Transit Network Sensitivity Analysis

Transit network conditions change everyday. While those changes should be considered for modifying a transit network, formulating and optimizing the whole transit network may be a costly, difficult task. This article uses a developed transit network design model to examine how optimal transit networks should be developed based on changes in input elements of the transit network. Three major inputs—demand, travel speed, and transfer penalty—are chosen for the sensitivity analysis. Different optimal transit networks and their characteristics are generated, and the relationship between inputs and outputs is discussed. Using the sensitivity analysis, three typical transit networks—transferoriented transit, transfer-avoidance transit, and directly-connected transit—are introduced. Optimal types of transit networks are suggested based on transit network situations. Introduction It is not easy to design an optimal transit network because of complexity in formulation and optimization. Although current techniques of optimization enable operators to design more efficient transit networks, optimizing whole networks is extremely costly and presents difficulties in implementing changes. The situation around the transit network changes everyday. Although those changes appear small, after a certain period of time they can become big enough Journal of Public Transportation, Vol. 9, No. 1, 2006 92 to alter the transit network. However, designing a totally new transit network is not easy because of the complexity of the optimization process and the users’ ability to adapt to a totally new transit network. Thus, rather than designing a new transit network, in many situations modifying an existing one is a better alternative. In modifying a transit network, it is important to understand the relationship between transit network design inputs and outputs. To produce outputs using different inputs for the transit network, it is necessary to build a model to generate a transit network. In this research, Lee’s model (Lee 1998; Lee and Vuchic 2005) is used. With Lee’s model, first basic network inputs are applied. Then, to pursue sensitivity analysis, different inputs are used to compare the outputs, so the relationship between inputs and outputs can be analyzed. Finally, using the results of the sensitivity analysis, three typical types of the transit networks are developed. The Model for the Transit Network Design Much research has been done to improve transit network design. Numerous scholars, including Newell (1979) and Baaj and Mahmassani (1991), have pointed out that traditional mathematical programming has difficulties in generating an optimal transit network due to nonlinearity and nonconvexity of the model, combinatorial explosion, multiobjective nature, and spatial layout of routes. With the improvement of search algorithms and computer technology, important heuristic research has been done (Hasselström 1981; Baaj and Mahmassani 1991; Shih, Mahmassani, and Baaj 1998; Ceder and Israeli 1998; Pattnaik, Mohan, and Tom 1998; Chien, Yang, and Hou 2001). All of these studies are based on the combinatorial search approach. One key point of the combinatorial approach is efficient generation of sample spaces, which are candidate routes and candidate sets of routes. Depending on the generated sample spaces, the optimality of the results is basically decided, even if an improvement procedure follows. Also, the number of generated candidate routes and candidate sets of routes are critical in this method. If the numbers are too large, then this method becomes close to the all-enumeration method. If they are too small, it is hard to generate good routes and sets of routes for the sample spaces. Thus, this approach tends to rely on the network designer’s knowledge to obtain a good simplified sample space. Also, consistency and generalization of the network designer’s knowledge are required. Another key point is the flexibility of Transit Network Sensitivity Analysis 93 the methodology in respect to handling constraints. Although the combinatorial search approach may yield good results with given fixed inputs, it is not flexible enough to include certain dynamic inputs, particularly those such as variable transit demand. Lee’s model uses the iterative approach to solving the transit network design problem. This approach is flexible enough to deal with dynamic characteristics of transit network design. To execute this methodology, the computer software TRANED (TRAnsit NEtwork Designer) was programmed with C++. Algorithm of the TRANED Unlike auto travel, which increases auto travel time with increased auto travel demand due to congestion, increased transit travel demand decreases transit travel time due to the higher service frequency. However, to have more transit riders under fixed transit demand, circuitous routing is unavoidable. Circuitous routing results from a trade-off relationship between in-vehicle travel time and waiting time in a transit network. The methodology of this research is based on the “concentration of flow” concept, which was introduced and used by Rea (1971) and Hasselström (1981), although they limited its usage to the realization and applications as mentioned. The iterative approach in this article looks for the minimum total travel time network starting from generating the minimum in-vehicle travel time network. The transit network is gradually improved by increasing in-vehicle travel time while decreasing waiting time. This algorithm consists of three major steps: generation of an initial network, assignment, and network improvement. They are followed by a supporting step, network analysis. These steps are iterated until the optimal transit network is generated, as shown in Figure 1. The generated optimal transit network provides direct connections to major travel flows, while also providing shorter waiting times to minor travel flows by generating circuitous travel paths. The first step involves generating the initial network with the minimum number of routes using the shortest path algorithm (Dijkstra 1959; Whiting and Hillier 1960; Dantzig 1967). This step provides minimum in-vehicle travel time paths to all origin-destination pairs. For this procedure, the shortest paths for all origin-destination pairs are generated; included paths are then eliminated to avoid unnecessary overlapping paths. The second step repeats the transit assignment procedure, which concentrates transit travel flow to certain routes. This procedure allows higher frequencies of Journal of Public Transportation, Vol. 9, No. 1, 2006 94 Figure 1. Final Procedure for Transit Network Design for the Basic TRANED Model Transit Network Sensitivity Analysis 95 certain routes and shorter total travel time. As a result, less efficient routes are eliminated from the network. The third step improves the transit network by changing the alignments of routes. After building an initial network and adjusting it to assignment procedure, some alignment changes of certain routes for the improvement of the network should be considered for reducing users’ travel times. After stabilizing frequencies of routes in the transit network through repeated assignment procedures, routes are reviewed and alignments are changed where necessary. Less frequent routes require longer waiting times that cause longer travel times so they would be considered first. Since the network consists of selected routes, routes in Baaj and Mahmassani’s initial network may need to be split and branches changed in addition to merging routes (1991). However, the procedure in this analysis merges routes and removes unused nodes for network improvements, because the initial network of this study starts from all shortest travel time routes. There are two cases for merging routes. One involves merging routes that have shared trucks and same-directed branches; the other has shared trucks and opposite-directed branches. If branches of two routes go from the same station of the shared trunk section, it is called same-directed branches. If branches of two routes go from the different stations of the shared trunk section, it is referred to as opposite-directed branches. Network analysis is the supporting step to generate outputs resulting from the above steps. The outputs of each step, such as number of routes, total travel time, and frequency of routes, are compared to those of the previous step. The results of this procedure were generated and compared with other research (Mandle 1979; Baaj and Mahmassani 1991) to prove the validation of the methodology (Lee 1998). The results show that transit networks generated by TRANED generally require less travel time for users. This basic model is simple; however, because of the flexibility of the mathematical programming of the iterative approach, this methodology can add various realistic constraints to the basic model. Additional constraints to those in the basic model are operational and financial limitations, coordination with existing service (intermodal coordination), express service, schedule information for users, and variable transit demand. Journal of Public Transportation, Vol. 9, No. 1, 2006 96 Inputs and Outputs of the Transit Network To generate a transit network using Lee’s model, input elements for the model required are as follows: • Template network (basic network with links and nodes); • Origin-destination travel demand; • Distance or in-vehicle travel time on each link by mode; • Transit unit (TU) capacity of given mode; • Relative weight for waiting time compared to in-vehicle travel time; • Transfer penalty; and • Relative weight for transfer time compared to in-vehicle travel time. For the purpose of analyzing the network generated by TRANED, the following network characteristics are also computed by TRANED in addition to the basic output-network configuration and frequencies of routes: • Network configuration or route configurations [-]; • Frequencies of routes [vehicle/h]; • Total in-vehicle travel time in the network [person-minutes/h]; • Total waiting time in the network [prs-min/h]; • Total transfer time in the network [prs-min/h]; • Total transfer penalties in the network [prs-min/h]; • Total travel time in the network [prs-min/h]; • Total travel time except in-vehicle travel time [prs-min/h]; • Travel demand without transfer [prs]; • Travel demand requiring transfer [prs]; • Total travel demand [prs]; • Degree of circuity [%]; • Number of routes [-]; • Total route length in the network [km]; • Average route length [km]; and • Total vehicle operational time in the network [veh-min/h]. Transit Network Sensitivity Analysis 97 Most of the outputs are self-explanatory, but some require additional explanation. The degree of circuity is the parameter showing the indirectness of travel. There are two types of circuities: physical circuity and time circuity. While physical circuity represents circuity of routes, time circuity represents circuity of travel. The main differences between the two are transfer time and penalty. While physical circuity does not include transfer time and penalty as extra costs, time circuity considers them as extra costs due to the indirectness of a route. Time circuity, used in this study, is the ratio of the extra travel time after boarding a transit vehicle due to the indirectness of routes, possible transfer time, and transfer penalties to the shortest in-vehicle travel time (equation 1). Degree of circuity in the network is the average of an individual user’s degree of circuity. DOC [%] = 100 · , (1)