مطالعه شبیه سازی طراحی سیستم حمل و نقل پاسخگویی به تقاضا

In this paper we study the impact on productivity of specific operating practices currently used by demand responsive transit (DRT) providers. We investigate the effect of using a zoning vs. a no-zoning strategy and time-window settings on performance measures such as total trip miles, deadhead miles and fleet size. It is difficult to establish closed-form expressions to assess the impact on the performance measures of a specific zoning practice or time-window setting for a real transportation network. Thus, we conduct this study through a simulation model of the operations of DRT providers on a network based on data for DRT service in Los Angeles County. However, the methodology is quite general and applicable to any other service area. Our results suggest the existence of linear relationships between operating practices and performance measures. In particular we observe that for each minute increase in time-window size the service saves approximately 2 vehicles and 260 miles driven and that a no-zoning strategy is able to satisfy the same demand by employing 60 less vehicles and driving 10,000 less total miles with respect to the current zoning strategy.

The passage of the Americans with Disabilities Act (ADA) has changed the landscape for demand responsive transit systems. First, the demand for this type of transit service has experienced tremendous growth. In Los Angeles County alone more than 5000 vans and 4200 cabs provide service, generating 8 million trips per year. Second, besides creating a larger demand, ADA also set strict guidelines for the providers on trip denials and on-time performance (Lewis et al., 1998). In essence, transit agencies today are expected to provide better services while experiencing increased usage for demand responsive transit systems. The National Transit Summaries and Trends (NTST) report for 2002 indicates that the average cost per passenger trip for DRT systems is $20.8 with fares ranging from $1.5 to $3.00. By way of contrast, the average cost per trip for fixed-route lines is $2.4 with fares being roughly 25% of the cost. Therefore, DRT services are still a highly subsidized service and it is imperative for agencies to analyze and investigate their current practices to identify possible cost reductions or productivity improvements. To measure productivity and cost of the DRT system we consider different performance measures, such as fleet size, total miles and deadhead miles. The deadhead miles are defined as the empty trip miles driven by the vehicle between the drop-off point of a customer to the pick-up point of another customer. Note that with ridesharing a vehicle may not be empty driving from a drop-off point to a pick-up point and the miles driven in these cases would not count as deadhead miles. A reduction in deadhead miles can either cause a reduction in the total number of miles driven by a vehicle (hence reducing cost) or allow a vehicle to serve more customers on a given day (hence increasing productivity). Some studies outline the potential positive impacts of Advanced Public Transportation Systems (APTS) on productivity and cost (Stone et al., 1994, Goeddel, 1996, Ben-Akiva et al., 1996, Chira-Chavala and Venter, 1997, Wallace, 1997, Schweiger and McGrane, 1999, Higgins et al., 2000 and Stone et al., 2000). Palmer et al. (2004) show also how financial incentives and penalties can have a negative impact on productivity. That is, providers may schedule in an inefficient manner in order to ensure that they are on time to receive the incentive or avoid the penalty. But there are other factors that have an influence on the performance of DRT systems and the objective of this research is to study the impact on productivity and cost of specific operating practices currently used by DRT providers. They are the time-window setting and the zoning. The length of the time-window that specifies the time range in which the provider must pick-up the customer is an important factor impacting productivity and cost. For example, a time-window of 20 min and a scheduled pick-up time of 3:00 pm would mean that the vehicle must pick-up the passenger by 3:20 pm at the latest to be considered on-time. Typically, providers have financial incentives or penalties for meeting on-time goals. Naturally, customers prefer small time-windows. However, in order to maintain small time-windows, transit agencies may have to decrease the ridesharing and increase their fleet size, contributing to increased cost and less productivity. Therefore, the setting of the time-window size needs to balance customer service with the impact on productivity and cost. Currently, Access Service Inc. (ASI), the agency responsible for coordinating paratransit DRT service in Los Angeles County, uses a 20 min time-window whereas many other agencies use a 30 min time-window. A number of DRT agencies divide their service area into regions contracting the service in each of them to a different provider to simplify the management of the service. This practice, known as zoning, is also motivated by the drivers’ preference to be assigned to a smaller region instead of the whole service area. This is a common practice for DRT agencies (paratransit, taxi services, etc.) all over the US especially when the service area is large. We distinguish between a centralized vs. decentralized control depending upon the number of regions in the service area. In centralized control, the service is aggregated into a single region; in decentralized control multiple regions are created. For example, ASI utilizes a decentralized control strategy dividing its service area into six regions (see Fig. 1). The pick-up location of the customer request determines the region and the corresponding provider responsible for the service. It is not uncommon that the pick-up and drop-off locations of a request are in different regions. In fact, according to the data provided by ASI, around 20% of the trips originating in the Northern region of Los Angeles County have a drop-off location outside that region. Hence, the return trip will be done by a different provider regardless of the dwell time of the customer at their drop-off location coming at the expense of a significant number of deadhead miles. Furthermore, in this situation, the customer is required to make two different reservations, one for each provider. In contrast, a hurdle toward implementing a more centralized strategy is that the Computer Aided Dispatching (CAD) systems of the different providers need to efficiently communicate among themselves in order to effectively manage such a design. Although there is a significant body of work in the literature on scheduling and routing DRT systems (see e.g., Ioachim et al., 1995, Savelsbergh and Sol, 1995, Toth and Vigo, 1997, Borndörfer et al., 1999, Desaulniers et al., 2000, Diana and Dessouky, 2004, Lu and Dessouky, 2004 and Lu and Dessouky, 2006), there has been no research performed comparing the performance of a centralized controlled DRT system with a decentralized one. Diana et al. (2005) developed analytical equations to determine the fleet size as a function of the time-window for a square service area. However, no similar equations exist for general service areas and for estimations of the total and deadhead miles. Thus, the effect of the time-window size on productivity and cost in general has also not been quantified. This paper addresses this gap by studying the impact of these issues on the operations of a representative large-scale DRT service. Due to the difficulty of developing closed-form expressions between the operating practices and the performance measures, a simulation model is used in this study. The simulation model is based on demand data provided by ASI for Los Angeles County. We analyze the effect of varying the time-window size (from 10 to 45 min) and we compare the current decentralized approach with a centralized strategy where any vehicle can pick-up any customer regardless of the service region. In addition we investigate the effect of centralizing only part of the service area, merging two regions together. Although the results of the simulation model pertain to the Los Angeles County network, the simulation methodology described here is quite general. In fact, a similar study can be conducted for any DRT service with basic data (vehicle fleet, service parameters and description of demand), and therefore the methodology is easily adaptable and applicable to other service areas. In addition, the results of this study provide insights on the dependency between performance measures and operating practices for DRT services in general. In fact, the geometry of the service area and the demand distribution of Los Angeles County utilized in this simulation model are quite standard as we describe later. Most urban areas (especially in the US) serviced by DRT systems would have similar configurations and we do not expect major differences on the nature of the relationships between the performance measures and operating practices for a number of other DRT providers. Simulation tools are very powerful to evaluate systems’ performance and they have been extensively utilized in the literature in a variety of fields including transportation. Wilson et al. (1970) pioneered the use of simulation to compare different heuristics to assess the influence of the service area, the demand density, and the service quality on the fleet size requirements. Regan et al. (1996) evaluate the performance of different load acceptance and assignment strategies for a dynamic distribution problem. Larson et al. (2002) examines the impact of dynamism on the quality of the solution for the Partially Dynamic Traveling Repairman Problem. Only a few applications are specifically concerned with paratransit systems. Fu (2002) develops a simulation model to assess the potential effects of the latest advances in information technologies on dial-a-ride paratransit systems. Deflorio et al. (2002) propose a simulation model to evaluate the performance of a DRT system scheduled using the insertion algorithm by Jaw et al. (1986) when dealing with random events like late customers and not on-time vehicles. Lipmann et al., 2002 and Hauptmeier et al., 2000 take traffic conditions into account to evaluate the performance of DRT systems. Some studies (Feuerstein and Stougie, 2001 and Bailey and Clark, 1987) have investigated changes of performance when the dial-a-ride system is run with various numbers of vehicles. Haghani and Banihashemi (2002) address the relation between efficiency of vehicles and town size. Shinoda et al. (2004) compare by simulation the performance of dial-a-ride system vs. a fixed-route system in urban areas varying various parameters. Quadrifoglio and Dessouky (2007a) also perform a simulation study to test the efficiency of the insertion heuristic scheduling algorithm for Mobility Allowance Shuttle Transit (MAST) systems, a hybrid transit solution that merges the flexibility of DRT systems and the low cost operability of traditional fixed-route bus services. The same authors (Quadrifoglio and Dessouky, 2007b) use simulation to perform a sensitivity analysis of the performance of a MAST system varying the shape of its service area. Diana (2006) assesses by simulation the influence on the effectiveness of a DRT scheduling algorithm by Diana and Dessouky (2004) of typical dynamic parameters such as percentage of real time requests and interval between call-in time and requested pick-up time. The remainder of the paper is organized as follows. In Section 2, we analyze the historical demand data of a representative large-scale agency (ASI). In Section 3 we describe the simulation model used to represent the Los Angeles County DRT system. This simulation model is described in sufficient detail so that it can serve as a source for simulations on other DRT system environments. Section 4 presents the results; finally the conclusions are outlined in Section 5.

In this paper we quantified how much productivity and cost of Demand Responsive Transit (DRT) services are affected by two managerial practices: the time-window size setting and a centralized vs. decentralized strategy. Access Services Inc. (ASI), which is the designated consolidated transportation service agency to coordinate paratransit service within the Los Angeles County, provided us with demand data to generate statistical distributions used for a simulation model for our analyses. Although the results pertain to the network considered, the simulation methodology described here is quite general and easily applicable to any other large service area. The results of this study provide general insights on the dependency between performance measures and operating practices for large DRT services. We identified quasi-linear relationships between the performance measures and the independent variable, either the time-window size or the zoning policy. For the time-window size effect, we built linear regression models and observed that for each minute increased in the time-window size the service saves approximately 2 vehicles and 260 miles driven, while satisfying the same demand. Increasing the time-window size would also lower the customer satisfaction, thus managers have to carefully balance these two effects while setting the size. About the zoning policy, we observed that a centralized strategy is able to satisfy the same demand by employing 60 less vehicles and driving 10,000 less total miles with respect to a decentralized strategy. Most of the improvement is due to the drastic reduction of deadhead miles driven in the no-zoning (centralized) case. This increased efficiency has to be carefully balanced with the added complexity arising while managing centralized systems. Future research would include using approximations in order to build analytical models to quantify the zoning and the time-window size effects and compare their findings with the ones from this simulation analysis.