On Dynamic Information and Patterns of Cooperative Behaviours: a Probabilistic Model with Economic Analysis
F Leurent, T P Nguyen, UPE, LVMT, Ecole des Ponts ParisTech, FR
The effects of traffic information on the network assignment of uninformed users are modelled analytically to address various patterns of cooperative behaviour among the user classes, including user equilibrium, system optimum and partial cooperation
In a road network, the congestion delays include the recurrent delays determined by the flow pattern and the laws of traffic, and the non-recurrent delays due to traffic incidents, accidents or other random events, such as weather hazard. The non-recurrent causes cannot be forecasted by the individual user. To tackle congestion, the network operator can avail itself of a wide set of tools and resources, including long run capacity planning, medium run operations planning and short run or even real-time traffic management by dynamic adaptation of traffic signals, of the local limit speed, of the fare of HOT lanes etc. Traffic management also includes demand management through quality setting, pricing and information provision which are closely related with Dynamic Traffic Information (DTI). Actually the user chooses his route and/or departure time on the basis of his knowledge about the network state. The disposal of sharp information enables the road user to react in real-time to traffic disturbances and to cooperate in some way to the overall performance.
The provision of DTI makes a complex issue of which objective, contents, target, diffusion medium, equipment type, equipment rate etc. In particular the interplay of the congestion sources and physical laws with the provision of DTI calls for a model, useful to analyse and simulate the phenomena hence to gain a better understanding. The distinction of congestion sources and their interplay with DTI has been addressed correctly for the choice of departure time by Small and Noland (1995), Leurent (2001, 2004), although the analytical approach does not include the feedback of user re-timing in congestion. Concerning route choice, dynamic simulation in the 2000s (e.g. Lo and Szeto, 2004) has taken the same line as static simulation in the 1990s (Van Vuren and Watling, 1991; Maher and Hughes, 1995) by assuming that informed users would perceive a mean travel time, whereas uninformed users would experience disturbed travel times. In fact, this stands exactly opposite to the essence of dynamic disturbances and information. In our first paper (Leurent and Nguyen, 2008), two classes of users respectively informed or not are considered; the informed users have DTI about the actual travel time conditions, whereas the unequipped users only know about the average travel times. This is a novel assignment model since it distinguishes two layers of user equilibrium in traffic, associated with two time scales in demand perception and behaviour: an upper layer of short run decision-making by informed users as opposed to a lower level of long run decision-making by uninformed users, each layer constraining the other.
The main purpose of the paper is to provide a route choice model that deals with recurrent congestion as well as incidental congestion, the provision of dynamic information and network users that choose their route in a rational way according to the information available to them, in order to study various patterns of cooperation among the two user classes. In each class the user behaviour is assumed to be either selfish, or class-cooperative, or cross-class altruistic, or fully cooperative. This makes a set of 16 cooperative patterns, ranging from User Equilibrium (UE) where both classes are selfish to System Optimum (SO) where both classes are fully cooperative. Network performance is assessed in terms of average cost in various points of view: the gain to the individual user equipped or not, or the average, collective utility of DTI. Also the SO case makes a benchmark for all cooperative patterns; it leads us to study the interplay of DTI diffusion and system optimization, an issue that had been not much clear so far.
A simple, two-link network is considered with linear travel time functions of link flow, additive random disturbances in travel times and two classes of users, respectively informed of disturbances in travel time or not. Thus closed-form formulae are provided for the main variables of interest, which enable one to analyze clearly their sensitivity to the model parameters.
The model application yields a series of practical indications. First, the re-routing of informed users in the occurrence of a disruption tends to compensate the discrepancy between the two routes, which is evaluated along a criterion specific to the informed users. Second, as the equipment rate increases the individual gain of being equipped is reduced. Third, DTI provides positive profit to the overall traffic but an enhancement of DTI provision may be detrimental. Fourth, some cooperative patterns enable to enlarge the efficiency area of DTI provision with respect to the equipment rate. The issue of information credibility is discussed.
Association for European Transport