8.2 ROUTE CHOICE BEHAVIOUR:

Transcription

1 8.2 ROUTE CHOICE BEHAVIOUR: The most fundamental element of any traffic assignment is to select a criterion which explains the choice by driver of one route between an origin-destination pair from among the number of potential paths available Wardrop criterion: Wardrop had proposed two criteria that might be used to predict the paths between an origin and destination pair. They are: 1. System optimal equilibrium criterion. 2. User optimal equilibrium criterion. System equilibrium criterion: the trip times on all the routes actually used are equal and less than those which would be experienced by a single vehicle on any unused route The first criterion is quite likely in practice. It is assumed that traffic will tend to settle down into an equilibrium situation in which no driver can reduce his journey time by choosing a new route. The relationship labelled average travel time shows the variation in the average travel time faced by individual vehicles as the traffic volume increases. For example, when the traffic volume is 2000vehicles per hour, each vehicle will experience an average travel time of 5.0 minutes per mile. When the volume is 3000 vehicles per hour, then each vehicle will experience an average travel time of 15.0 minutes per vehicle. The second relationship labelled marginal travel time, shows the increase in the aggregate travel time experienced by all vehicles as traffic volume increases. At low traffic volumes, the marginal or additional total travel time contributed to all vehicles by an additional vehicle entering the traffic stream is small. At a volume of 3000 vehicles per hour the average travel time per vehicle is 15 minutes. The marginal travel time imposed on the set of vehicles by one additional vehicle is 105 minutes. The extra vehicle would actually experience a travel term increased by 90 minutes.

2 Figure 8.3 Variation of Travel Timee with Traffic Volume Wardrop s first criterion is equivalent to the notion of average cost pricing of economic theory. Drivers might be regarded as acting selfishlyy in that they consider only their own individual travel times in making route choice decisions,, and not the manner in which their route choice influences the aggregate travel time experienced by all motorists. That is, they base their route choice decisions on the average travel time relationship. User equilibrium criterion: The average journey times of all motorists are a minimum which implies that the aggregatee vehicle hours spent in travelling is a minimum. A user optimal pattern refers to the individual point of view of each motorists who tends to be unaware of, or at least to be unresponsive to, certain costs he imposes on others. Hence the driver will rationally not take into account these costs inn his travel related decisions. Drivers are only concerned with the private costs that they must bear themselves such as petrol costs, the time cost of making the trip and maintaining the vehicle. Consequently, motorists tend to underestimate the social cost of trip that should include all impacts of their activities on others. A path flow is called Wardrop user equilibrium when no driver has less costly alternate route.

3 Wardrop restated each path in use operates at minimum cost and each unused path shows at least minimum cost. Wardrop s second criterion implies that motorists select their routes according to the marginal cost criterion of economic theory. Drivers are thought to as acting as though they are aware of the way in which their route choices influence travel times of all drivers using the road network. If motorists react to the marginal costs they create when they choose a route, then the total travel time of all vehicles using the system will be minimized. A number of studies of the route selection behaviour of motorists have shown that motorists behave according to some criterion intermediate between the two criteria. Blunden and Taylor both argue that wardrop s second criterion describes the route choices of motorists better than Wardrop s first criterion. However, this evidence is far from conclusive and most of the traffic assignment techniques used on a routine basis in urban transport studies assumes that Wardrop s second criterion governs trip-distribution behaviour. The other trip-distribution techniques assume that the minimum individual average travel times govern trip-distribution behaviour Diversion Curves Diversion curve models was developed in early 1950s to know how many drivers would be diverted from arterial streets to a proposed freeway in order to make decisions related to the geometric design and capacity of proposed urban freeways. This model employs empirically derived curves to compute the percentage of trips that would use the freeway in route between two points on some measure of relative impedance between the freeway route and the fastest arterial route between the two points. California diversion curves These curves used travel-time and travel-distance differences between two alternative paths to estimate the percentage of trips that would use the freeway. The formula for determining percentage usage of the freeway in route between two points is given by

4 Where p = percentage usage, d = distance saved in miles, t = time saved in minutes, The diversion curve developed by Californiaa diversion curve method is shown in figure 8.4. Figure 8.4 California diversion curves Detroit diversion curves The Detroit Area Transportation study estimated diversion from a somewhat different viewpoint, still using a two-parameter approach. In this case, the parameters found to be related to freeway usage were the ratio of expressway speed to arterial speed, and the ratio of expressway distance to arterial distance. In each case the minimum applicable path was used for the ratio computations. The diversion curve developed by Detroit Area Transportation Study is given in fig 8.5.

5 Figure 8.5 Detroit diversion curves Bureau of Public Roads Diversion Curve Undoubtedly, the most widely used method of diversionn is that which is available in the Bureau of Public Road s series of trafic planning computerr programs. This form of diversion is dependenat on one parameter only, the ratio of travel times by the quickest combined arterial- single freeway route to the quickest arterial-only route. With a one-parameter relationship, one diversion curve defines the relationship. The form of S-shaped diversion curve is similar to those used in the Detroit study for higher speed ratios. Total freeway usage occurs when the travel time ratios fall below 48% while no freeway usage can bee anticipated when the travel time ratio exceeds 150% of the quickest surface route.diversionn curve developed by Bureau of Public Road s is given in Figure 8.6.

6 Zone to Zone usage of freeway in percent % USAGE EQUAL TIME TRAVEL TIME RATIO PASSENGER CARS Figure 8.6 Diversion curve developed by Bureau of Public Road s The following formula can be fitted to these curves: Where p = percent of traffic diverted to new system t r = travel time ratio =.