSPORT Neila BHOURI, Pablo LOTITO bstract. This paper proposes a traffic-responsive urban traffic control strategy allowing a real time passive public transport priority. The proposed strategy is based on a store and forward modeling of both of the private vehicle and Public transport traffic. The regulator is designed using the linear quadratic, which allows a traffic responsive co-ordinated control for wide-area networks. The objective of this strategy is to control the junctions traffic lights in order to improve the traffic performance on the sections at the precise times when public transport is using the service sections. simulation example is provided to demonstrate the efficiency of the proposed strategy. 1. Introduction Several measures aiming at improving bus travel times are used through the world, including exclusive or reserved lanes for Public Transport, parking ban on highways, urban toll aiming at reducing road traffic, static or dynamic guidance using variable message signs to direct private vehicles to less loaded or less annoying for Public Transport routes, and priority to buses at traffic light controlled crossroads. The bus priority at traffic lights can operate in a passive or active way. For the passive way the lanes with buses receive priority without any individual detection of the buses. The most known passive strategy is TRNSYT [9], acting off-line. The active method consists in changing the crossroad signals, to give the priority to the detected buses. ctive public transport priority is largely the most used methodology : CRONOS [1], PRODYN [7], SCOOT [8], SCTS [2], SPPORT [6] TRFCOD [4], TUC [3]. The most used measures aiming at giving the priority to PT vehicles are the green phase extension, the green phase advance, the red truncation, the phase skipping, the stage recall, the special stage introduction. neila.bhouri@inrets.fr pablo.lotito@inrets.fr Institut National de Recherche sur les Transports et leur sécurité, 2 venue du Général Malleret- Joinville rcueil cedex. France.

2 424 N. Bhouri, P. Lotito These measures, however, could cause confusion to the motorists, loss of coordination, and long delays to traffic stream, as noted by [10]. It also can be contrary to the PT regulation strategies which have the regularity of the service as main objective. Indeed, the PT priority as practiced by all the mentioned strategies, may result in buses running ahead of schedule. From our viewpoint, a bus priority strategy based on the bus individual level, whether it is applied at isolated crossroads or on sets of crossroads, cannot have any global vision of the traffic on a whole region. This may imply secondary effects, indeed, it can enable to direct traffic on congested road sections or crossroads, resulting in general deteriorated traffic conditions, including bus traffic conditions. Our goal is to favor Public Transport, developing a regulation strategy which takes into account the traffic intermodal global situations on a whole region. The built strategy, will reduce the congestion giving priority to the arcs on the buses trajectories at the precise times when the buses are present, but not when the bus is not present. 2. The network model The traffic model consists in a store and forward model and a traffic conservation equation. It is similar to the model used in the urban traffic control strategy TUC [3]. The PT model that we propose consists in a delay equation, compatible with a macroscopic representation of the traffic in spite of an individual taking into account of the PT vehicles. The network is represented by junctions j J and arcs a. The traffic on each arc, expressed on passenger car units (pcu), is modeled by number of vehicles conservation equation : x a (k+ 1)= x a (k)+ T[q a (k) u a (k)] (1) Where x a is the number of vehicles of all traffic modes within the arc a, expressed in (pcu), q a and u a are the inflow and outflow, respectively on arc a over the period [kt, (k+1)t] with k a discrete time index and T the control interval; d a and s a are the demand and the exit flow, respectively (see Figure 1). junction M rc a I M q a x a junction N u a τ b,a rc b Figure 1. Store nd Forward. In order to point out the control variables, which are the effective green times of different stages, we use the old store and forward modeling approach, introduced by [5] and still

3 n intermodal traffic control strategy for private vehicle used in various works for road traffic control. It considers that all vehicles entering an arc a, are stored at the end of the arc, and leave it with the saturation flow S a. u a (k)= S a if the arc a has r.o.w. 0 otherwise (2) Flow (ua) Sa Ga C Time Figure 2. Store nd Forward. This implies that, within the cycle time C, the outflow of the arc a, at the discrete time kt, is given by : u a (k)= S a.g a (k) (3) C where G a (k) is the effective green time when the arc a has r.o.w. Using equation (3) imposes that :. the time step T cannot be shorter than the cycle time C. the model cannot describe the effect of offset for consecutive junctions. the model does not describe the oscillations of vehicle queues on the approaches, which implies that we consider that all permissible movements of an incoming link receive the r.o.w. simultaneously. The inflow to arc a is given by ω I M t ω,a u ω (k), where t ω,a withω I M are the turning rates towards arc a from the arcs that enter the junction M. Choosing the control interval T equal to the cycle time C Equation. 1 became : x a (k+ 1)= x a (k)+[ t ω,a S ω g M,i (k) S a g M,i (k)] (4) ω I M i O N The Public Transport vehicles are modeled by a delay equation : xa b (k+ 1)= xb a (k τ) (5) where x b a is the PT vehicles number on the arc a. τ is a fixed parameter expressing the mean time spent by a PT vehicle to travel from the arc a to the arc a. Normallyτ represents the total time spent by the PT vehicle from arc a to the arc a and takes real values. However, due to the use of the Linear Quadratic optimization algorithm, τ must

4 426 N. Bhouri, P. Lotito be a multiplier of the control interval T and hence of the cycle control interval C. For our case,τis considered equal to a one interval time if there is not a stop in the section otherwise it is equal to two: xa(k+ b 1)= xa b (k 1) x b a (k) if the public transport vehicle has a stop on the arc otherwise This simplification is consistent with the use of the store and forward modeling approach, as it consider that within a time cycle, both PT vehicles and PV are stored on the arc before going through the junction during the green time. The intermodal network model can be hence written in the following form : (6) X(k+1)= X(k)+BG(k) X b (k+1)= b 0 X b(k)+ b 1 X b(k 1) (7) 3. The optimization problem What we want is to reduce the congestion, giving priority to the traffic conditions on the arcs on the buses trajectories at the precise times when the buses are present. That is we do not want to reduce congestion on an arc belonging to a bus path when a bus is not present. Usually the way of reducing congestion is to minimize k( X(k) 2 ) (see Diakaki and al. [3]). What we want to reduce is the number of cars that are at the same time on the same arc as the buses, i.e., k,a x a (k)x b a(k)= k X(k) t X b (k). We allow a trade-off between both criteria using a linear combination of both as we can see in the system of equation (8). min G J(G)= (α(x(k)x b (k))+β X(k) 2 ) k s.t. X(k+ 1)= X(k)+ BG(k) X b (k+ 1)= b 0 X b(k)+ b 1 X b(k 1) (8) 4. Simulation Investigations We will present in the full paper, simulation results of the strategy applied to a regular network of 8 junctions, 32 arcs. we consider two buses trajectories, as showed on (Figure.3).

5 n intermodal traffic control strategy for private vehicle τ 12,23 τ 32, G 2, G 4, τ 82,73 72 G 2, τ 62, G 4, G 7, G 5, G 7,2 G 5, Figure 3. Example. References [1] F. Boillot, S. Midenet, and J. Pierrelée. Real-life cronos evaluation. In Tenth International Conference on Road Traffic Information and Control, number 472, pages IEE London, pril [2] W. Chen, G. Jarjees, and C. Drane. new approach for bus priority at signalised intesections. In RRB Transport Research LTD Conference, 19th, Sydney-ustralia, [3] C. Diakaki, M. Papageorgiou, and K. boudolas. multivariable regulator approach to traffic-responsive network-wide signal control. Control Engieneering Practice, 10: , [4] P. Furth and T. Muller. Trafcod : method for stream based control of actuated traffic signals. In 78th nnual meeting of the Transportation Research Board, Washington, US, [5] D. Gazis and R. Potts. The oversaturated intersection. In 2nd International Symposium on Traffic Theory, pages , London, UK, [6] B. Han and S. Yagar. Real-time control of traffic with bus ans streetcar interactions. In Proceeding of the 6th IEE International Conference on road traffic monitoring and control, pages , London, UK, [7] J. Henry and J. Farges. P.t. priority and prodyn. In Proceeding of the first World Congress On pplications of Transport Telematics and Intelligent Vehicle Highway Systems, pages , Paris-France, 1994.

6 428 N. Bhouri, P. Lotito [8] P. Hunt, D. Roberston, R. Bretherton, and M.C.Royle. The scoot on-line traffic signal optimization technique. Traffic Engineering & Control, 23: , [9] D. Roberston and R. Vincent. Bus priority in a network of fixed-time signals. Laboratory Report 666, TRRL, UK, [10]. Scabardonis. Control strategies for transit priority. TRR, 1727( ):20 26, 2000.