Dynamic Trip Assignment-Simulation Model for Intermodal Transportation Networks

Transcription

1 52 Transportation Research Record 1771 Paper No Dynamic Trip Assignment-Simulation Model for Intermodal Transportation Networks Khaled F. Abdelghany and Hani S. Mahmassani A dynamic trip assignment-simulation model for urban intermodal transportation networks is presented. The model considers different travel modes, such as private cars, buses, metro-subway, and high-occupancy vehicles. The model captures the interaction between mode choice and traffic assignment under different information provision strategies. It implements a multiobjective assignment procedure in which travelers choose their modes and routes based on a range of evaluation criteria. The model assumes a stochastically diverse set of travelers in terms of their relevant choice criteria and access and response to the supplied information. The model overcomes many of the known limitations of static tools used in current practice. These limitations relate to the types of alternative measures that may be presented and evaluated and to the policy questions that planning agencies are increasingly asked to address. Considerable research over the past decade has been directed toward modeling route choice dynamics in urban transportation networks. Most existing and proposed dynamic traffic assignment (DTA) models have focused on passenger cars as the principal, if not the sole, component of urban traffic and the main source of traffic congestion. These models do not provide the capability of assigning transit trips and capturing the interaction between mode choice and traffic assignment. Ignoring such interaction limits the applicability of these models in congested urban networks that include a considerable number of transit and intermodal trips. For instance, the DYNASMART (dynamic network assignment simulation model for advanced road telematics) simulation-assignment model (1, 2) includes buses as part of the vehicular mix; these follow prespecified routes and timetables. However, the assignment of individual trips to the transit lines and the choice of mode of travel are exogenous to the model. As such, the model s capabilities are not sufficient to evaluate a range of intelligent transportation system user services targeting public transportation systems (APTS) and certain advanced traveler information systems (ATIS) intended to serve transit and intermodal system users. Such capabilities require explicit representation of the supply characteristics of the system, in the form of a multidimensional network model of the available modes and their interaction along links as well as at nodes, and the user decision processes that govern the choice of mode or intermodal combination along with the associated path. A DTA-simulation model for intermodal urban transportation networks that provides these capabilities is presented here. The model framework is a generalization of the approach underlying the DYNASMART simulation-assignment model. The implementation is a major reengineered extension of the previous capabilities of the Department of Civil Engineering, ECJ 6.2, University of Texas at Austin, Austin, TX software. However, the intermodal framework is not limited to this particular simulation-assignment tool and could be implemented with alternative platforms. The new model approach considers intermodal transportation networks consisting of different travel modes such as private cars, buses, metro-subway, and high-occupancy vehicles (HOVs). The model captures the interaction between mode choice and traffic assignment under different traveler information provision strategies. It implements a multiobjective assignment procedure in which travelers choose their modes and routes based on a range of choice criteria. The model assumes a stochastically diverse set of travelers in terms of underlying preferences (relevant choice criteria and associated trade-off rules) as well as in terms of access and response to the supplied information. The modeling tool is intended primarily for operational planning applications, and it could also be used in conjunction with real-time traffic management systems. As a within-day dynamic assignment procedure, it overcomes many of the known limitations of static tools used in current practice. These limitations relate to the types of alternative measures that may be analyzed and to the policy questions planning agencies are increasingly asked to address. A review of mode-route choice modeling is presented in the next section. The conceptual framework and structure of the model are then presented, followed by a description of the vehicle simulation components, especially those pertaining to the newly implemented transit and intermodal elements. Two sections present the assignment components of the model, which include the multiobjective shortest path algorithm and the mode-route choice procedures. A set of simulation experiments designed to illustrate the capabilities of the model are presented, followed by discussion of the results. Concluding comments and areas for future research are outlined in the final section. MODE-ROUTE CHOICE DYNAMICS IN INTERMODAL NETWORKS Several approaches have been proposed over the past two decades to model and analyze transportation networks with several interacting modes. These approaches have addressed primarily static assignment problems jointly with mode choice. Early contributions considered the multimodal version of the problem, in which an entire trip takes place by a single mode of travel from origin to destination (3 9). Trips are hence separated by mode and separately assigned to each mode s subnetwork, with possible interactions captured through the link performance functions when transit vehicles and passenger cars share the same right-of-way. In these approaches, intermodal trips are modeled as a sequence of independent trips generated at the initial origin node and at intervening transfer nodes where travelers switch to differ-

2 Abdelghany and Mahmassani Paper No ent modes. The transfer phenomenon inherent in intermodal trips is not represented in these models. In another similar approach, intermodal trips are considered in the formulations by defining every feasible combination of modes or a subset of the more meaningful combinations of modes as a new mode that is added to the mode choice set (10, 11). Different assignment procedures have been proposed in the literature for transit trips, typically for the static case. A review is given by Baaj (12). An early approach, similar to the automobile assignment, assigns passengers to the minimum expected travel time path in the transit network (13, 14). A more reasonable behavioral representation of the choice process defines a set of feasible paths from which passengers can choose to minimize their expected travel times (15 18). For example, Spiess and Florian (15) used the term optimal strategy to describe a feasible path in the traveler s choice set. The number of strategies a traveler may choose from depends mainly on the information that is available during the trip. The method proposed by Andersson (19) moves toward more realistic behavior representation of the passengers choice than simply minimizing the travel time. It enumerates a set of paths among which one is selected by a rather elaborate set of heuristic rules that appear to work quite well in practice. An example of these heuristic rules is also presented by Han and Wilson (20) and implemented by Baaj and Mahmassani (21) and Shih and Mahmassani (22) in their transit network design model. The brief overview of existing approaches reveals several types of limitations. Foremost among these is the incomplete representation of intermodal trips, by not allowing explicitly for transfers between modes, associated waiting times, and other unique attributes of intermodal travel. Second, limitations exist in modeling the supply interactions among the various available modes, especially when the infrastructure is shared. The third set of limitations arises from the assumption of static versus time-varying network conditions, including time-varying demand and associated congestion patterns. The limitations of static assignment models for congested network modeling, for both automobiles and transit modes, are well recognized in the literature (23), particularly with regard to ATIS-ATPS applications. The last, but not least, set of limitations arises from the behavioral assumptions governing user s choice of mode or intermodal combinations along with selection of a specific path in the associated intermodal network. For example, most existing formulations consider travel time as the only criterion for mode-route choice, thereby ignoring the trade-offs among the conflicting criteria that travelers usually consider in their decision process, such as access and waiting times, parking cost, and number of transfers. Dial (24) proposed an algorithm for the bicriterion traffic assignment problem. The two criteria considered are assumed to be flow dependent and integrated through a generalized cost function. However, the problem is formulated only for the single-mode static case. Introducing these considerations in the interest of greater behavioral realism in mode choice and assignment procedures generally introduces mathematical complications that preclude direct application of mathematical programming models to well-behaved formulations. Hence, a simulationbased approach to the dynamic assignment problem in intermodal networks is adopted in this work in an attempt to combine behavioral realism with tractability, efficiency, and relevance to practice. CONCEPTUAL MODEL The model represents several modal networks through a single integrated multidimensional network. Associated with each link are two state vectors for each time interval, representing the number of vehicles of each class on the link and the associated cost incurred by each class in traversing that link (when the link is entered during the specified time interval). There is no restriction on the number and types of vehicle classes that may be considered in the model. Typical classes of relevance to the study of intermodal networks include automobiles, trucks, and various types of transit modes. They may also include HOV vehicles. The associated cost vector provides the principal mechanism for designating certain links for particular classes. For example, a very high cost for a single-occupant automobile on a certain link, coupled with the actual travel time for an HOV, could indicate a special HOV facility. Similarly, a transit network may be represented to allow both exclusive (for example, underground rail) and shared right-of-way (e.g., buses). Transfer penalties at major transfer nodes in the network are explicitly modeled. For each traveler, the waiting time until the arrival of the next vehicle that serves the chosen transit line and the parking cost at the park-and-ride facility are considered when the different travel options are evaluated. The model captures explicitly the dynamic interactions between mode choice and traffic assignment in addition to the resulting evolution of the network conditions. It determines the time-dependent assignment of individual trips to the different mode routes in the network, including the corresponding arc flows and transit vehicles loading. Figure 1 presents the modeling framework and the different components designed to address the problem requirements. As noted, the model can accept as demand input a file listing the population of travelers, their attributes and travel plans (including origins, destinations, time of departure), and mode choice if known. However, a more likely way to apply the model is to generate travelers on the basis of prespecified time-dependent origin-destination zonal demands. Each generated traveler is assigned a set of attributes, which include his or her trip starting time, generation link, final destination, and a distinct identification number. A binary indicator variable is also assigned to each traveler to denote car ownership status. In parallel, transit vehicles are generated according to a predetermined timetable and follow predetermined routes. Prevailing travel times on each link are estimated with the vehicle simulation component, which moves vehicles and captures the interaction between automobiles and transit vehicles, as described later. The model also estimates other measures that may be used by travelers as criteria to evaluate the different mode-route options, including travel distances, parking cost, highway tolls, transit fares, out-of-vehicle time, and number of transfers along the route. A mode-route decision module is activated at fixed intervals to provide travelers with a superior set of mode-route options. The activation interval (usually in the range of 3 5 min) is set so that the variation in network conditions is captured, while retaining desirable computational performance for the procedure. The route-mode decision module consists of a multiobjective shortest path algorithm designed for large-scale intermodal transportation networks, which is described separately. This multiobjective shortest path algorithm generates a set of superior paths in terms of the set (or a suitable subset) of attributes listed. Considering a diverse set of travelers behavioral rules and different levels of information availability and response, travelers evaluate the different mode-route options and choose a preferred one. These behavior rules and response mechanisms are implemented through a behavior component within the model as described in a later section. Each option represents an initial plan that a traveler follows (unless he or she receives en route real-time information of a better plan) to reach his or her final destination. This plan describes the

3 54 Paper No Transportation Research Record 1771 FIGURE 1 Overall modeling framework. mode(s) used and the route to be followed including any transfer node(s) along the route. Based on the available options, a traveler may choose a pure mode or a combination of modes to reach his or her final destination. If a traveler chooses a private car for the whole trip or part of it, a car is generated and moved into the network with a starting time equal to its driver s starting time. Each newly generated vehicle is assigned a number unique to that vehicle. Vehicles are then moved in the network subject to the prevailing traffic conditions until they reach their final destinations or the next transfer node along the prespecified route (in the case of an intermodal trip). If a traveler chooses a transit mode, he or she is assigned to a transit line so that the destination of this passenger is a node along the route followed by the bus line. If no single line is found or if the passenger is not satisfied with the available single line, the passenger is assigned to a path composed of two lines with one transfer node, so that the destination of the passenger is a node along the route followed by the second bus. If two such lines are not found, the search is continued for three lines with two transfers. It is assumed that no passenger is willing to incur more than two transfers in his or her trip. Thus, if no path with a maximum of two transfers is available, the trip is indicated as infeasible. Given the passenger s origin node, the nearest transit stop along the first line in the passenger s path is determined, and he or she waits until the arrival of the next vehicle that serves that transit line. When a transit vehicle arrives at a certain stop, all passengers waiting for a vehicle serving that line board the vehicle (subject to a capacity constraint) and head toward either their final destination or the next transfer node along their route. On arrival of a vehicle (private car or transit vehicle) to a certain destination node, this destination is compared with the final destinations of the travelers on board. If it matches the final destination of a traveler, the current time is recorded for this traveler as his or her arrival time. If they are different, the traveler transfers to the next transit line in his or her plan. The nearest stop is again determined and the traveler waits for his or her next transit vehicle. The time difference between arrival at the transfer node and boarding of the next line is calculated as the waiting time at the current transfer node for this traveler. This process is continued until all vehicles reach their final destination. If a traveler misses the initially assigned transit vehicle because of late arrival or because the vehicle does not have enough space, the model allows the traveler to replan his or her trip. The available options are regenerated for the traveler, and he or she makes a selection according to the decision process described in a later section. VEHICLE MOVEMENT SIMULATION The vehicular traffic flow simulation logic in DYNASMART has been adapted to better represent interactions among transit vehicles and automobiles. The essential features of the traffic flow simulation logic have been described elsewhere and are not repeated here (1, 2). For completeness, those elements that pertain to transit vehicle simulation in the context of the overall traffic flow simulation are briefly described. This simulation component is a time-based simulation that moves individual vehicles along links according to local speeds determined consistently with macroscopic traffic stream models (a speed-density relation, of modified Greenshield s form, is used in this implementation). Every time step, the number of vehicles on each link is cal-

4 Abdelghany and Mahmassani Paper No culated by using conservation principles; numbers in each class of vehicles in the traffic mix are kept separately. Consistent with the macroscopic logic for modeling vehicle interactions, average passenger car equivalent factors are used to convert each vehicle type to the equivalent passenger car units. The resulting equivalent-car concentration is then calculated for each link and used to estimate the corresponding speed through the speed-density relation. These speeds, updated continually to reflect prevailing conditions, determine vehicular movement on that link. Queueing and turning maneuvers at junctions are explicitly modeled, thereby ensuring adherence to first-in, first-out principles and traffic control devices at junctions. Vehicles that reach the end of the link and are unable to move to a downstream link because of capacity limitations join the back of a queue of vehicles at the downstream end of the link. The physical size of the queue is explicitly represented in the simulation, resulting in the division of the link into a moving part and a queueing part. Vehicles that reach the back of the queue must wait until vehicles ahead of them are discharged. All inflow and outflow constraints that limit the number of vehicles entering and leaving each link under the prevailing traffic control are implemented. The right-of-way among competing movements is allocated according to the existing control element at every intersection. The outflow constraints limit the maximum number of vehicles allowed to leave any given approach of an intersection, reflecting the available vehicles in queue and outflow capacities of the approach under the prevailing control. The inflow constraints bound the total number of vehicles that are allowed to enter a link. These constraints bound the total number of vehicles from all approaches that can be accepted by the receiving link, which reflects both physical storage consideration and inflow throughput capacity. If a bus stop is located along a particular link, and a bus is stopped there, the storage capacity of the link is reduced accordingly to represent the bus stopping effect. In addition, the inflow and outflow rates of this link are adjusted based on the location of the bus stop within the link. A near-end stop (located at the upstream end of the link) reduces the link inflow rate and a far-end stop (located at the downstream end of the link) reduces the link outflow rate. The factors by which the storage capacity and the flow rates are reduced can vary from one complete lane blockage to zero lane blockage in the event of a special-purpose bus bay. DYNASMART allows representation of complete transit networks with both exclusive and shared infrastructure. This flexibility is allowed by its integrated multidimensional network representation as described previously. A set of bus lines is defined in terms of the constituent routes, for which the average headway, stop locations, and vehicle capacities are specified. Different bus capacities may be specified for the different routes. Given a timetable, buses are generated from their origin terminals and moved in the network along their prespecified routes following prevailing traffic conditions. The model tracks all buses along their routes and records their respective arrival times at each stop. On arrival at a bus stop, buses are held to allow passengers to board and alight. The number of passengers on-board (bus occupancy) is updated, representing the new bus occupancy, which is also tracked along the vehicles routes. If a vehicle is full, no passengers are allowed to board and all waiting passengers are reassigned to the next bus or to another trip plan. The model is capable of simulating special bus services such as express service with limited stops and bus services with different deadheading strategies in which some stops may be skipped under certain conditions. The metro-subway service model is quite similar to the bus service model in most of its features. However, metro vehicles are assumed to have their separate right-of-way and hence move at predetermined speeds. MULTIOBJECTIVE SHORTEST PATH ALGORITHM As mentioned previously, the model applies a multiobjective assignment procedure. This is implemented through a multiobjective shortest path algorithm that is designed especially for large-scale intermodal networks. This section defines briefly the multiobjective shortest path problem and describes the algorithm implemented within the current version of the model. More detail can be found elsewhere (25). Compared with the traditional single-objective shortest path (SOSP) problem, the multiobjective shortest path (MOSP) problem has two main characteristics: First, in the normal sense of optimal solution, the multiobjective shortest path problem generally has no optimal solution, in that there is no guarantee that a single path that simultaneously optimizes all objectives exists. For instance, in a transportation network, the least expensive paths usually have the longest travel time, and the fastest ones are usually the most expensive. Nevertheless, the set of pareto optimal or nondominated paths can be determined. This set has the following characteristics: for any nondominated path, it is not possible to determine a path that improves some of its objectives without at least one of the remaining ones getting worse. Second, the MOSP is known to be a nonpolynomial-hard problem (26), which means that there exists a family of graphs for which the number of optimal paths grows exponentially with the number of nodes in the network. Listing these paths would require an exponential number of operations, and thus no polynomial behavior can be expected. The implemented MOSP algorithm defines an intermodal transportation network as a set of layers so that each layer represents the subnetwork of a certain mode. It determines the nondominated paths from all nodes in the network to all destinations. The logic of the implemented algorithm is based on the divide and conquer technique in which the nondominated subpaths between every two transfer nodes in the network are first determined. The search in this step includes all modes subnetworks (layers) connecting these two transfer nodes. These nondominated subpaths are then composed together to generate the nondominated (single mode and intermodal) paths between the origin and the final destination. Different algorithms have been suggested in the literature to determine the nondominated paths between two nodes (26 29). Abdelghany and Mahmassani (25) implemented and compared two of these algorithms for the purpose of application to intermodal DTA: the multilabeling shortest path algorithm and the k-shortest path algorithm. The idea of the multilabeling algorithm is that the function equation is extended from a scalar function to a vector-valued function so that all objectives under consideration are included. In addition, the standard minimization performed at each node is replaced by the selection of the nondominated paths. The idea of using the k-shortest path algorithm is that paths are being determined by nondecreasing order of one of the objectives until all or at least a considerable number of the nondominated paths are determined. The number of nondominated paths in the final set depends mainly on the value of the parameter k. The multilabeling algorithm was found to outperform the k-shortest path algorithm in terms of the number of determined nondominated paths in the experiments conducted. However, the k-shortest path algorithm succeeded in finding a considerable number of these nondominated paths (at low value of k) in much less

5 56 Paper No Transportation Research Record 1771 execution time. For this reason, the k-shortest path algorithm is implemented in this model. The k-shortest path implementation guarantees polynomial time execution on the model subnetworks. It also allows the generation of k paths from each origin to all destinations when a conventional single-objective assignment is being performed. MODE-ROUTE CHOICE MODELING The model assumes a stochastically diverse set of travelers with different relevant choice criteria and response mechanisms to externally supplied information. The model framework allows implementation of different mode-route choice models that might adequately represent the travelers behavior. The implemented model could be deterministic or stochastic and could be based on compensatory or noncompensatory choice rules. Deterministic models assume the availability of perfect information for travelers and that travelers choose the best alternative based on the available information. Stochastic models (e.g., logit form or probit form), on the other hand, take into consideration that information might not be perfect and that travelers may have different perceptions of the supplied information. For the experiments presented here, travelers are assumed to evaluate the different available alternatives either at the start of or during (in the case of en route information availability) their trip based on a deterministic utility function. The multiobjective k-shortest path algorithm with k = 3 is used to generate the different attributes for the nondominated paths from every node to every destination. This function combines all the attributes in one generalized cost measure. Travelers evaluate the generalized cost of the different alternatives and choose the one with the minimum generalized cost. EXPERIMENTAL DESIGN Different sets of simulation experiments are designed to illustrate the functionality and the capabilities of the model and to show the significance of including the mode choice dimension in the DTA framework. Figure 2 presents the test network used in these experiments, which represents the south central corridor in the Fort Worth, Texas, area. The network consists of a freeway (I-35W) surrounded by a street network with a total of 178 nodes and 441 links, distributed over 13 zones. Twelve bus lines are assumed to connect these zones through the main corridors in the network as indicated (Figure 2, bold lines). Although the highway network is the actual system currently in operation in the area, the transit network is introduced here for illustrative purposes only and does not correspond to available service (which is very limited). A total demand of about 11,000 travelers is generated over 20 min of the peak period. The simulation is terminated and statistics are collected when all travelers reach their final destinations. Travelers are assumed to have pretrip information on available alternatives. They are also assumed to evaluate these different alternatives according to a prespecified deterministic utility function, in which the attributes associated with each alternative are evaluated in terms of a generalized cost measure. Two main attributes are considered in these experiments: total travel time and total travel cost for the trip. A fixed value of time across all travelers taken as $6.00/h is used to calculate the generalized cost measure. Of course, a distribution of these values could readily be used instead. All travelers are assumed to own a car and to consider transit and intermodal trips that involve at most one transfer along the trip. Thus, four modal options are assumed to be available for each individual as follows: private car, one bus line, two bus lines with one connecting transfer, and park-and-ride with one intermodal transfer. In all experiments, the average travel time for all travelers, average travel time for passengers only, and average vehicular travel time (for buses and automobiles) are recorded. In addition, the trip shares of the four options mentioned previously are presented. The effect of different information supply strategies is examined in the first set of experiments. Four different information schemes are considered, which are partly confounded with the awareness level of different modal and intermodal routing alternatives. Providing travelers with information on transit availability and opportunities for easy transfer and parking availability might induce many private car users to leave their cars and use a transit mode. The first scheme represents the full information scheme in which travelers are assumed to have perfect information on transit lines, opportunities for transfer between these lines, and park-and-ride facilities in the network (full information). The second scheme assumes that travelers have no information on the transit service in the network. All travelers in this case are assumed to use their private cars (no transit information). The third information scheme assumes that travelers have no information on the available transfer options between the different transit lines. Passengers use buses only if there is a single line connecting their origin to the desired final destination (no transfer information). The last scheme considers the case of not having information on the park-and-ride facilities in the network (no parking information). Thus, travelers cannot switch from their private cars to buses. The second set of experiments studies the effect of private car operating-toll cost on trip modal split and resulting overall network performance. The case in which trip travel time is considered as the only choice criterion is compared with other cases in which both trip time and trip cost are considered in evaluating the different travel options. A fixed cost per link that ranges from $0.00 to $0.30 is assumed. This cost represents out-of-pocket cost for tolls and hidden operating cost that travelers might consider. In this set of experiments, all bus lines are assumed to operate at a frequency of 24 buses/h with the flat fare taken as $0.50. Free parking is assumed for all private car users. In addition, all travelers are assumed to have full information about the modal and intermodal routing alternatives in the network (full information scheme). The third set of experiments studies the effect of parking availability and pricing on travelers mode-route choice and overall network performance. A flat fee (that does not depend on parking duration) that ranges from $0.00 to $4.00 is assumed at all parking facilities in the network. Fees are imposed on all private car drivers who use their cars for the whole trip or for only part of it (park-andride trip). In these experiments, all bus lines are operated at a frequency rate of 24 buses/h and $0.50 flat fare. A full information scheme in which all travelers are assumed to have complete information about all possible travel mode options is used. The last set of experiments examines the effect of transit availability on modal split and resulting overall network performance. The network performance is compared under three bus frequency levels: 12, 24, and 40 buses/h. These frequencies are assumed to be the same for all the bus lines. Results are obtained for two cases: the operating-toll cost of the private car is ignored, and an operating-toll cost of $0.20 per link is assumed across all private car users. A flat bus fare, taken as $0.50, is assumed for the 12 bus lines. In addition, no parking fees are imposed at any of the parking facilities in the net-

6 FIGURE 2 Test network showing simulated transit lines.

7 58 Paper No Transportation Research Record 1771 work, and all travelers are assumed to have full information about all possible travel options. SIMULATION RESULTS AND ANALYSIS Figure 3 presents the network performance under the four information schemes. Three different measures are used to compare the different information supply schemes that include average traveler travel time, average passenger travel time, and average vehicular (buses and automobiles) travel time. As indicated in Figure 3, the best network performance in terms of the average vehicle travel time and the average passenger travel time is obtained under the full information scheme. When no transit information is available, the transit trip share decreases significantly, which results in more private car use and more network congestion. An increase of 21 percent is observed in the average traveler travel time. Similarly, when no information about the transfer opportunities is available, fewer travelers consider the parkand-ride and the two-bus trips as travel options. This also results in more private car use and more network congestion; the average vehicle travel time is increased by about 31 percent, and the average passenger travel time is increased by about 49 percent. Finally, the absence of parking information, which provides the opportunity for easy transfers between cars and the different transit modes, increases private car use and accordingly increases the average vehicle travel time and the average passenger travel time by about 25 and 39 percent, respectively. Table 1 presents the effect of private car operating-toll cost on modal split and network performance. When trip cost is ignored, and travel time is considered as the only choice criterion, the model estimates fewer than 2 percent of travelers using transit. Including trip cost as a relevant choice criterion beside the trip travel time increases the estimated transit share. This share increases linearly with the increase in trip cost. At $0.15 per link, the model estimates about 15 percent of the travelers use transit. This percentage jumps to 47 percent when $0.30 per link is assumed. A significant improvement in the network performance is observed with the increase in transit share. For example, the average traveler travel time decreases by about 5 percent when $0.10 per link is assumed. Corresponding savings of about 18 and 8 percent are estimated in the average passenger travel time and the average vehicle travel time, respectively. The model appears to adequately capture the sensitivity of mode choice to pricing, which is an important characteristic to evaluate measures such as congestion pricing and high-occupancy toll lanes. Although the model requires calibration to the specific conditions of the study area, the exploratory results examined here suggest some likely degree of success of pricing mechanisms to induce some modal shifts. The effect of imposing parking fees on private car users is presented in Table 2. It presents the case when the parking fees are imposed at the final destination of the trip and also at all park-andride facilities in the network. Considering such fees in the travelers mode-route choice process reduces the private car share and increases the transit share. For example, introducing a flat parking fee of $2.00 reduces the private car share by about 9 percent. The reduction in the private car share leads to a reduction in the average travel time by about 10 percent. When the fee is increased to $4.00, the private car share decreases by about 16 percent and the average traveler travel time is improved by about 17 percent. Table 3 presents the effect of increasing the bus service frequency on bus trip share and overall network performance. Based on the obtained results, increasing the bus service frequency does not significantly affect the bus trip share. For example, doubling the service frequency from 12 to 24 buses/h has a very slight effect on the transit share in the zero cost scenario and increases the transit share by only 2 percent (the park-and-ride share is included in this percentage) in the $0.20 travel cost scenario. Although an increase in bus service frequency reduces the average passenger waiting time, the average overall travel time by bus is still higher than that by car. Assuming that all travelers have access to a private car, very few private car users are attracted to use the bus in the zero cost scenario. When the private car trip cost is considered in the mode choice process, more travelers appear to be attracted by the improvement in the bus service as indicated in Table 3. In the zero cost scenario, the increase in the number of running buses slightly increases the FIGURE 3 Effect of information supply schemes on network performance.

8 Abdelghany and Mahmassani Paper No TABLE 1 Effect of Private Cars Operating Cost and Road Toll Cost on Modal Split and Traffic Assignment TABLE 2 Effect of Imposing Parking Fee at Final Destinations and Transfer Nodes on Modal Split and Traffic Assignment TABLE 3 Effect of Bus Frequency on Modal Split and Traffic Assignment at Levels of Link Pricing average vehicle travel time. The frequent bus stops and heavy interaction between automobiles and buses increase the overall congestion level. On the other hand, when the trip cost is considered and more travelers are estimated to use the bus, the average vehicle travel time and the average passenger travel time are improved. As such, improving transit service alone may not be sufficient to attract private car users to rely more on transit and reduce private car use. Other measures that cause them to reduce car use (e.g., information about transit mode availability, imposing parking fees, tolls) have to be accompanied by improvements in transit service as indicated by the results of these experiments. CONCLUSIONS This paper presents a dynamic trip assignment model for urban intermodal transportation networks. The model captures the dynamic interaction between mode choice and traffic assignment and also estimates the effect of this interaction on overall network performance. The model implements a multiobjective dynamic trip assignment procedure in which travelers choose their mode route based on a range of choices. A set of simulation experiments is designed to illustrate the different capabilities of the model. These experiments illustrate the significance of including the mode choice dimension in the

9 60 Paper No Transportation Research Record 1771 DTA framework and also show the importance of the multiobjective assignment procedure incorporated in the model. One set of experiments studies the effect of different traveler information provision strategies. Providing information about transit service availability, opportunity of easy transfer between different transit lines, and parking availability induces many private car users to leave their cars and use a transit mode. Other measures such as imposing roadway tolls and parking fees on private car users and improving transit service are also examined. It should be noted that these results are intended to illustrate the application of a dynamic simulation-assignment methodology to the analysis of intermodal transportation networks. As such, the specific conclusions should be viewed with proper caution, as they reflect several aspects that may be specific to the test bed network, transit service, and demand loading and characteristics that are considered in this paper. Further research is planned for calibrating the model with real data. The model can also be used to explore promising ways to deploy APTS and ATIS by investigating the effect of different penetration and information availability levels. The use of the model to examine mixes of the control measures presented and different information provision schemes is also under consideration. REFERENCES 1. Jayakrishnan, R., H. S. Mahmassani, and T.-Y. Hu. An Evaluation Tool for Advanced Traffic Information and Management Systems in Urban Network. Transportation Research C, Vol. 2, No. 3, 1994, pp Mahmassani, H. S., et al. DYNASMART-X: Real-Time Dynamic Traffic Assignment System System Implementation and Software Design. Technical Report ST067-85, Vol. III. Center for Transportation Research, University of Texas at Austin, Sept Florian, M. A. Traffic Equilibrium Model of Travel by Car and Public Transit Modes. Transportation Science, Vol. 11, No. 2, 1977, pp Florian, M., and S. Nguyen. A Combined Distribution Modal Split and Trip Assignment Model. Transportation Research B, Vol. 12, 1978, pp Florian, M., and M. Los. Determining Intermediate Origin-Destination Matrices for the Analysis of Composite Mode Trips. Transportation Research B, Vol. 13, No. 2, 1978, pp Abdulaal, M., and L. LeBlanc. Methods for Combining Modal Split and Equilibrium Assignment Models. Transportation Science, Vol. 13, No. 2, 1979, pp LeBlanc, L., and K. Fahrangian. Efficient Algorithms for Solving Elastic Demand Traffic Assignment Problems and Modal Split Assignment Problems. Transportation Science, Vol. 15, No. 4, 1981, pp Florian, M., and H. Spiess. On Binary Mode Choice/Assignment Models. Transportation Science, Vol. 17, No. 1, 1983, pp Sheffi, Y. Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Models. Prentice Hall, Englewood Cliffs, N.J., Wardrop, J. G. Some Theoretical Aspects of Road Traffic Research. Proceedings of the Institution of Civil Engineers, Vol. II, 1952, pp Fernandez, E., J. DeCea, M. Florian, and E. Cabrera. Network Equilibrium Models with Combined Modes. Transportation Science, Vol. 28, No. 1, 1994, pp Baaj, M. H. The Transit Network Design Problem: An AI-Based Approach. Ph.D. dissertation. University of Texas at Austin, Dial, R. B. Transit Pathfinder Algorithm. Highway Research Record 205. HRB, National Research Council, Washington, D.C., 1967, pp Le Clercq, F. A Public Transport Assignment Method. Traffic Engineering and Control, Vol. 14, No. 2, 1972, pp Spiess, H., and M. Florian. Optimal Strategies: A New Assignment Model for Transit Networks. Transportation Research B, Vol. 23, No. 2, 1989, pp DeCea, J., et al. Optimal Strategies and Optimal Routes in Public Transit Assignment Models: An Empirical Comparison. Traffic Engineering and Control, Vol. 29, No. 10, 1988, pp Nguyen, S., and S. Pallottino. Equilibrium Traffic Assignment for Large Scale Transit Networks. European Journal of Operation Research, Vol. 37, 1988, pp Hickman, M., and D. Berndtien. Transit Service and Path Choice Models in Stochastic and Time-Dependent Networks. Transportation Science, Vol. 31, No. 2, 1997, pp Andersson, J. A Method for the Analysis of Transit Networks. Advances in Operation Research, 1977, pp Han, A. F., and N. H. Wilson. The Allocation of Buses in Heavily Utilized Networks with Overlapping Routes. Transportation Research B, Vol. 16, No. 3, 1982, pp Baaj, M. H., and H. S. Mahmassani. TRUST: A Lisp Program for the Analysis of Transit Route Configurations. In Transportation Research Record 1283, TRB, National Research Council, Washington, D.C., 1990, pp Shih, M.-C., and H. S. Mahmassani. A Design Methodology for Bus Transit Networks with Coordinated Operations. Center for Transportation Research, University of Texas at Austin, Srinivas, P. System Optimal Dynamic Traffic Assignment in Congested Networks with Advanced Information Systems. Ph.D. dissertation. University of Texas at Austin, Dial, R. B. Bicriterion Traffic Assignment: Efficient Algorithms Plus Examples. Transportation Research B, Vol. 31, No. 5, 1997, pp Abdelghany, K., and H. Mahmassani. Multi-Objective Shortest Path Algorithm for Large Scale Intermodal Networks. Paper presented at INFORMS, Philadelphia, Fall Hansen, P. Bicriterion Path Problems. In Multiple Criteria Decision Making: Theory and Applications (G. Fandel and T. Gal, eds.), Springer, Heidelberg, Germany, 1980, pp Dial, R. B. A Model and Algorithm for Multicriteria Route-Mode Choice. Transportation Research B, Vol. 13, 1979, pp Climaco, J. N., and E. Q. Martin. A Bicriterion Shortest Path Algorithm. European Journal of Operation Research, Vol. 11, 1982, pp Sancho, N. F. A New Type of Multi-Objective Routing Problem. Engineering Optimization, Vol. 14, 1988, pp