Capacity constrained accessibility of high-speed rail The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Shen, Yu, and Jinhua Zhao. “Capacity Constrained Accessibility of High-Speed Rail.” Transportation (September 18, 2015). As Published http://dx.doi.org/10.1007/s11116-015-9660-8 Publisher Springer US Version Author's final manuscript Citable link http://hdl.handle.net/1721.1/106667 Terms of Use Creative Commons Attribution-Noncommercial-Share Alike Detailed Terms http://creativecommons.org/licenses/by-nc-sa/4.0/ Transportation DOI 10.1007/s11116-015-9660-8 Capacity constrained accessibility of high-speed rail 1,2 1 Yu Shen • Jinhua Zhao Ó Springer Science+Business Media New York 2015 Abstract This paper proposes an enhanced measure of accessibility that explicitly considers circumstances in which the capacity of the transport infrastructure is limited. Under these circumstances, passengers may suffer longer waiting times, resulting in the delay or cancellation of trips. Without considering capacity constraints, the standard measure overestimates the accessibility contribution of transport infrastructure. We esti- mate the expected waiting time and the probability of forgoing trips based on the M/GB/1 type of queuing and discrete-event simulation, and formally incorporate the impacts of capacity constraints into a new measure: capacity constrained accessibility (CCA). To illustrate the differences between CCA and standard measures of accessibility, this paper estimates the accessibility change in the Beijing–Tianjin corridor due to the Beijing– Tianjin intercity high-speed railway (BTIHSR). We simulate and compare the CCA and standard measures in five queuing scenarios with varying demand patterns and service headway assumptions. The results show that (1) under low system loads condition, CCA is compatible with and absorbs the standard measure as a special case; (2) when demand increases and approaches capacity, CCA declines significantly; in two quasi-real scenarios, the standard measure overestimates the accessibility improvement by 14–30 % relative to the CCA; and (3) under the scenario with very high demand and an unreliable timetable, the CCA is almost reduced to the pre-BTIHSR level. Because the new CCA measure effectively incorporates the impact of capacity constraints, it is responsive to different arrival rules, service distributions, and system loads, and therefore provides a more realistic representation of accessibility change than the standard measure. Keywords Accessibility Á Capacity constraint Á Discrete event simulation Á High-speed rail Á Queuing theory & Jinhua Zhao [email protected] 1 Department of Urban Studies and Planning at Massachusetts Institute of Technology, Cambridge, USA 2 DECIVIL/CERIS at Instituto Superior Te´cnico, Universidade de Lisboa, Lisbon, Portugal 123 Transportation Introduction Accessibility, as a vital nexus between transportation and land use systems, is widely used in both scientific studies and policy-making practices. Hansen’s (1959) seminal work on accessibility first demonstrated two important elements in its measurement, the ‘‘spatial distribution of activities’’ and the ‘‘ability/desire to overcome spatial separation.’’ Fol- lowing Hansen’s work, there have been numerous works studying the definitions, mea- sures, and applications of accessibility. These works have been systematically reviewed by Bhat et al. (2000), Geurs and Ritsema Van Ecka (2001), Geurs and van Wee (2004) and Curtis and Scheurer (2010). In evaluating the relationship between land use and trans- portation strategies, Geurs and van Wee (2004) identify four basic perspectives on accessibility measures: (1) infrastructure-based measures, e.g. levels of congestion or average travel speed on the road network; (2) location-based measures, e.g. the sum of the product of jobs and travel time from origin to destination; (3) person-based measures, e.g. the activities in which an individual can participate within a given time budget; and (4) utility-based measures, e.g. the derived logsum of utilities from a combined mode-desti- nation choice set. In studies of the accessibility impacts of high-speed rail (HSR), the location-based measures are the most commonly used measurements (Baptiste et al. 2003; Gutie´rrez 2001; Gutie´rrez et al. 1996; Gutie´rrez and Urbano 1996; Shen et al. 2014; Spiekermann and Wegener 2006; Vickerman and Ulied 2009). Though given in various mathematical forms, location-based measures can be generically expressed as: XJ ÀÁÀÁ Ai ¼ gOj fIij ; ð1Þ j¼1 ÀÁ where Ai location-based accessibility indicator at origin i; gOj activity function of opportunities Oj, e.g. population,ÀÁ number of jobs in destination j, representing the ‘‘spatial distribution of activities’’; fIij impendence function of generalized travel cost or travel time from origin i to destination j, reflecting the element of ‘‘the ability/desire to overcome spatial separation.’’ The specific forms of Eq. (1) vary according to research purposes. Bhat et al. (2000) show thatÀÁ past studies have developed abundant mathematical forms of the activity function gOj . Recent studies have further refined the measures of accessibility by inte- grating different theories into the calculation of activity functions, e.g. the competition of opportunities at destination, or the evaluation of equity (Geurs and van Wee 2004; Lucas et al. 2015; van Wee et al. 2001). As macro-level measures, accessibility models tend not to incorporate the details of transit operations in order to maintain the simplicity of the models in general cases. However, we argue that there is at least one important operational detail to model: capacity constraint, which could have significant impact on the accessi- bility measure in the planning and strategic phases of transport development. The dis- cussion of capacity constraints is mainly found in research on transit network assignments (see Leurent (2011) and more details in ‘‘Capacity constraints in transit networks’’ section). A review from Kitamura (2009) reveals the importance of capacity effects on measuring accessibility and also shows that past studies fail to establish links between these two.ÀÁ As shown in Bhat et al. (2000), there is little discussion of the impendence function, fIij , especially from an operational perspective. Thus, there is a clear gap between the acces- sibility literature and the transit network assignment literature. This paper aims to bridge the two by focusing on circumstances in which the capacity of transport infrastructure or 123 Transportation service is limited, and explicitly incorporating capacity constraints into the accessibility measurement. In their review of accessibility measurements, Curtis and Scheurer (2010) point out that travel time is possibly the most commonly used measure to quantify travel impediment. In a transit network, waiting time (or transfer time) is an essential component of travel time calculation. Past studies convey the significance of travel time reliability (Bates 2001; Geurs and van Wee 2004) but do not take into account constraints on service capacity. This results in two common assumptions: (1) that waiting time can be estimated simply by taking the half of headway as expected waiting time (Curtis and Scheurer 2010), or by taking half of headway multiplied by a function of the coefficient of headway variation (Osuna and Newell 1972); (2) that all passengers are able to get onto the trains, i.e. no one is left behind. In densely populated areas, especially during peak hours, both assumptions could significantly diverge from reality. When capacity is constraining, passenger boarding becomes probabilistic. For those who are left behind, the service effectively becomes unavailable; for those who board the train, actual waiting times can be far longer than the expected waiting time estimated by the public transit timetable. By ignoring capacity constraints and making these unrealistic assumptions, the standard measure may sub- stantially overestimate the accessibility impact of a new infrastructure or service. The problem can affect both urban public transit networks and intercity railway networks, including HSR, whenever demand approaches the service capacity. Capacity constraints in transit networks From the interactions between passengers, vehicles, stations, and lines emerge various capacity issues, which are classified by Leurent (2011) into seven groups: (1) the vehicle capacity of an infrastructure; (2) the operational capacity of vehicle fleet in a route; (3) the passenger capacity of a vehicle; (4) the capacity of vehicles covering a route during a certain period; (5) the passenger capacity of a station; (6) the vehicle storage and move- ment capacity of a station; and (7) the capacity of a station for interface with personal transport modes. Among these capacity phenomena, the literature review of Fu et al. (2012) points out that ‘‘the waiting time for boarding a transit vehicle at a stop/platform is an indispensable factor that needs special treatment.’’ The estimation of passengers’ waiting time becomes more complicated under scenarios with capacity constraints. In recent years, some multi-agent transit assignment models, e.g. BusMezzo, have been implemented to simulate the performance of public transit networks based on a set of capacity enhancement schemes (Cats 2013; Cats and Jenelius 2015). Focusing on stations, previous studies propose various assumptions about boarding strategies