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Space-time dynamics: A modeling approach for commuting departure time on linked datasets
Journal of Transport Geography 82 (2020) 102548
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Space-time dynamics: A modeling approach for commuting departure time on linked datasets Han Donga, Cinzia Cirillob, a b
T
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Transurban North America, Suite T500, 7900 Westpark Drive, Tysons, VA 22102, United States Department of Civil and Environmental Engineering, University of Maryland, College Park, 3250 Kim Engineering Building, College Park, MD 20742, United States
A R T I C LE I N FO
A B S T R A C T
Keywords: Departure time Data linkage Discrete choices Dynamic in travel behavior
Commuters' departure time related decisions are important in time geography. Analytic tools have been proposed to capture the inherent choice determinants both in time and space. Although the dynamic aspects of the problem have been identified, most of the existing studies are based on static models. In this paper, a dynamic modeling framework is proposed to explore the relationship between commuters' departure time choices and the evolution of en route traffic. A data linkage method is developed to create an integrated dataset that enables the observation of commuters' reaction to changes in travel time and traffic conditions over time. A regional household travel survey is linked to travel information obtained from the Google Maps application program interface (API), creating a synthetic longitudinal dataset. Two decision rules are applied to model commuters' response to the evolution of traffic. The results indicate that travel time, distance to work location, flexibility in working schedule, expected arrival time, and commuters' sociodemographic influence departure time choices. It is also found that accounting for dynamics improves model fit and out-of-sample predictions. Both the dynamic model and the proposed data linkage method contribute to the understanding of human activities in space and time and can be used to enhance transportation demand analysis and urban policy studies.
1. Introduction Transportation geographers and urban planners concur that both spatial and temporal factors should be taken into account when designing the future of cities and regions and proposing innovative solutions to transportation related issues. The need for spatio-temporal representation of human activities has resulted into the rapid development of disaggregate analysis and modeling tools to improve both theoretical understanding and policy evaluation (Janelle and Gillespie, 2004). In transport geography the majority of the existing works builds on the conceptual breakthroughs by Hägerstrand (1970), especially in the modeling of individual activity behavior (Doherty, 2003; Dijst, 2004). More recently, geographers have played prominent roles in extending the underlying theory of time geography (Miller and Wu, 2000; Janelle and Gillespie, 2004) that proposes a constraints-oriented approach to understanding human activities in space and time. Decisions about departure time are fundamental to identify the spatio-temporal conditions for human activities. In Spatio-Temporal Prism theory (STP), departure and arrival time are among the parameters to be identified for the definition of its vertices that in turn identify the space time paths (Miller, 2015). Activity participation is
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determined by the location and timing of anchors that require presence (such as home and work) and is constrained by the time budget for access activities. Daily paths are also affected by the ability to trade time for space and the availability of information and communication technologies (ICTs) (Miller, 2015). The time geography, of which temporal related decisions are an important component, is a powerful conceptual framework for understanding constraints on human activity participation in space and time. However, rigorous, analytical definitions of basic time geography entities and relationships are not fully developed (Miller, 2005). This paper investigates commuters' scheduling choices and aims at capturing the dynamic in their decision making process. The models proposed and the associated results respond to the need of better theoretical framework and analyses tool to understand the timing of work and the effects of Information Communication Technology (ICT). More specifically, the choice of leaving home to work is updated every ten minutes by considering actual travel time to destination and expectation of future travel conditions. The framework explicitly models the optimal time to depart, and updates network travel conditions as they become available. A data linkage method is applied to construct the database needed for the analysis; a regional household travel survey is
Corresponding author. E-mail address: [email protected] (C. Cirillo).
https://doi.org/10.1016/j.jtrangeo.2019.102548 Received 15 February 2019; Received in revised form 10 September 2019; Accepted 18 September 2019 0966-6923/ © 2019 Elsevier Ltd. All rights reserved.
Journal of Transport Geography 82 (2020) 102548
H. Dong and C. Cirillo
and Parry, 1991; Chen and Mahmassani, 1993; Koutsopoulos et al., 1994; Vaughn et al., 1993). In particular, Mahmassani and Liu (1999) used an interactive multi-user simulator to examine the day-to-day commuter behavior under real-time information. Ben-Elia and Shiftan (2010) proposed a learning-based model of route-choice behavior which investigated the impact of ATIS and personal experiences on users' route choices. Both studies are based on data collected in controlled lab experiments. More broadly the advances in ICTs and the exponential growth of the information available to people are expected to altering the space–time constraints of daily life. Nowadays, real-time traffic information has become available to commuters through different apps and online data providers. Google pulls in traffic data from multiple sources for its Maps app, including information from police and local transportation departments. Waze, a company Google acquired in 2013, has mobile apps for Android and iOS devices. Waze members can use the app for navigation to a destination and to report traffic observations and incidents along the route. The Regional Integrated Transportation Information System (RITIS) is an automated data sharing, dissemination, and archiving system maintained by the Center of Advanced Transportation Technology (CATT) at the University of Maryland. Among a number of services and measures provided, the general public can get access to real time data feeds, including travel time, accident and weather conditions. The availability and the accessibility of real time information is changing the way commuters make travel related decisions and requires a shift in the paradigms used to model traveler behavior, especially dynamic in decision making. Only recently, models that explicitly account for the temporal dimension of individual choices have been introduced in the field of transportation. Models of this type are derived from Rust (1987) who proposed a structural dynamic approach to solve an optimal stopping problem. In his first application the manager of a bus company (Harold Zurcher) had to decide when to replace the engine of his bus fleet. This model that applies to a single agent and to homogeneous products is still largely applied in economics (see Aguirregabiria and Mira, 2007) for a comprehensive review of dynamic discrete choice models). In transportation and handful number of applications exist. Fosgerau et al. (2013) used a dynamic discrete choice framework in the context of route choice; in particular, a recursive logit (RL) models path choice as a sequence of link choices. Liu and Cirillo (2018) have developed a generalized modeling framework for vehicle ownership related decisions and applied it to model the adoption of green vehicles. The model allows for multiple agents' decisions, models heterogeneous products and accounts for the volatility in vehicle characteristics and fuel price over time. From the review presented in this section, it is evident that dynamic modeling approaches would contribute to a better understanding on where individuals are in space and how they trade time under constraints when deciding about the time to go to work.
linked to pre-trip travel time information obtained from Google Map API. In addition, impacts of traffic evolution on departure time decisions are tested under two different behavioral scenarios: 1) Perfect Knowledge of traffic conditions and 2) Uncertainty in traffic conditions. The remaining of this study is organized as follows. A review of existing studies on commuters' departure time is provided in Section 2. Section 3 describes the two major data sources used in this study and the proposed data linkage method. In Section 4, a dynamic framework is introduced and adapted to the problem of departure time under deterministic and stochastic knowledge of traffic conditions. In Section 5, the proposed models are estimated and validated, results compared to static logit models. The end Section summarizes the empirical results and outlines the major contributions. 2. Literature review An operational framework for departure time decisions exist in transportation demand modeling, where these decisions are commonly modeled using Multinomial Logit Models (MNL) (see e.g. Abkowitz, 1981; Small, 1982; McCafferty and Hall, 1982). Departure time based on MNL specifications have been included in four step models of both trip and tour types, or in more advanced activity based models (Bradley et al., 2010). The day is divided into a limited number of discrete time periods, and logit is applied to capture the tradeoff between alternative time-of-day windows. Utility functions are defined in terms of individuals' socio-demographics, level of service variables (travel time and travel cost), and work schedule. Logit type models suffer from a number of limitations: it is not possible to model correlation among adjacent time periods, observations from the same individual are assumed to be independent and decisions are static as well as all the variables included in the utility functions. To relax these constraints, other approaches have been proposed; more advanced models for departure time decisions include nested logit (Chin, 1990), cross nested logit (Bajwa et al., 2008), continuous cross-nested logit (Lemp et al., 2010), and error components logit (De Jong et al., 2003; Hess et al., 2007). These types of GEV models mainly capture correlation across subsequent time intervals, but are unable to model dynamic in decisionmaking. Moreover, a discrete representation of departure time has several drawbacks. The time interval duration that constitutes the discrete alternatives is discretionary and could lead to different estimates and model fits, and aggregation precludes analyses at a very fine time resolution. Continuous-time hazard duration models have been proposed for trip departure time choice. Following this approach, Bhat and Steed (2002) modeled departure time choice on an entire day for urban shopping trips with a non-parametric continuous hazard model. However, applications of hazard-based models are still quite limited. The dynamic decision process of commuters, especially departure time decisions, is worthy of investigation. Mahmassani and Chang (1986) studied day-to-day dynamics of commuters' patterns in a series of simulation experiments. Factors that were considered important to study trip makers' behavior include: schedule delay, or the absolute value of the difference between desired and actual arrival time; travel time, and its variation from one day to the next; and traffic flow quality descriptors (concentration, speed and volume). Results showed that commuters tend to remain with the same choices until the actual schedule delay exceeds tolerable values. This adjustment takes place in response to learning from one's repeated experience and outside information sources. The study is based on heuristics as modeling individual decision making and learning in highly dynamic systems is complex. The effect of real-time information on driver decision making has been of interest to the transportation community since the 90s. Early studies were mainly based on laboratory experiments due to the limited deployment of Advanced Transportation Information System (ATIS) technologies (Mahmassani and Herman, 1990). Several studies have provided insights into trip makers' decision processes under different types of ATIS-provided information (Adler et al., 1993; Bonsall
3. Data linkage Automobiles and smart phones are great facilitators of personal time–space convergence and extensibility (Janelle and Gillespie, 2004). Also, travel and communication activities of individuals and institutions are being increasingly monitored; GPS devices provide a means for tracking real-time and in detail individual's behavior. In this study we use traditional survey data from a regional household diary to extract information about spatial location of fixed activities (home and work) and about temporal decisions (time to depart from home to work). These data are augmented by extracting information about traffic conditions from commonly available GPS devices. Specifically, two data sources are linked in the study: (1) The 2007–2008 TPB-BMC Household Travel Survey (HHTS), which is a regional household travel survey that records socio-demographic, spatial and temporal information about daily trip and activity schedule (trip purpose, trip origin and 2
Journal of Transport Geography 82 (2020) 102548
H. Dong and C. Cirillo
destination (OD) centroid locations, for the same time of day and weekday observed in HHTS survey, were requested from Google Maps Distance Matrix API. A 10-min time interval is adopted for the three hours observed which means that seventeen time periods are available for each commute leg and to each respondent observed in HHTS.
Table 1 HHTS sample – descriptive statistics. Variable name
Mean
Std. error
Min
Max
Trip distance (mile) No. of people in household No. of students in household No. of driving license holders in household No. of workers in household No. of vehicles in household Average household income ($×104) Young (age 19–25) Adult (age 26–45) Senior (age 46–60) Gender (female = 0, male = 1) Ownership of household Vehicle per worker
12.52 2.39 0.68 1.86 1.67 1.93 11.78 0.04 0.44 0.42 0.51 0.81 1.24
10.69 1.08 1.00 0.70 0.64 0.73 5.29 0.19 0.50 0.49 0.50 0.39 0.52
0.20 1.00 0.00 1.00 1.00 0.00 0.50 0.00 0.00 0.00 0.00 0.00 0.00
65.30 4.00 5.00 5.00 5.00 3.00 20.00 1.00 1.00 1.00 1.00 1.00 3.00
3.3. Data linkage methodology As anticipated, a data linkage method is applied to combine these two datasets. This method allows data of a single individual to be compiled from different data sources, enabling more powerful and effective analyses to be carried out. In particular, datasets created through linking individual records constitute a critical resource for research in health, epidemiology, economics, sociology and many other areas (i.e. Vaughn et al., 1993). It is expected that speed relative to the same OD pair shows a similar pattern for a given time of day and day of week. Thus, differences in travel time between the same OD pair for the same time and the same weekday from two data sources can be expressed as a linear relation of difference in distance traveled and error component. In this study, travel time obtained from ATIS system is linked to the HHTS through Eq. (1).
destination, and trip departure and arrival time) of household in the Washington DC metropolitan area; and (2) Travel time information obtained from Google Maps. The two files are linked by considering the following key variables: origins and destinations of each trip in the HHTS, the time of day and the day of the week in which the trips were observed.
TitA − γtitA = α + κ (ditA − DitA) + εi,
3.1. The 2007–2008 TPB-BMC household travel survey (HHTS)
(1)
TitA
where is the travel time of individual i at the actual departure time t in HHTS. titA is the travel time that is obtained from ATIS for the same departure time t of the same weekday, DitA is the commuting distance in HHTS, ditA is the commuting distance for the same OD pair obtained from ATIS for the departure time t; α, γ, κ are the associated parameters, εi is an individual-specific random term. Table 2 reports the results obtained from the linkage model. All the estimates are significant with the expected sign. It should be noted that only a single travel time record for each commuting trip could be obtained from the HHTS survey. To enrich the , γ ̂ and κ ̂ are then applied to infer dataset, the estimated parameters α travel time Tit of individual i using tit, dit, Dit over the whole three hour period that was modeled. In order to recover the actual arrival time of it of respondent i are then adjusted each trip in the sample, estimated T with the difference between actual observed travel time TitA and estiit + TitA -T itA , which is T itA . Based on the inferred travel mated travel time T time and work start time, other time varying variables are calculated, which are described as follows:
The HHTS was collected by the Metropolitan Washington Council of Governments (MWCOG) from February 2007 to April 2008; it gathers information about demographics, socioeconomic variables and one-day trip making characteristics of residents in the Washington DC Metropolitan area. The data are geocoded at the Traffic Analysis Zone (TAZ) level, with a centroid location in each zone. For this study, only commuter trip legs from home to work by car as driver with final destination in the Washington area were selected. In total, 938 observations matched these criteria. Descriptive statistics related to the population selected are reported in Table 1. The origin and destination distributions are showed together with distance normalized by travel time in Fig. 1a and b respectively. Average travel speeds between ODs are represented with colors ranging from yellow to red. As indicated in Fig. 1a, trips originating in urban area tend to have lower travel speed than trips originating from rural area. 3.2. Advanced travel information system (ATIS)
• DE : Time difference between the expected arrival time and the it
Travel information is now available to travelers through different channels, and real time information about travel time and traffic conditions can be easily requested or accessed using Application Programming Interface (API). For example, Google Maps Distance Matrix API provides users with the fastest route between a given OD pair and for a specific time. The dataset used for this study, which contains actual and future travel time between home and work locations, was constructed using Google Maps. However, only future and real-time traffic information is available from Google Maps while historical data cannot be retrieved. Since Google Maps uses historical data to predict future traffic, we believe that future traffic conditions based on Google Maps are more stable and represent better trends in traffic than real-time information. Data were requested using Google Maps Distance Matrix API on Nov. 6th, 2016 for the upcoming two weeks. Work start time is defined as a reference point to construct the database. In prospect theory, it has been found that commuters use arrival time information to decide about their daily departure choices (Senbil and Kitamura, 2004). In the HHTS survey, we found that > 85% of commuters in the sample choose to depart from home within the time window that starts two hours before work start time and ends one hour after (Fig. 2). Travel time and trip distances between origin-
• •
work start time of commuter i at time t. DEit < 0 if commuter arrives before start time; DEit > 0 if commuter arrives after start time. IPit: Indicator of late penalty. If commuter has fixed working schedule and arrives after work start time, IPit = 1. Otherwise, IPit = 0. ILit: Indicator of being late. If commuter arrives after work start time, ILit = 1. Otherwise, ILit = 0.
4. A dynamic framework for departure time choices In this section we provide the mathematical formulation (for further details please see Cirillo et al., 2016) for modeling spatio-temporal dynamics in decisions related to departure from home to the work location and a behavioral interpretation of the framework proposed. Commuters are observed during a three-hour time window (two hours before work start time and one hour after), which has been divided into seventeen intervals of ten minutes each. According to our modeling framework, at each time period the individual chooses to stay at his home location or to depart (binary choice) depending on information relative to actual travel time and his (her) expectations about future traffic conditions. The sequence of decisions overt time can be represented as a decision tree (see Fig. 3). Scheduling related variables 3
Journal of Transport Geography 82 (2020) 102548
H. Dong and C. Cirillo
Fig. 1. a. Distribution of commuting trips' origins. b. Distribution of commuting trips' destinations.
αi= α, and λi= λ, i = 1, …, I. Travel time and the associated variability is the dynamic variable considered in this study. λi is a vector of parameters related to yit; ϵit is an individual-specific random term, whose components are independently and identically extreme value (GEV) distributed among individuals and periods.
(DE, IP, IL), socio-demographic characteristics, work location might affect his/her decisions. This problem is treated as an optimal stopping problem over a finite time horizon, where the commuter decides about the optimal time to leave home. Once the commuter decides to leave for work, his (her) chain of decisions is terminated. Two behavioral assumptions are considered: 1. Perfect information on future travel time; 2. Uncertainty in future traffic conditions. The first assumes that travel time trends will behave according to past information derived by historical data available through ATIS; the second assumes that travel time is a random variable and that a random walk (Eq. (9)) will determine future traffic conditions.
The decision process can be described as follows: at time t, each commuter decides whether to start the trip to work or to postpone until the optimal time τ, which is the departure time that maximizes commuter's utility. Commuter's departure decision regarding the time to leave home for work can be treated as an optimal stopping problem (Eq. (2)).
4.1. The model formulation
τ−1
Dt (bit , cit ) = max
Consider a set of commuters i = {1 … I} and time periods t = 0, 1, …, T, commuter i has two options at time t:
τ
(2)
It is important to note that the expectation in (2) is taken with respect to the dynamic variable travel time specified as yt. The equation can be transformed from (2) into
• Stay at home and obtain a one-period payoff defined as c . This is a it
•
⎧ ∑ cit + E yτ [biτ | yt ] ⎫⎬, ⎨ k=t ⎩ ⎭
utility function which is a linear combination of attributes related to commuter's socio-demographics and working schedule characteristics (xit), and of a parameter vector (θi); Leave home for work and obtain a final payoff uit. It is assumed that the departure choices are consistent at each time t, and that the final payoff is expressed as a random utility function: bit = u (xit, yit, θi, λi, εit) where xit, θi are defined as above, while yit is a random vector of dynamic attributes of road condition at time t. Although departure time decisions vary across commuters, parameters here are assumed to be the same over individuals, i.e. θi= θ,
Dt (bit , cit ) = max {bit , cit + Et + 1 [bi,t+1 , ci, t + 1 | yt ] } ,
(3)
Based on (3), we see that the decision process simply consists in leaving home at time t or remaining at home and postpone the decision to depart and take the payoff cit plus the future return. We now define, Wi (yt) as the reservation utility level for driver i:
Wi (yt ) = cit + E yt + 1 [bi, t + 1 , ci, t + 1 | yt ], Then the optimal stopping problem is given by: 4
(4)
Journal of Transport Geography 82 (2020) 102548
H. Dong and C. Cirillo
Fig. 1. (continued)
Γ(yt ) = {bit | bit > Wi (yt ) } ,
def
(5)
πi0t (yt ) = Pit [Dt (bit ) = Wi (yt ) | yt ] = Pit [bit ≤ Wi (yt )] = Fv (Wi (yt ), yt ) = e−e
Using Eq. (5), (3) can be simplified as
Dt (bit ) = max {bit , Wi (yt ) } ,
(Wi (yt ) − rit ) ,
(7)
where rit is the mode of distribution of bit. The probability of leaving home is consequently equal to h (yt) = 1 − πi0t(yt).
(6)
Commuter i will choose to leave home at time t only when bit > Wi(yt). If i is randomly drawn from the population, the analyst can compute the probability of postponing the departure until next period as: 16.00% 14.00% 12.00% 10.00% 8.00% 6.00% 4.00% 2.00% 0.00%
-24.0 -11.0 -7.6 -6.5 -5.2 -4.1 -2.7 -2.2 -1.7 -1.2 -0.9 -0.7 -0.6 -0.4 -0.3 -0.1 0.0 0.1 0.2 0.3 0.5 0.8 1.1 1.5 2.2 5.0
Dsitribution of observations
−
Gaps between departure time and work start time (hr) Fig. 2. Distribution of time difference between departure time and work start time. 5
Journal of Transport Geography 82 (2020) 102548
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anticipate the traffic just one step ahead with E [D3] = 0. Fig. 3 shows the structure of the estimation process.
Table 2 Data linkage model – estimation results. Variable Name
Coefficient
Constant Travel time tit Difference between ATIS and HHTS distances (dit − Dit) ⁎⁎⁎
α γ κ
Estimates (Std. Error in parenthesis)
4.3. Rules in departure time decisions
0.1998⁎⁎⁎ (0.017) 0.7558⁎⁎⁎ (0.037) −0.0074⁎⁎⁎ (0.002)
Real-time travel time information is expected to alter spatial and temporal patterns of human activities. Our theoretical framework is designed to capture these effects through the definition of the expected utility. The future appears uncertain to commuters, and this evolution needs to be represented in some sort. It is proposed to estimated expectation of future traffic conditions from the respondent's perspective instead of using market (equilibrium) values, as it is commonly done in dynamic discrete choice models used in economics (Rust, 1987; Fosgerau et al., 2013). In this sense, this research experiments with two different decision processes: perfect knowledge of travel time and stochastic travel time.
Significant at the 95% level.
4.2. The dynamic estimation processes We first summarize the parameters to be estimated in the dynamic departure time problem:
• θ, a vector of parameters related to commuter i's attributes x ; • λ, a vector of parameters related to dynamic attributes of traffic
• Perfect knowledge of travel time (PK): The dynamic model is esti-
it
condition at time t, yjt;
The parameters' estimation is performed by maximizing the likelihood function: I
(θ, λ ) =
•
H
∏ ∏ Pit [Dt (vit ) | θ, λ], i=1 t=1
(8)
here the probability follows the distribution of the variables ϵit, as in Eqs. (6) and (7), given the values of the parameters, I is the number of commuters, and H is the number of time periods over which we observe each commuter. Simulated log-likelihood estimation method is used to optimize Eq. (8). In the estimation process, the probability of πi0t depends on the calculation of Wit, as Eq. (4). The key step during the estimation process is to identify the expected utility, Eyt+1[vi, t+1, ci, t+1| yt]. At each time period, commuters are assumed to account for traffic condition in future scenarios, which is determined by travel time and travel time variability over time. The time horizon is composed of a limited number of time periods. At time t, the driver faces two possible alternatives: leave home or stay; at t + 1, those who are still at home face these two scenarios again. Thus, the decision process is formulated by means of a decision tree (see Fig. 3). The following steps describe the procedure to calculate πi0, 0and the expectation Ey1[D(vi1, ci1)| i], which is denoted by E [D1] for simplification purpose. Given that the traffic conditions are changing over time, here it is assumed that individuals make prediction only for one period ahead. Therefore, at time t = 0, the driver can anticipate the future characteristics of the traffic at time period t = 1. E [D2] = 0 because individual knows nothing about the traffic conditions at t = 2 when faced with the decisions at t = 0. The process of calculating E [D1] is recursive with known utility at the end of the perspective horizon. Wi(y0) can be obtained after calculating E [D1]. This step is repeated to calculate πi0, 1with the same assumption that driver can
mated assuming that commuters have “perfect knowledge” of future travel time. At time t, commuters know exactly how the traffic will be in the next 10 min. Future travel time yi, t+1 are assumed to be known and are extracted from the linked dataset. Stochastic travel time (AR(1)): Traffic is assumed to follow a stochastic process where dynamic variables change according to a random walk with a drift. Autoregressive (AR) models are used to model this time-varying process; in particular we use an AR(1) model to calculate travel time Tt+1 based on the value observed at time t:
Tt + 1 = αTt + ψ + ξt ,
(9)
In Eq. (9)α is the dependence factor, ψ is the drift, ξt is a normally distributed error term with mean zero and variance σ2. Based on the traffic data available for the study region, it is found that the dependence factor (α) is equal to 0.9967, the drift (ψ) is equal to 0.0058, and the standard deviation (σ) of the error term is 0.0192. Those values are used to compute the choice probability of waiting at home or departing according to the dynamic formulation described in previous sections. 5. Model estimation results and validation In this section we present results from model estimation; the interpretation of the results is based on econometric considerations and more importantly on their implications on the spatial and temporal components of the individual activity program. All results are shown in Table 3; where we report estimates for the dynamic model with perfect knowledge (PK) and with stochastic travel time AR(1). All the estimates are specific of the alternative departing at the current time period. Household and individual characteristics (age; gender; and household vehicle ownership), time varying variables (difference of en-route travel times across subsequent time periods, T; expected early arrival time, DE), space-time constraints (commuting distance; and working
Fig. 3. Scenario tree. 6
Journal of Transport Geography 82 (2020) 102548
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Table 3 Model estimation results. Variable name
ASCdep Adult (dummy) Male (dummy) Number of vehicles Travel time (T) Time difference between expected arrival time and work start time (DE) Trip distance Fixed working schedule (dummy) No. of observation LL(0) LL(final) pseudo R2 RMSD
Dynamic logit with PK
Dynamic logit with AR(1)
Logit
Estim.
t-stat
Estim.
t-stat
Estim.
t-stat
6.579 −0.243 0.142 −0.070 −0.076 0.118 0.034 0.145 940.0 −8085.2 −2273.2 0.719 0.113
30.6 −2.5 1.5 −1.1 −36.4 53.6 6.1 1.6
12.410 −0.598 0.259 −0.560 −0.121 0.179 0.061 0.026 940.0 −8085.2 −2358.1 0.708 0.113
55.5 −7.21 1.3 −6.3 −21.4 93.6 2.9 0.1
3.419 −0.120 0.018 0.019 −0.053 0.074 0.017 0.266 8595.0 −5957.6 −2348.8 0.606 0.125
15.1 −1.5 0.2 0.3 −15.6 29.9 3.2 3.4
schedule), are part of the final specification.
5.3. Time-Space constraints The positive coefficient estimated for trip distance attests that commuters with longer commuting trips are forced to leave home earlier, due probably to the uncertainties in travel time for long distances. The work location in spatial geography is one of the possible coupling constraints or location that individual has to join for shared activities, including work (Miller, 2015). Our analysis indicates that distant work locations have a significant effect on the determination of the time-space prism and in particular on its temporal vertices. The variable related to fixed working schedule, although not very significant in the dynamic formulation, is positive indicating that commuters with fixed working schedule prefer to start their trip earlier due to potential delay penalty.
5.1. Individual and household sociodemographic As expected, socio-demographic variables shape individuals' spacetime prism form, and in particular its vertices. As noted by Pendyala et al. (2002) while a trip is observable and is by definition always contained in a prism, the prism itself can rarely be defined because the constraints that define these vertices are not observed in survey from official sources like Regional or National travel survey. Interesting our results are in line with what found by the same authors when trying to identify the vertices of a space-time prisms from trip data. For example, the number of vehicles in the household is found to be significant in the dynamic model and the negative coefficient reveals that household with more vehicles are likely to start their trip later in the morning. Obviously, owning more cars give to commuters the flexibility to drive alone to the work place and to start their commute later. Male commuters are more likely to push earlier the morning commute vertex, while adults are actually leaving home later, presumably having greater flexibility than younger people.
5.4. Comparison among models and validation When comparing estimates of these two dynamic models, some interesting results are revealed. Time varying variables (such as travel time, DE, and trip distance) of the dynamic model with perfect knowledge have weaker effects on departure decisions. For example, estimate of travel time in is −0.076 and − 0.121 respectively for the model assuming perfect knowledge and stochastic variability of traffic conditions respectively. Coefficient estimates and model fit are compared to those obtained with static logit model. It should be noted that for the dynamic model the entire chain of decisions over the time periods that proceed the departure from home constitute one observation, while in the logit model each time period is treated as a single observation. This explain the difference in the number of observations for the dynamic and logit model respectively. The final likelihood value of two dynamic models is close. The fit of the models improves when considering the dynamic nature of the problem; the pseudo R2 increases from 0.606, the value obtained with the logit model, to 0.719 and 0.708 for dynamic models. In order to compare the prediction power of the models, we re-estimated the model on 80% of the available observations and then we applied the model estimates to predict the departure time choices in the remaining part of sample. Fig. 4 shows the estimated percentage of departures at each time interval. The real choices are characterized by peaks, which occur 50 min and 20 min before, and 30 min after work start. These peaks are quite difficult to recover with any of the formulations adopted, but the dynamic models mimic low and high values of departure choice probabilities better than static logit model. In order to quantify the error in predicting real choice probabilities, root mean square deviation (RMSD) is adopted as a measure of the differences between the true and the predicted values. Model with a higher RMSD has a poorer ability in predicting the market share. The
5.2. Time varying variables The travel time variable used in the model specification in Table 3 is the difference between travel time at current time period and travel time in the next time period. The negative value obtained for the travel time coefficient indicates that if travel time raises in the subsequent time period (resulting in a negative value of the difference), commuters are more likely to depart and not to postpone their departure time. It is interesting to note that the probability of departing at the current time period decreases with an increasing difference between the expected arrival time and work start time (DE). Also, it is found that commuters prefer to arrive closer to work start time if they expect to arrive before work starts (DEit < 0), and they prefer to delay their departures if they expect to arrive later than their work start time (DEit > 0). These results have direct consequences over the determination of individual's time-space prism. First, for fixed activities, the starting and end points in time of the prism are affected by traffic conditions and by the information on travel time received by the commuters. When the expected travel time increases, commuters tend to delay their departure time, presumably because they expect traffic conditions to improve. Second, the working start time is a strong temporal constraint in individuals' agenda and that the likelihood to incur in delays strongly impact departure time choices. Unfortunately, the indicators about late penalty (IP) and being late (IL) defined in Section 3.3 resulted not to be significant in our model specification. 7
Journal of Transport Geography 82 (2020) 102548
H. Dong and C. Cirillo
Percentage of trips
0.25 0.2 0.15
Real
0.1
Logit Dynamic logit with Pk
0.05
Dynamic logit with AR(1) 50
40
30
20
0
10
-20
-10
-30
-40
-50
-70
-60
-80
-90
-100
-110
0
Difference between depature time and work start time (min) Fig. 4. Percentage of departures at each time interval.
the traffic conditions, they would leave home earlier or much earlier when travel time increases, while changes in distance have less impact on departure time. The results also show that when commuters make decisions under uncertainty (based on the stochastic travel time rule), changes in distance and travel time would have comparable greater impacts on commuter's departure time.
RMSD is defined as:
RMSD (θ ) =
E ((θ − θ)2) =
T C ∑t ∑i = 1 Nt (θi, t − θi, t )2 T
C ∑t Nt
(10)
where C is the number of alternatives in the choice set, Nt is the number of observations at time t, θi is the market share of choice i. As showed in Table 3, the dynamic models with both perfect knowledge and AR(1) are superior to MNL and have the same RMSD.
7. Conclusions This paper has developed a rigorous analytical framework to model timing to work at individual level. It contributes to a better understanding of how ICT and in particular travel time information affect decision-making and ultimately shapes the Time-Space Prism of commuters. All these aspects are high in the agenda of transport geographers and modelers for their impacts on transport demand and urban forms. The methodology is based on a dynamic discrete choice model where sequences of departure time choices are modeled in response to traffic conditions under two decision rules; the first assumes perfect knowledge of travel time over future periods, while the second accounts for the stochastic nature of traffic conditions. Data extracted from a regional household travel survey and travel information obtained from Google Maps are linked based on spatial and temporal characteristics of the commuting trips. The dynamic model specified for the two different decision rules proposed are estimated and compared to a static logit model. The empirical results provide important insights into the determinants of commuter's departure time choices, and on the way they shape the time space prisms and its vertices.
6. Scenario testing As road conditions change overtime, commuters may change their routes to shorten their travel time and/or travel distance. Changes in travel time and travel distance might also lead to different departure time choices. Thus, the section here is to test the impacts of travel time and travel distance changes on commuters' departure time choices using the proposed dynamic framework. We carried out two tests where travel time and travel distance are increased respectively by 10% and 20%, and for each of the scenarios proposed we calculated how commuters change their behavior concerning departure time decisions. The rise in travel time and travel distance, together with the uncertainty in future travel conditions, are expected to increase the likelihood of leaving home for work earlier in order to arrive on time at the final destination. The results of scenario testing under two dynamic models (Table 4) is consistent with the general expectation and with the sign of the parameters estimated. If commuters had perfect knowledge (Pk) of Table 4 Scenario test. Difference between departure time and work start time (min)
Dynamic logit with PK
Dynamic logit with AR(1)
Base Scenario
Changes in diff. (Travel Time + 10%)
Changes in diff. (Travel Time + 20%)
Changes in diff. Distance +10%)
Changes in diff. (Distance +20%)
Base Scenario
Changes in diff. (Travel Time + 10%)
Changes in diff. (Travel Time + 20%)
Changes in diff. (Distance +10%)
Changes in diff. (Distance +20%)
−110 −100 −90 −80 −70 −60 −50 −40 −30 −20 −10 0 10 20 30 40 50
0.8% 1.3% 2.1% 3.4% 4.6% 6.5% 9.8% 10.8% 12.1% 14.9% 10.9% 8.6% 7.1% 3.0% 1.9% 1.3% 0.4%
0.1% 0.2% 0.2% 0.3% 0.3% 0.5% 0.4% 0.3% 0.1% −0.3% −0.5% −0.6% −0.5% −0.2% −0.1% −0.1% 0.0%
0.3% 0.3% 0.5% 0.6% 0.7% 0.9% 0.8% 0.5% 0.1% −0.6% −1.0% −1.1% −1.0% −0.4% −0.3% −0.2% −0.1%
0.1% 0.1% 0.1% 0.1% 0.1% 0.2% 0.1% 0.0% 0.0% −0.1% −0.2% −0.2% −0.1% −0.1% 0.0% 0.0% 0.0%
0.1% 0.2% 0.2% 0.2% 0.2% 0.3% 0.2% 0.1% −0.1% −0.3% −0.3% −0.3% −0.3% −0.1% −0.1% −0.1% 0.0%
0.5% 0.9% 1.7% 2.9% 4.3% 6.9% 10.9% 12.7% 14.6% 15.8% 10.3% 7.3% 5.9% 2.5% 1.6% 1.1% 0.3%
0.1% 0.2% 0.2% 0.3% 0.5% 0.6% 0.5% 0.3% −0.2% −0.7% −0.6% −0.4% −0.4% −0.1% −0.1% −0.1% 0.0%
0.3% 0.3% 0.5% 0.7% 1.0% 1.1% 0.8% 0.5% −0.5% −1.5% −1.1% −0.8% −0.7% −0.3% −0.2% −0.1% 0.0%
0.1% 0.1% 0.1% 0.2% 0.2% 0.2% 0.1% 0.0% −0.2% −0.3% −0.2% −0.2% −0.1% −0.1% 0.0% 0.0% 0.0%
0.2% 0.2% 0.2% 0.3% 0.4% 0.4% 0.2% 0.0% −0.3% −0.6% −0.4% −0.3% −0.2% −0.1% −0.1% 0.0% 0.0%
8
Journal of Transport Geography 82 (2020) 102548
H. Dong and C. Cirillo
Modeling estimation results help analysts better understand spatial and temporal characteristics of commuter morning patterns. Expected travel time to work, expected time of arrival together with working starting time, all of which depend on traffic conditions and its variability, are among the major constraints when people decide about travel and activities. Distance to work and rigid working schedules widen the space-time prism, by pushing departure time earlier. The effect of sociodemographics is unstable across the model specifications tested. An higher number of vehicles in the household provides more flexibility and allows commuters to start their commute later; being an adult is also found to delay the choice to depart to work. Goodness of fit statistics and out of sample validation confirms that the dynamic approach is superior to standard logit model. Despite the difficulty in recovering the peaks in demand, the dynamic formulations proposed are able to approach low and high peaks of departure choice probabilities better than static logit model. The econometric-based methodology applied to the departure time problem and the data linkage approach provides transportation analysts and modelers with an innovative tool analysis to study the spatial and temporal characteristics of individual activity patterns. Given the relevance of the problem, the current study can be extended in several directions. First, the proposed model only considers travelers' commuting trips. Traveler's decisions about non-work trips (i.e. shopping, leisure, social trips) can also be included in the model for a comprehensive consideration of all the activities in the time-space prism. Second, the regional and national household travel surveys should be linked to real-time traffic information as they become available. Third, in order to generalize the results obtained it is necessary to calibrate and validate the model with traffic information collected over longer time periods. Finally, reliability of en-route traffic should also be considered as a variable in the model.
drivers’compliance with route guidance advice. Transp. Res. Rec. 1306, 59–68. Bradley, M., Bowman, J.L., Griesenbeck, B., 2010. SACSIM: an applied activity-based model system with fine-le spatial and temporal resolution. J. Choice Model. 31, 5–31. Chen, P.S.T., Mahmassani, H.S., 1993. Dynamic interactive simulator for studying commuter behavior under real-time traffic information supply strategies. Transp. Res. Rec (No. 1413). Chin, A.T., 1990. Influences on commuter trip departure time decisions in Singapore. Transp Res. Part A: General 245, 321–333. Cirillo, C., Xu, R., Bastin, F., 2016. A dynamic formulation for car ownership modeling. Transp. Sci. 50, 322–335. De Jong, G., Daly, A., Pieters, M., Vellay, C., Bradley, M., Hofman, F., 2003. A model for time of day and mode choice using error components logit. Transp Res Part E: Logist Transp Rev 393, 245–268. Dijst, M., 2004. ICTs and accessibility: an action space perspective on the impact of new information and communication technologies. Transport developments and innovations in an evolving world 27–46. Doherty, S.T, 2003. Activity Attribute Decision Sequencing. Paper presented at the 82nd Annual Meeting of the Transportation Research Board. D.C., Washington. Fosgerau, M., Frejinger, E., Karlstrom, A., 2013. A link based network route choice model with unrestricted choice set. Transp. Res. B Methodol. 56, 70–80. Hägerstrand, T., 1970. What about people in regional science? Pap. Reg. Sci. Assoc. 241, 6–21. Hess, S., Daly, A., Rohr, C., Hyman, G., 2007. On the development of time period and mode choice models for use in large scale modelling forecasting systems. Transp. Res. A Policy Pract. 419, 802–826. Janelle, D.G., Gillespie, A., 2004. Space–time constructs for linking information and communication technologies with issues in sustainable transportation. Transp. Rev. 246, 665–677. Koutsopoulos, H.N., Lotan, T., Yang, Q., 1994. A driving simulator and its application for modeling route choice in the presence of information. Transp. Res. Part C: Emerg. Technol. 22, 91–107. Lemp, J.D., Kockelman, K.M., Damien, P., 2010. The continuous cross-nested logit model: formulation and application for departure time choice. Transp. Res. B Methodol. 445, 646–661. Liu, Y., Cirillo, C., 2018. A generalized dynamic discrete choice model for green vehicle adoption. Transp. Res. A 2018 (114), 288–302. Mahmassani, H.S., Chang, G.L., 1986. Experiments with departure time choice dynamics of urban commuters. Transp. Res. B Methodol. 204, 297–320. Mahmassani, H.S., Herman, R., 1990. Interactive experiments for the study of tripmaker behaviour dynamics in congested commuting systems. Dev. Dyn. Act. Based Appr. Travel Anal. 272–298. Mahmassani, H.S., Liu, Y.H., 1999. Dynamics of commuting decision behaviour under advanced traveller information systems. Transp. Res. Part C: Emerg. Technol. 72, 91–107. McCafferty, D., Hall, F.L., 1982. The use of multinomial logit analysis to model the choice of time to travel. Econ. Geogr. 583, 236–246. Miller, H.J., 2005. A measurement theory for time geography. Geogr. Anal. 371, 17–45. Miller, H.J., 2015. Selected Keynote Speech Abstracts. Can we build geographic knowledge from big data? In Spatial Data Mining and Geographical Knowledge Services ICSDM, Data-driven geography, pp. 2015. Pendyala, R.M., Yamamoto, T., Kitamura, R., 2002. On the formulation of time-space prisms to model constraints on personal activity-travel engagement. Transportation. 29, 73–94. Rust, J., 1987. Optimal replacement of GMC bus engines: an empirical model of Harold Zurcher. Econometrica: J. Econ. Soc. 555, 999–1033. Senbil, M., Kitamura, R., 2004. Reference points in commuter departure time choice: a prospect theoretic test of alternative decision frames. Intell. Transp. Sys. 81, 19–31. Small, K.A., 1982. The scheduling of consumer activities: work trips. Am. Econ. Rev. 723, 467–479. Vaughn, K.M., Abdel-Aty, M.A., Kitamura, R., Jovanis, P.P., Yang, H., Kroll, N.E., Post, R., Oppy, B., 1993. Experimental analysis and modeling of sequential route choice under an advanced traveler information system in a simplistic traffic network. Transp. Res. Rec. 1408, 75–82. Wu, Y.‐H., Miller, H.J., 2001. Computational Tools for Measuring Space–Time Accessibility within Dynamic Flow Transportation Networks. Journal of Transportation and Statistics 4 (2/3), 1–14.
Acknowledgements We thank the editor and two anonymous reviewers for their constructive comments, which helped us to improve the manuscript. References Abkowitz, M.D., 1981. An analysis of the commuter departure time decision. Transportation 103, 283–297. Adler, J.L., Recker, W.W., McNally, M.G., 1993. A conflict model and interactive simulator FASTCARS for predicting en route driver behavior in response to real-time traffic condition information. Transportation 202, 83–106. Aguirregabiria, V., Mira, P., 2007. Sequential estimation of dynamic discrete games. Econometrica 75, 1–53. Bajwa, S., Bekhor, S., Kuwahara, M., Chung, E., 2008. Discrete choice modeling of combined mode and departure time. Transportmetrica 42, 155–177. Ben-Elia, E., Shiftan, Y., 2010. Which road do I take? A learning-based model of routechoice behavior with real-time information. Transp. Res. A Policy Pract. 444, 249–264. Bhat, C.R., Steed, J.L., 2002. A continuous-time model of departure time choice for urban shopping trips. Transp. Res. B Methodol. 363, 207–224. Bonsall, P., Parry, T., 1991. Using an interactive route-choice simulator to investigate
9
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Journal of Transport Geography journal homepage: www.elsevier.com/locate/jtrangeo
Space-time dynamics: A modeling approach for commuting departure time on linked datasets Han Donga, Cinzia Cirillob, a b
T
⁎
Transurban North America, Suite T500, 7900 Westpark Drive, Tysons, VA 22102, United States Department of Civil and Environmental Engineering, University of Maryland, College Park, 3250 Kim Engineering Building, College Park, MD 20742, United States
A R T I C LE I N FO
A B S T R A C T
Keywords: Departure time Data linkage Discrete choices Dynamic in travel behavior
Commuters' departure time related decisions are important in time geography. Analytic tools have been proposed to capture the inherent choice determinants both in time and space. Although the dynamic aspects of the problem have been identified, most of the existing studies are based on static models. In this paper, a dynamic modeling framework is proposed to explore the relationship between commuters' departure time choices and the evolution of en route traffic. A data linkage method is developed to create an integrated dataset that enables the observation of commuters' reaction to changes in travel time and traffic conditions over time. A regional household travel survey is linked to travel information obtained from the Google Maps application program interface (API), creating a synthetic longitudinal dataset. Two decision rules are applied to model commuters' response to the evolution of traffic. The results indicate that travel time, distance to work location, flexibility in working schedule, expected arrival time, and commuters' sociodemographic influence departure time choices. It is also found that accounting for dynamics improves model fit and out-of-sample predictions. Both the dynamic model and the proposed data linkage method contribute to the understanding of human activities in space and time and can be used to enhance transportation demand analysis and urban policy studies.
1. Introduction Transportation geographers and urban planners concur that both spatial and temporal factors should be taken into account when designing the future of cities and regions and proposing innovative solutions to transportation related issues. The need for spatio-temporal representation of human activities has resulted into the rapid development of disaggregate analysis and modeling tools to improve both theoretical understanding and policy evaluation (Janelle and Gillespie, 2004). In transport geography the majority of the existing works builds on the conceptual breakthroughs by Hägerstrand (1970), especially in the modeling of individual activity behavior (Doherty, 2003; Dijst, 2004). More recently, geographers have played prominent roles in extending the underlying theory of time geography (Miller and Wu, 2000; Janelle and Gillespie, 2004) that proposes a constraints-oriented approach to understanding human activities in space and time. Decisions about departure time are fundamental to identify the spatio-temporal conditions for human activities. In Spatio-Temporal Prism theory (STP), departure and arrival time are among the parameters to be identified for the definition of its vertices that in turn identify the space time paths (Miller, 2015). Activity participation is
⁎
determined by the location and timing of anchors that require presence (such as home and work) and is constrained by the time budget for access activities. Daily paths are also affected by the ability to trade time for space and the availability of information and communication technologies (ICTs) (Miller, 2015). The time geography, of which temporal related decisions are an important component, is a powerful conceptual framework for understanding constraints on human activity participation in space and time. However, rigorous, analytical definitions of basic time geography entities and relationships are not fully developed (Miller, 2005). This paper investigates commuters' scheduling choices and aims at capturing the dynamic in their decision making process. The models proposed and the associated results respond to the need of better theoretical framework and analyses tool to understand the timing of work and the effects of Information Communication Technology (ICT). More specifically, the choice of leaving home to work is updated every ten minutes by considering actual travel time to destination and expectation of future travel conditions. The framework explicitly models the optimal time to depart, and updates network travel conditions as they become available. A data linkage method is applied to construct the database needed for the analysis; a regional household travel survey is
Corresponding author. E-mail address: [email protected] (C. Cirillo).
https://doi.org/10.1016/j.jtrangeo.2019.102548 Received 15 February 2019; Received in revised form 10 September 2019; Accepted 18 September 2019 0966-6923/ © 2019 Elsevier Ltd. All rights reserved.
Journal of Transport Geography 82 (2020) 102548
H. Dong and C. Cirillo
and Parry, 1991; Chen and Mahmassani, 1993; Koutsopoulos et al., 1994; Vaughn et al., 1993). In particular, Mahmassani and Liu (1999) used an interactive multi-user simulator to examine the day-to-day commuter behavior under real-time information. Ben-Elia and Shiftan (2010) proposed a learning-based model of route-choice behavior which investigated the impact of ATIS and personal experiences on users' route choices. Both studies are based on data collected in controlled lab experiments. More broadly the advances in ICTs and the exponential growth of the information available to people are expected to altering the space–time constraints of daily life. Nowadays, real-time traffic information has become available to commuters through different apps and online data providers. Google pulls in traffic data from multiple sources for its Maps app, including information from police and local transportation departments. Waze, a company Google acquired in 2013, has mobile apps for Android and iOS devices. Waze members can use the app for navigation to a destination and to report traffic observations and incidents along the route. The Regional Integrated Transportation Information System (RITIS) is an automated data sharing, dissemination, and archiving system maintained by the Center of Advanced Transportation Technology (CATT) at the University of Maryland. Among a number of services and measures provided, the general public can get access to real time data feeds, including travel time, accident and weather conditions. The availability and the accessibility of real time information is changing the way commuters make travel related decisions and requires a shift in the paradigms used to model traveler behavior, especially dynamic in decision making. Only recently, models that explicitly account for the temporal dimension of individual choices have been introduced in the field of transportation. Models of this type are derived from Rust (1987) who proposed a structural dynamic approach to solve an optimal stopping problem. In his first application the manager of a bus company (Harold Zurcher) had to decide when to replace the engine of his bus fleet. This model that applies to a single agent and to homogeneous products is still largely applied in economics (see Aguirregabiria and Mira, 2007) for a comprehensive review of dynamic discrete choice models). In transportation and handful number of applications exist. Fosgerau et al. (2013) used a dynamic discrete choice framework in the context of route choice; in particular, a recursive logit (RL) models path choice as a sequence of link choices. Liu and Cirillo (2018) have developed a generalized modeling framework for vehicle ownership related decisions and applied it to model the adoption of green vehicles. The model allows for multiple agents' decisions, models heterogeneous products and accounts for the volatility in vehicle characteristics and fuel price over time. From the review presented in this section, it is evident that dynamic modeling approaches would contribute to a better understanding on where individuals are in space and how they trade time under constraints when deciding about the time to go to work.
linked to pre-trip travel time information obtained from Google Map API. In addition, impacts of traffic evolution on departure time decisions are tested under two different behavioral scenarios: 1) Perfect Knowledge of traffic conditions and 2) Uncertainty in traffic conditions. The remaining of this study is organized as follows. A review of existing studies on commuters' departure time is provided in Section 2. Section 3 describes the two major data sources used in this study and the proposed data linkage method. In Section 4, a dynamic framework is introduced and adapted to the problem of departure time under deterministic and stochastic knowledge of traffic conditions. In Section 5, the proposed models are estimated and validated, results compared to static logit models. The end Section summarizes the empirical results and outlines the major contributions. 2. Literature review An operational framework for departure time decisions exist in transportation demand modeling, where these decisions are commonly modeled using Multinomial Logit Models (MNL) (see e.g. Abkowitz, 1981; Small, 1982; McCafferty and Hall, 1982). Departure time based on MNL specifications have been included in four step models of both trip and tour types, or in more advanced activity based models (Bradley et al., 2010). The day is divided into a limited number of discrete time periods, and logit is applied to capture the tradeoff between alternative time-of-day windows. Utility functions are defined in terms of individuals' socio-demographics, level of service variables (travel time and travel cost), and work schedule. Logit type models suffer from a number of limitations: it is not possible to model correlation among adjacent time periods, observations from the same individual are assumed to be independent and decisions are static as well as all the variables included in the utility functions. To relax these constraints, other approaches have been proposed; more advanced models for departure time decisions include nested logit (Chin, 1990), cross nested logit (Bajwa et al., 2008), continuous cross-nested logit (Lemp et al., 2010), and error components logit (De Jong et al., 2003; Hess et al., 2007). These types of GEV models mainly capture correlation across subsequent time intervals, but are unable to model dynamic in decisionmaking. Moreover, a discrete representation of departure time has several drawbacks. The time interval duration that constitutes the discrete alternatives is discretionary and could lead to different estimates and model fits, and aggregation precludes analyses at a very fine time resolution. Continuous-time hazard duration models have been proposed for trip departure time choice. Following this approach, Bhat and Steed (2002) modeled departure time choice on an entire day for urban shopping trips with a non-parametric continuous hazard model. However, applications of hazard-based models are still quite limited. The dynamic decision process of commuters, especially departure time decisions, is worthy of investigation. Mahmassani and Chang (1986) studied day-to-day dynamics of commuters' patterns in a series of simulation experiments. Factors that were considered important to study trip makers' behavior include: schedule delay, or the absolute value of the difference between desired and actual arrival time; travel time, and its variation from one day to the next; and traffic flow quality descriptors (concentration, speed and volume). Results showed that commuters tend to remain with the same choices until the actual schedule delay exceeds tolerable values. This adjustment takes place in response to learning from one's repeated experience and outside information sources. The study is based on heuristics as modeling individual decision making and learning in highly dynamic systems is complex. The effect of real-time information on driver decision making has been of interest to the transportation community since the 90s. Early studies were mainly based on laboratory experiments due to the limited deployment of Advanced Transportation Information System (ATIS) technologies (Mahmassani and Herman, 1990). Several studies have provided insights into trip makers' decision processes under different types of ATIS-provided information (Adler et al., 1993; Bonsall
3. Data linkage Automobiles and smart phones are great facilitators of personal time–space convergence and extensibility (Janelle and Gillespie, 2004). Also, travel and communication activities of individuals and institutions are being increasingly monitored; GPS devices provide a means for tracking real-time and in detail individual's behavior. In this study we use traditional survey data from a regional household diary to extract information about spatial location of fixed activities (home and work) and about temporal decisions (time to depart from home to work). These data are augmented by extracting information about traffic conditions from commonly available GPS devices. Specifically, two data sources are linked in the study: (1) The 2007–2008 TPB-BMC Household Travel Survey (HHTS), which is a regional household travel survey that records socio-demographic, spatial and temporal information about daily trip and activity schedule (trip purpose, trip origin and 2
Journal of Transport Geography 82 (2020) 102548
H. Dong and C. Cirillo
destination (OD) centroid locations, for the same time of day and weekday observed in HHTS survey, were requested from Google Maps Distance Matrix API. A 10-min time interval is adopted for the three hours observed which means that seventeen time periods are available for each commute leg and to each respondent observed in HHTS.
Table 1 HHTS sample – descriptive statistics. Variable name
Mean
Std. error
Min
Max
Trip distance (mile) No. of people in household No. of students in household No. of driving license holders in household No. of workers in household No. of vehicles in household Average household income ($×104) Young (age 19–25) Adult (age 26–45) Senior (age 46–60) Gender (female = 0, male = 1) Ownership of household Vehicle per worker
12.52 2.39 0.68 1.86 1.67 1.93 11.78 0.04 0.44 0.42 0.51 0.81 1.24
10.69 1.08 1.00 0.70 0.64 0.73 5.29 0.19 0.50 0.49 0.50 0.39 0.52
0.20 1.00 0.00 1.00 1.00 0.00 0.50 0.00 0.00 0.00 0.00 0.00 0.00
65.30 4.00 5.00 5.00 5.00 3.00 20.00 1.00 1.00 1.00 1.00 1.00 3.00
3.3. Data linkage methodology As anticipated, a data linkage method is applied to combine these two datasets. This method allows data of a single individual to be compiled from different data sources, enabling more powerful and effective analyses to be carried out. In particular, datasets created through linking individual records constitute a critical resource for research in health, epidemiology, economics, sociology and many other areas (i.e. Vaughn et al., 1993). It is expected that speed relative to the same OD pair shows a similar pattern for a given time of day and day of week. Thus, differences in travel time between the same OD pair for the same time and the same weekday from two data sources can be expressed as a linear relation of difference in distance traveled and error component. In this study, travel time obtained from ATIS system is linked to the HHTS through Eq. (1).
destination, and trip departure and arrival time) of household in the Washington DC metropolitan area; and (2) Travel time information obtained from Google Maps. The two files are linked by considering the following key variables: origins and destinations of each trip in the HHTS, the time of day and the day of the week in which the trips were observed.
TitA − γtitA = α + κ (ditA − DitA) + εi,
3.1. The 2007–2008 TPB-BMC household travel survey (HHTS)
(1)
TitA
where is the travel time of individual i at the actual departure time t in HHTS. titA is the travel time that is obtained from ATIS for the same departure time t of the same weekday, DitA is the commuting distance in HHTS, ditA is the commuting distance for the same OD pair obtained from ATIS for the departure time t; α, γ, κ are the associated parameters, εi is an individual-specific random term. Table 2 reports the results obtained from the linkage model. All the estimates are significant with the expected sign. It should be noted that only a single travel time record for each commuting trip could be obtained from the HHTS survey. To enrich the , γ ̂ and κ ̂ are then applied to infer dataset, the estimated parameters α travel time Tit of individual i using tit, dit, Dit over the whole three hour period that was modeled. In order to recover the actual arrival time of it of respondent i are then adjusted each trip in the sample, estimated T with the difference between actual observed travel time TitA and estiit + TitA -T itA , which is T itA . Based on the inferred travel mated travel time T time and work start time, other time varying variables are calculated, which are described as follows:
The HHTS was collected by the Metropolitan Washington Council of Governments (MWCOG) from February 2007 to April 2008; it gathers information about demographics, socioeconomic variables and one-day trip making characteristics of residents in the Washington DC Metropolitan area. The data are geocoded at the Traffic Analysis Zone (TAZ) level, with a centroid location in each zone. For this study, only commuter trip legs from home to work by car as driver with final destination in the Washington area were selected. In total, 938 observations matched these criteria. Descriptive statistics related to the population selected are reported in Table 1. The origin and destination distributions are showed together with distance normalized by travel time in Fig. 1a and b respectively. Average travel speeds between ODs are represented with colors ranging from yellow to red. As indicated in Fig. 1a, trips originating in urban area tend to have lower travel speed than trips originating from rural area. 3.2. Advanced travel information system (ATIS)
• DE : Time difference between the expected arrival time and the it
Travel information is now available to travelers through different channels, and real time information about travel time and traffic conditions can be easily requested or accessed using Application Programming Interface (API). For example, Google Maps Distance Matrix API provides users with the fastest route between a given OD pair and for a specific time. The dataset used for this study, which contains actual and future travel time between home and work locations, was constructed using Google Maps. However, only future and real-time traffic information is available from Google Maps while historical data cannot be retrieved. Since Google Maps uses historical data to predict future traffic, we believe that future traffic conditions based on Google Maps are more stable and represent better trends in traffic than real-time information. Data were requested using Google Maps Distance Matrix API on Nov. 6th, 2016 for the upcoming two weeks. Work start time is defined as a reference point to construct the database. In prospect theory, it has been found that commuters use arrival time information to decide about their daily departure choices (Senbil and Kitamura, 2004). In the HHTS survey, we found that > 85% of commuters in the sample choose to depart from home within the time window that starts two hours before work start time and ends one hour after (Fig. 2). Travel time and trip distances between origin-
• •
work start time of commuter i at time t. DEit < 0 if commuter arrives before start time; DEit > 0 if commuter arrives after start time. IPit: Indicator of late penalty. If commuter has fixed working schedule and arrives after work start time, IPit = 1. Otherwise, IPit = 0. ILit: Indicator of being late. If commuter arrives after work start time, ILit = 1. Otherwise, ILit = 0.
4. A dynamic framework for departure time choices In this section we provide the mathematical formulation (for further details please see Cirillo et al., 2016) for modeling spatio-temporal dynamics in decisions related to departure from home to the work location and a behavioral interpretation of the framework proposed. Commuters are observed during a three-hour time window (two hours before work start time and one hour after), which has been divided into seventeen intervals of ten minutes each. According to our modeling framework, at each time period the individual chooses to stay at his home location or to depart (binary choice) depending on information relative to actual travel time and his (her) expectations about future traffic conditions. The sequence of decisions overt time can be represented as a decision tree (see Fig. 3). Scheduling related variables 3
Journal of Transport Geography 82 (2020) 102548
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Fig. 1. a. Distribution of commuting trips' origins. b. Distribution of commuting trips' destinations.
αi= α, and λi= λ, i = 1, …, I. Travel time and the associated variability is the dynamic variable considered in this study. λi is a vector of parameters related to yit; ϵit is an individual-specific random term, whose components are independently and identically extreme value (GEV) distributed among individuals and periods.
(DE, IP, IL), socio-demographic characteristics, work location might affect his/her decisions. This problem is treated as an optimal stopping problem over a finite time horizon, where the commuter decides about the optimal time to leave home. Once the commuter decides to leave for work, his (her) chain of decisions is terminated. Two behavioral assumptions are considered: 1. Perfect information on future travel time; 2. Uncertainty in future traffic conditions. The first assumes that travel time trends will behave according to past information derived by historical data available through ATIS; the second assumes that travel time is a random variable and that a random walk (Eq. (9)) will determine future traffic conditions.
The decision process can be described as follows: at time t, each commuter decides whether to start the trip to work or to postpone until the optimal time τ, which is the departure time that maximizes commuter's utility. Commuter's departure decision regarding the time to leave home for work can be treated as an optimal stopping problem (Eq. (2)).
4.1. The model formulation
τ−1
Dt (bit , cit ) = max
Consider a set of commuters i = {1 … I} and time periods t = 0, 1, …, T, commuter i has two options at time t:
τ
(2)
It is important to note that the expectation in (2) is taken with respect to the dynamic variable travel time specified as yt. The equation can be transformed from (2) into
• Stay at home and obtain a one-period payoff defined as c . This is a it
•
⎧ ∑ cit + E yτ [biτ | yt ] ⎫⎬, ⎨ k=t ⎩ ⎭
utility function which is a linear combination of attributes related to commuter's socio-demographics and working schedule characteristics (xit), and of a parameter vector (θi); Leave home for work and obtain a final payoff uit. It is assumed that the departure choices are consistent at each time t, and that the final payoff is expressed as a random utility function: bit = u (xit, yit, θi, λi, εit) where xit, θi are defined as above, while yit is a random vector of dynamic attributes of road condition at time t. Although departure time decisions vary across commuters, parameters here are assumed to be the same over individuals, i.e. θi= θ,
Dt (bit , cit ) = max {bit , cit + Et + 1 [bi,t+1 , ci, t + 1 | yt ] } ,
(3)
Based on (3), we see that the decision process simply consists in leaving home at time t or remaining at home and postpone the decision to depart and take the payoff cit plus the future return. We now define, Wi (yt) as the reservation utility level for driver i:
Wi (yt ) = cit + E yt + 1 [bi, t + 1 , ci, t + 1 | yt ], Then the optimal stopping problem is given by: 4
(4)
Journal of Transport Geography 82 (2020) 102548
H. Dong and C. Cirillo
Fig. 1. (continued)
Γ(yt ) = {bit | bit > Wi (yt ) } ,
def
(5)
πi0t (yt ) = Pit [Dt (bit ) = Wi (yt ) | yt ] = Pit [bit ≤ Wi (yt )] = Fv (Wi (yt ), yt ) = e−e
Using Eq. (5), (3) can be simplified as
Dt (bit ) = max {bit , Wi (yt ) } ,
(Wi (yt ) − rit ) ,
(7)
where rit is the mode of distribution of bit. The probability of leaving home is consequently equal to h (yt) = 1 − πi0t(yt).
(6)
Commuter i will choose to leave home at time t only when bit > Wi(yt). If i is randomly drawn from the population, the analyst can compute the probability of postponing the departure until next period as: 16.00% 14.00% 12.00% 10.00% 8.00% 6.00% 4.00% 2.00% 0.00%
-24.0 -11.0 -7.6 -6.5 -5.2 -4.1 -2.7 -2.2 -1.7 -1.2 -0.9 -0.7 -0.6 -0.4 -0.3 -0.1 0.0 0.1 0.2 0.3 0.5 0.8 1.1 1.5 2.2 5.0
Dsitribution of observations
−
Gaps between departure time and work start time (hr) Fig. 2. Distribution of time difference between departure time and work start time. 5
Journal of Transport Geography 82 (2020) 102548
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anticipate the traffic just one step ahead with E [D3] = 0. Fig. 3 shows the structure of the estimation process.
Table 2 Data linkage model – estimation results. Variable Name
Coefficient
Constant Travel time tit Difference between ATIS and HHTS distances (dit − Dit) ⁎⁎⁎
α γ κ
Estimates (Std. Error in parenthesis)
4.3. Rules in departure time decisions
0.1998⁎⁎⁎ (0.017) 0.7558⁎⁎⁎ (0.037) −0.0074⁎⁎⁎ (0.002)
Real-time travel time information is expected to alter spatial and temporal patterns of human activities. Our theoretical framework is designed to capture these effects through the definition of the expected utility. The future appears uncertain to commuters, and this evolution needs to be represented in some sort. It is proposed to estimated expectation of future traffic conditions from the respondent's perspective instead of using market (equilibrium) values, as it is commonly done in dynamic discrete choice models used in economics (Rust, 1987; Fosgerau et al., 2013). In this sense, this research experiments with two different decision processes: perfect knowledge of travel time and stochastic travel time.
Significant at the 95% level.
4.2. The dynamic estimation processes We first summarize the parameters to be estimated in the dynamic departure time problem:
• θ, a vector of parameters related to commuter i's attributes x ; • λ, a vector of parameters related to dynamic attributes of traffic
• Perfect knowledge of travel time (PK): The dynamic model is esti-
it
condition at time t, yjt;
The parameters' estimation is performed by maximizing the likelihood function: I
(θ, λ ) =
•
H
∏ ∏ Pit [Dt (vit ) | θ, λ], i=1 t=1
(8)
here the probability follows the distribution of the variables ϵit, as in Eqs. (6) and (7), given the values of the parameters, I is the number of commuters, and H is the number of time periods over which we observe each commuter. Simulated log-likelihood estimation method is used to optimize Eq. (8). In the estimation process, the probability of πi0t depends on the calculation of Wit, as Eq. (4). The key step during the estimation process is to identify the expected utility, Eyt+1[vi, t+1, ci, t+1| yt]. At each time period, commuters are assumed to account for traffic condition in future scenarios, which is determined by travel time and travel time variability over time. The time horizon is composed of a limited number of time periods. At time t, the driver faces two possible alternatives: leave home or stay; at t + 1, those who are still at home face these two scenarios again. Thus, the decision process is formulated by means of a decision tree (see Fig. 3). The following steps describe the procedure to calculate πi0, 0and the expectation Ey1[D(vi1, ci1)| i], which is denoted by E [D1] for simplification purpose. Given that the traffic conditions are changing over time, here it is assumed that individuals make prediction only for one period ahead. Therefore, at time t = 0, the driver can anticipate the future characteristics of the traffic at time period t = 1. E [D2] = 0 because individual knows nothing about the traffic conditions at t = 2 when faced with the decisions at t = 0. The process of calculating E [D1] is recursive with known utility at the end of the perspective horizon. Wi(y0) can be obtained after calculating E [D1]. This step is repeated to calculate πi0, 1with the same assumption that driver can
mated assuming that commuters have “perfect knowledge” of future travel time. At time t, commuters know exactly how the traffic will be in the next 10 min. Future travel time yi, t+1 are assumed to be known and are extracted from the linked dataset. Stochastic travel time (AR(1)): Traffic is assumed to follow a stochastic process where dynamic variables change according to a random walk with a drift. Autoregressive (AR) models are used to model this time-varying process; in particular we use an AR(1) model to calculate travel time Tt+1 based on the value observed at time t:
Tt + 1 = αTt + ψ + ξt ,
(9)
In Eq. (9)α is the dependence factor, ψ is the drift, ξt is a normally distributed error term with mean zero and variance σ2. Based on the traffic data available for the study region, it is found that the dependence factor (α) is equal to 0.9967, the drift (ψ) is equal to 0.0058, and the standard deviation (σ) of the error term is 0.0192. Those values are used to compute the choice probability of waiting at home or departing according to the dynamic formulation described in previous sections. 5. Model estimation results and validation In this section we present results from model estimation; the interpretation of the results is based on econometric considerations and more importantly on their implications on the spatial and temporal components of the individual activity program. All results are shown in Table 3; where we report estimates for the dynamic model with perfect knowledge (PK) and with stochastic travel time AR(1). All the estimates are specific of the alternative departing at the current time period. Household and individual characteristics (age; gender; and household vehicle ownership), time varying variables (difference of en-route travel times across subsequent time periods, T; expected early arrival time, DE), space-time constraints (commuting distance; and working
Fig. 3. Scenario tree. 6
Journal of Transport Geography 82 (2020) 102548
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Table 3 Model estimation results. Variable name
ASCdep Adult (dummy) Male (dummy) Number of vehicles Travel time (T) Time difference between expected arrival time and work start time (DE) Trip distance Fixed working schedule (dummy) No. of observation LL(0) LL(final) pseudo R2 RMSD
Dynamic logit with PK
Dynamic logit with AR(1)
Logit
Estim.
t-stat
Estim.
t-stat
Estim.
t-stat
6.579 −0.243 0.142 −0.070 −0.076 0.118 0.034 0.145 940.0 −8085.2 −2273.2 0.719 0.113
30.6 −2.5 1.5 −1.1 −36.4 53.6 6.1 1.6
12.410 −0.598 0.259 −0.560 −0.121 0.179 0.061 0.026 940.0 −8085.2 −2358.1 0.708 0.113
55.5 −7.21 1.3 −6.3 −21.4 93.6 2.9 0.1
3.419 −0.120 0.018 0.019 −0.053 0.074 0.017 0.266 8595.0 −5957.6 −2348.8 0.606 0.125
15.1 −1.5 0.2 0.3 −15.6 29.9 3.2 3.4
schedule), are part of the final specification.
5.3. Time-Space constraints The positive coefficient estimated for trip distance attests that commuters with longer commuting trips are forced to leave home earlier, due probably to the uncertainties in travel time for long distances. The work location in spatial geography is one of the possible coupling constraints or location that individual has to join for shared activities, including work (Miller, 2015). Our analysis indicates that distant work locations have a significant effect on the determination of the time-space prism and in particular on its temporal vertices. The variable related to fixed working schedule, although not very significant in the dynamic formulation, is positive indicating that commuters with fixed working schedule prefer to start their trip earlier due to potential delay penalty.
5.1. Individual and household sociodemographic As expected, socio-demographic variables shape individuals' spacetime prism form, and in particular its vertices. As noted by Pendyala et al. (2002) while a trip is observable and is by definition always contained in a prism, the prism itself can rarely be defined because the constraints that define these vertices are not observed in survey from official sources like Regional or National travel survey. Interesting our results are in line with what found by the same authors when trying to identify the vertices of a space-time prisms from trip data. For example, the number of vehicles in the household is found to be significant in the dynamic model and the negative coefficient reveals that household with more vehicles are likely to start their trip later in the morning. Obviously, owning more cars give to commuters the flexibility to drive alone to the work place and to start their commute later. Male commuters are more likely to push earlier the morning commute vertex, while adults are actually leaving home later, presumably having greater flexibility than younger people.
5.4. Comparison among models and validation When comparing estimates of these two dynamic models, some interesting results are revealed. Time varying variables (such as travel time, DE, and trip distance) of the dynamic model with perfect knowledge have weaker effects on departure decisions. For example, estimate of travel time in is −0.076 and − 0.121 respectively for the model assuming perfect knowledge and stochastic variability of traffic conditions respectively. Coefficient estimates and model fit are compared to those obtained with static logit model. It should be noted that for the dynamic model the entire chain of decisions over the time periods that proceed the departure from home constitute one observation, while in the logit model each time period is treated as a single observation. This explain the difference in the number of observations for the dynamic and logit model respectively. The final likelihood value of two dynamic models is close. The fit of the models improves when considering the dynamic nature of the problem; the pseudo R2 increases from 0.606, the value obtained with the logit model, to 0.719 and 0.708 for dynamic models. In order to compare the prediction power of the models, we re-estimated the model on 80% of the available observations and then we applied the model estimates to predict the departure time choices in the remaining part of sample. Fig. 4 shows the estimated percentage of departures at each time interval. The real choices are characterized by peaks, which occur 50 min and 20 min before, and 30 min after work start. These peaks are quite difficult to recover with any of the formulations adopted, but the dynamic models mimic low and high values of departure choice probabilities better than static logit model. In order to quantify the error in predicting real choice probabilities, root mean square deviation (RMSD) is adopted as a measure of the differences between the true and the predicted values. Model with a higher RMSD has a poorer ability in predicting the market share. The
5.2. Time varying variables The travel time variable used in the model specification in Table 3 is the difference between travel time at current time period and travel time in the next time period. The negative value obtained for the travel time coefficient indicates that if travel time raises in the subsequent time period (resulting in a negative value of the difference), commuters are more likely to depart and not to postpone their departure time. It is interesting to note that the probability of departing at the current time period decreases with an increasing difference between the expected arrival time and work start time (DE). Also, it is found that commuters prefer to arrive closer to work start time if they expect to arrive before work starts (DEit < 0), and they prefer to delay their departures if they expect to arrive later than their work start time (DEit > 0). These results have direct consequences over the determination of individual's time-space prism. First, for fixed activities, the starting and end points in time of the prism are affected by traffic conditions and by the information on travel time received by the commuters. When the expected travel time increases, commuters tend to delay their departure time, presumably because they expect traffic conditions to improve. Second, the working start time is a strong temporal constraint in individuals' agenda and that the likelihood to incur in delays strongly impact departure time choices. Unfortunately, the indicators about late penalty (IP) and being late (IL) defined in Section 3.3 resulted not to be significant in our model specification. 7
Journal of Transport Geography 82 (2020) 102548
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Percentage of trips
0.25 0.2 0.15
Real
0.1
Logit Dynamic logit with Pk
0.05
Dynamic logit with AR(1) 50
40
30
20
0
10
-20
-10
-30
-40
-50
-70
-60
-80
-90
-100
-110
0
Difference between depature time and work start time (min) Fig. 4. Percentage of departures at each time interval.
the traffic conditions, they would leave home earlier or much earlier when travel time increases, while changes in distance have less impact on departure time. The results also show that when commuters make decisions under uncertainty (based on the stochastic travel time rule), changes in distance and travel time would have comparable greater impacts on commuter's departure time.
RMSD is defined as:
RMSD (θ ) =
E ((θ − θ)2) =
T C ∑t ∑i = 1 Nt (θi, t − θi, t )2 T
C ∑t Nt
(10)
where C is the number of alternatives in the choice set, Nt is the number of observations at time t, θi is the market share of choice i. As showed in Table 3, the dynamic models with both perfect knowledge and AR(1) are superior to MNL and have the same RMSD.
7. Conclusions This paper has developed a rigorous analytical framework to model timing to work at individual level. It contributes to a better understanding of how ICT and in particular travel time information affect decision-making and ultimately shapes the Time-Space Prism of commuters. All these aspects are high in the agenda of transport geographers and modelers for their impacts on transport demand and urban forms. The methodology is based on a dynamic discrete choice model where sequences of departure time choices are modeled in response to traffic conditions under two decision rules; the first assumes perfect knowledge of travel time over future periods, while the second accounts for the stochastic nature of traffic conditions. Data extracted from a regional household travel survey and travel information obtained from Google Maps are linked based on spatial and temporal characteristics of the commuting trips. The dynamic model specified for the two different decision rules proposed are estimated and compared to a static logit model. The empirical results provide important insights into the determinants of commuter's departure time choices, and on the way they shape the time space prisms and its vertices.
6. Scenario testing As road conditions change overtime, commuters may change their routes to shorten their travel time and/or travel distance. Changes in travel time and travel distance might also lead to different departure time choices. Thus, the section here is to test the impacts of travel time and travel distance changes on commuters' departure time choices using the proposed dynamic framework. We carried out two tests where travel time and travel distance are increased respectively by 10% and 20%, and for each of the scenarios proposed we calculated how commuters change their behavior concerning departure time decisions. The rise in travel time and travel distance, together with the uncertainty in future travel conditions, are expected to increase the likelihood of leaving home for work earlier in order to arrive on time at the final destination. The results of scenario testing under two dynamic models (Table 4) is consistent with the general expectation and with the sign of the parameters estimated. If commuters had perfect knowledge (Pk) of Table 4 Scenario test. Difference between departure time and work start time (min)
Dynamic logit with PK
Dynamic logit with AR(1)
Base Scenario
Changes in diff. (Travel Time + 10%)
Changes in diff. (Travel Time + 20%)
Changes in diff. Distance +10%)
Changes in diff. (Distance +20%)
Base Scenario
Changes in diff. (Travel Time + 10%)
Changes in diff. (Travel Time + 20%)
Changes in diff. (Distance +10%)
Changes in diff. (Distance +20%)
−110 −100 −90 −80 −70 −60 −50 −40 −30 −20 −10 0 10 20 30 40 50
0.8% 1.3% 2.1% 3.4% 4.6% 6.5% 9.8% 10.8% 12.1% 14.9% 10.9% 8.6% 7.1% 3.0% 1.9% 1.3% 0.4%
0.1% 0.2% 0.2% 0.3% 0.3% 0.5% 0.4% 0.3% 0.1% −0.3% −0.5% −0.6% −0.5% −0.2% −0.1% −0.1% 0.0%
0.3% 0.3% 0.5% 0.6% 0.7% 0.9% 0.8% 0.5% 0.1% −0.6% −1.0% −1.1% −1.0% −0.4% −0.3% −0.2% −0.1%
0.1% 0.1% 0.1% 0.1% 0.1% 0.2% 0.1% 0.0% 0.0% −0.1% −0.2% −0.2% −0.1% −0.1% 0.0% 0.0% 0.0%
0.1% 0.2% 0.2% 0.2% 0.2% 0.3% 0.2% 0.1% −0.1% −0.3% −0.3% −0.3% −0.3% −0.1% −0.1% −0.1% 0.0%
0.5% 0.9% 1.7% 2.9% 4.3% 6.9% 10.9% 12.7% 14.6% 15.8% 10.3% 7.3% 5.9% 2.5% 1.6% 1.1% 0.3%
0.1% 0.2% 0.2% 0.3% 0.5% 0.6% 0.5% 0.3% −0.2% −0.7% −0.6% −0.4% −0.4% −0.1% −0.1% −0.1% 0.0%
0.3% 0.3% 0.5% 0.7% 1.0% 1.1% 0.8% 0.5% −0.5% −1.5% −1.1% −0.8% −0.7% −0.3% −0.2% −0.1% 0.0%
0.1% 0.1% 0.1% 0.2% 0.2% 0.2% 0.1% 0.0% −0.2% −0.3% −0.2% −0.2% −0.1% −0.1% 0.0% 0.0% 0.0%
0.2% 0.2% 0.2% 0.3% 0.4% 0.4% 0.2% 0.0% −0.3% −0.6% −0.4% −0.3% −0.2% −0.1% −0.1% 0.0% 0.0%
8
Journal of Transport Geography 82 (2020) 102548
H. Dong and C. Cirillo
Modeling estimation results help analysts better understand spatial and temporal characteristics of commuter morning patterns. Expected travel time to work, expected time of arrival together with working starting time, all of which depend on traffic conditions and its variability, are among the major constraints when people decide about travel and activities. Distance to work and rigid working schedules widen the space-time prism, by pushing departure time earlier. The effect of sociodemographics is unstable across the model specifications tested. An higher number of vehicles in the household provides more flexibility and allows commuters to start their commute later; being an adult is also found to delay the choice to depart to work. Goodness of fit statistics and out of sample validation confirms that the dynamic approach is superior to standard logit model. Despite the difficulty in recovering the peaks in demand, the dynamic formulations proposed are able to approach low and high peaks of departure choice probabilities better than static logit model. The econometric-based methodology applied to the departure time problem and the data linkage approach provides transportation analysts and modelers with an innovative tool analysis to study the spatial and temporal characteristics of individual activity patterns. Given the relevance of the problem, the current study can be extended in several directions. First, the proposed model only considers travelers' commuting trips. Traveler's decisions about non-work trips (i.e. shopping, leisure, social trips) can also be included in the model for a comprehensive consideration of all the activities in the time-space prism. Second, the regional and national household travel surveys should be linked to real-time traffic information as they become available. Third, in order to generalize the results obtained it is necessary to calibrate and validate the model with traffic information collected over longer time periods. Finally, reliability of en-route traffic should also be considered as a variable in the model.
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