Impact of Flextime on Departure Time Choice for Home-Based Commuting Trips in Austin,Texas

Abstract

An increasing number of corporations and workplaces are providing flexible working hours or flextime for employees, which is expected to reduce congestion by redistributing the temporal pattern of commuters’ departure time. This study examines the impact of flextime on departure time choice using a Bayesian continuous-time hazard duration model. The model accommodates the time-varying effect of covariates and unobserved heterogeneity. Results from the Austin Household Travel Survey collected between 2017 and 2018 show that workers who have a flextime option choose to leave later, with a predominant effect deterring morning peak departures. Other trip and individual-specific variables, such as travelers’ job type, trip duration, number of trips during the travel day, and household income, are found to have significant impacts on departure time choice. The results also show that flextime is more effective in shifting the departure time for retail and service sector employees, for those whose journeys are longer, and for those who perform more daily activities. The findings of this study support the theory that implementing such policies may ease congestion by staggering the travel demand from peak to off-peak hours.

Keywords

congestion management congestion mitigation congestion mitigation or reduction managed lanes operations planning and analysis transportation demand management

Departure time choice is an important component of commuters’ trip-making behavior. At an individual level, the overall cost of commuting, including the penalties for travel time delays and early or late arrival, depends on departure time choice. At the system level, departure time choice determines the temporal pattern of vehicles occupying the network and the resulting level of service and congestion on urban roadways. The classic bottleneck theory was first formulated by Vickrey ( 1 ) to illustrate commuters’ trip-making behavior and the resulting congestion during peak hours. According to this simplified model, the potential bottleneck in a fixed capacity roadway is activated when flow exceeds capacity. As a result, commuters suffer delays from long queuing at congested bottlenecks. At the same time, they must consider the penalties for early and late arrival at their destination. Early arrival entails disutility, considering the opportunity cost of time, that is, the workers could enjoy their time better outside the workplace. Starting work early may not ensure higher wages earned in most cases. However, late arrival may entail greater disutility on grounds of punctuality. There may be various forms of penalties imposed by employers such as a warning, salary deduction, or even loss of the job. Thus, commuting cost is not simply a function of travel time, but is instead the total cost derived from travel time, delay, and early and late arrival ( 2 ). A flexible working schedule plays a significant part in this decision. By choosing flexible working hours, commuters can avoid late or early arrival penalties and minimize the overall commuting cost. If many travelers depart before or after peak hours, travel demand may be spread over a wider time window, thereby reducing peak congestion.

Existing studies that explore the traveler-level benefits associated with flextime also reveal that the most obvious benefit is avoiding congestion. Findings of these studies show that driving stress is lower for commuters who have a flextime alternative because they may choose to travel during off-peak hours ( 3 , 4 ). Moreover, flexible working hours allow for greater flexibility in lifestyle choices. For example, individuals may have time for other personal activities such as shopping, taking children to school, and doing other household-related tasks ( 5 ). Research has shown that early arrival at work is associated with an increase in time for leisure activities after work ( 5 – 7 ).

About 81 million workers, accounting for 57% of all full-time workers in the U.S.A., had the ability to choose a flexible schedule in 2018 ( 8 ). The Bureau of Labor Statistics ( 8 ) found that public sector employees are more likely to have flexible working hours than private sector employees. The COVID-19 pandemic reflects the importance of flexible work policies such as telecommuting, flextime, and staggered working hours. It seems obvious that workplace flexibility is having an immediate effect on traffic congestion during the pandemic because more people are working remotely from home. On the other hand, some employers still need their workers in the workplace, whereas others are planning for phased reopening. As workers are facing more activity constraints, such as childcare, online schooling, and other additional household responsibilities ( 9 ), schedule flexibility outside regular working hours is being increasingly prioritized in employment policies, and this trend is likely to continue in the future ( 10 ).

Understanding departure time choice is important for assessing the true impact of increasing flexibility in the workplace ( 11 ). Decision-making with regard to departure time depends on personal heterogeneity and institutional constraints. Previous studies analyzed departure time choice to examine the effectiveness of policies that affect commuting cost such as tolls, congestion pricing ( 12 , 13 ), information access, and travel time reliability ( 14 – 16 ). However, empirical evidence for the effect flextime has on departure time is relatively scarce ( 11 , 17 , 18 ). Discrete choice methods were used in earlier studies to analyze the impact of flextime on departure time, although such a choice is continuous in nature. This study applies a continuous-time proportional hazard duration model within a Bayesian framework, using data from the Austin Household Travel Survey for travel between 2017 and 2018. The model accommodates time-varying effects of several covariates and unobserved heterogeneity in departure time decision-making, with a flexible framework for controlling other individual-specific effects. The remainder of the paper is organized as follows. A detailed literature review on the impact of flextime on departure time choice is presented next. This is followed by data description and model specification. Findings from the model estimation are discussed next, and the paper ends with conclusions.

Literature Review

Few studies focus on the impact of flextime on work performance, mental well-being, work–family balance, wage difference, and urban productivity ( 3 , 6 , 19 –24). Even fewer papers analyze the impact of flextime on travel outcome ( 18 , 25 ). However, most of these studies indicate flextime schedules have a positive impact.

McCafferty and Hall ( 11 ) compared travel time choice before and after the closure of one central business district (CBD) road exit in Ontario, Canada. Although the study considered flextime to mean that workers had the flexibility to choose when to start work, it was used for sample selection instead of as an explanatory variable. The final sample included only those who had a flextime option, and the only variable found to be significant was income. The authors maintained that the poor model fit indicated the effectiveness of flextime in altering the temporal pattern of travel demand. However, because of the small sample size, the authors pointed out that their results were not conclusive for assessing the effectiveness of flextime. The authors suggested that including more explanatory variables over a larger sample size may improve the evaluation and accurately predict time choice behavior.

Chin ( 26 ) studied the effect of location, individual demographic characteristics, and occupational factors on departure time based on the implementation of the Area Licensing Scheme (ALS) in Singapore. Results showed that ALS had a heterogeneous impact on departure time choice for users of different travel modes. The greatest impact was on car users, whose departure time share before 7:30 a.m. rose from 28% to 42%. The study also revealed that low-income travelers were more likely to work in the production and manufacturing sectors, which often follow a rigid work schedule because the economies of production demand all assembly lines must be staffed. However, high-income travelers, for example, those who work in business, construction, administration, trade, sales, and clerical jobs, were also found to be less likely to vary their departure times.

He ( 18 ) used a multinomial logit (MNL) model to analyze the influence of flextime on the departure time of commuters in California’s two largest cities, Los Angeles and San Francisco. Trip data were drawn from the National Household Travel Survey 2009. Results indicated that workers from certain occupational categories, such as sales, professional, service, managerial, and technical jobs, were much more likely to depart during post-peak hours, whereas those in manufacturing, construction, and production chose to leave home during pre-peak hours. Similar findings were also reported by Chin ( 26 ) and Yoshimura and Okumura ( 27 ). Among other factors, travel distance, number of nonwork trips, and family composition were significant factors in departure time choice. The model included a flextime alternative as an explanatory variable. Those who had a flextime option preferred to depart later. Flextime increased the probability of post-peak departure by 7.41% and reduced the probability of departure in pre-peak and peak hours by 3.30% and 4.11%, respectively.

Whereas most studies defined flextime based on binary options of having flexible working schedules or not, Saleh and Farrell ( 17 ) used five factors to operationalize the level of flexibility: whether the employee could start work 30 min before or after the official start time, presence of dependent children in the family, nonwork family activity, and income. These factors reflect work schedule flexibility, nonwork flexibility, and financial flexibility. Using an MNL model, Saleh and Farrell ( 17 ) found that a higher level of flexibility encouraged people to depart later. The findings also show that nonwork flexibility and work schedule flexibility have a considerable influence on departure time choice. Those who have flexible work schedules may not be flexible in their work trips because of other nonwork-related commitments.

Shifts in departure time as a result of flextime are expected to redistribute the temporal pattern of traffic flow on urban arterial roads. Jovanis’s study ( 28 ) has been the only one to empirically test the potential of flextime for relieving highway congestion. The study simulated two flextime scenarios in downtown San Francisco. The first scenario examined the impact of a promotional flextime campaign in the financial district, which resulted in a few commuters changing their departure times. The second scenario did the same for the entire CBD area, and resulted in many commuters shifting their departure times. Results from the simulation showed that the first scenario produced substantial travel benefits in reduced travel time, fuel consumption savings, and fewer carbon monoxide and hydrocarbon emissions. Surprisingly, results from the second scenario were negative. As more commuters shifted to earlier time periods, congestion also shifted toward the early morning hours. However, the author concluded that the second scenario is unlikely to occur because flextime travelers can adjust their departure based on expected travel time. One implication of this study is that targeted implementation of flextime along corridors with a highly peaked traffic pattern can result in substantial travel benefits for commuters.

The nature of industry also plays an important role in firms’ decisions to adopt a flextime policy. Yoshimura and Okumura ( 27 ) developed a theoretical model to understand the optimal distribution of work start time. The model was formed under a flexible working hour arrangement for motor commuting considering the effect of temporal agglomeration. The study illustrates that when temporal agglomeration is weak, the optimal work start time is a totally flexible pattern in which all workers utilize flexible working hour arrangements. By contrast, when the temporal agglomeration is strong, the optimal solution shows a mixed pattern in which only a small fraction of workers have the option of flexible working. Findings from this theoretical modeling exercise imply that the decision to adopt flextime may vary from industry to industry, and that the level of temporal agglomeration plays an important role in this decision.

Data and Methodology

Study Area

This work focuses on the Austin, Texas region, which houses 2.2 million residents and is among the U.S.A.’s fastest growing metro areas ( 29 ). Traffic congestion has become a major concern for Austin because the rising travel demand has outgrown the transportation infrastructure, at least during peak times of day. Across U.S. regions, Austin ranks between 11th and 20th for metrics such as yearly delay per auto commuter, travel time index, commuter congestion cost per auto commuter, and commuter stress index ( 30 ). It is expected that many Austin drivers already adjust their travel time to cope with traffic congestion, but little is known about the specific effect of flextime on departure time.

Data

The Austin Household Travel Survey data for 2017–2018 contain household-, person-, vehicle-, and trip-level details. A total of 35,699 trips are collected across all trip types from 2,920 participating households. The survey area includes five counties within the Capital Area Metropolitan Planning Organization boundary: Hays, Travis, Williamson, Bastrop, and Caldwell.

The survey data include a binary variable for travelers having flexible work hours. However, detailed information about the flextime policy is unavailable. For example, workers may have an informal arrangement instead of a formal one, or may have a limitation on the number of days in a week a flextime option may be used. This is a limitation, because the effect of departure time choice for those with informal or limited flexible hours may not be uniform across all days, or the days reported in the data set. Nevertheless, this study hypothesizes that any flexibility in work hours should have a nonzero effect on departure time choice, and the methodology is set up with this in mind.

The proportion of workers in the study area having a flexible working schedule option is 30% (Table 1). Two peak-hour periods are expected during daily operation. Figure 1 shows that the morning peak hours are from 6:00 to 9:00 a.m., and the afternoon peak hours are from 4:00 to 7:00 p.m. With the focus of this paper being the impact of flextime on departure time choice, only home-based work trips (n = 1,809) are considered, and return trips were removed. People leave as early as 6:00 a.m., and the busiest hour is expected to be between 8:00 and 9:00 a.m. Overall, peak hours account for 66.1% of total trips, whereas the shares of pre-peak, post-peak (until midday), and after midday (12:00 noon) are 9.6%, 11.3%, and 13%, respectively.

Table 1.

Descriptive Statistics

	Pre-peak (before 6:00 a.m.)		Peak (6:00–9:00 a.m.)		Post-peak (after 9:00 a.m.)		Total
	Frequency	Row %	Frequency	Row %	Frequency	Row %	Frequency	% of Total
Total	174	9.6	1,195	66.1	440	24.3	1,809	100
Flextime
Yes	44	8.2	287	53.6	204	38.1	535	29.6
No	130	10.2	908	71.3	236	18.5	1274	70.4
Commute mode
Walk	0	0.0	19	67.9	9	32.1	28	1.6
Auto/van/truck driver	151	9.5	1053	66.3	384	24.2	1,588	87.8
Auto/van/truck passenger	14	12.1	72	62.1	30	25.9	116	6.4
Carpool/vanpool	2	22.2	5	55.6	2	22.2	9	0.5
Transit/bus	2	10.0	13	65.0	5	25.0	20	1.1
Taxi/paid limo	1	25.0	1	25.0	2	50.0	4	0.2
Bicycle	4	9.3	31	72.1	8	18.6	43	2.4
Motorcycle/moped	0	0.0	1	100.0	0	0.0	1	0.1
Sex
Male	113	12.4	574	62.8	227	24.8	113	50.5
Female	61	6.8	621	69.4	213	23.8	61	49.5
Ethnicity
Black/African American	21	14.8	84	59.2	37	26.1	142	7.8
Hispanic	46	16.6	165	59.6	66	23.8	277	15.3
Asian/Pacific Islander	3	2.8	70	66.0	33	31.1	106	5.9
Native American	1	11.1	6	66.7	2	22.2	9	0.5
White/Caucasian	100	8.3	813	67.9	285	23.8	1198	66.2
Others	3	3.9	57	74.0	17	22.1	77	4.3
Number of cars
0	7	26.9	15	57.7	4	15.4	26	1.4
1	35	10.9	202	62.9	84	26.2	321	17.7
2	69	7.4	643	69.0	220	23.6	932	51.5
3	49	12.6	245	63.1	94	24.2	388	21.4
≥4	14	9.9	90	63.4	38	26.8	142	7.8
Job category
Managerial/professional	54	6.5	615	74.0	162	19.5	831	45.9
Production	17	21.0	44	54.3	20	24.7	81	4.5
Construction	18	26.5	45	66.2	5	7.4	68	3.8
Sales/office	15	7.3	136	66.3	54	26.3	205	11.3
Service	66	10.9	341	56.5	197	32.6	604	33.4
Others	4	20.0	14	70.0	2	10.0	20	1.1
Land use type
Rural	96	68.6	24	17.1	20	14.3	140	7.7
Suburban	425	65.9	140	21.7	80	12.4	645	35.7
Urban	537	65.9	216	26.5	62	7.6	815	45.1
Urban intense	137	65.6	60	28.7	12	5.7	209	11.6
	Mean (SD)	Median	Mean (SD)	Median	Mean (SD)	Median	Mean (SD)	Median
Age	45.3 (12.8)	47	41.7 (12.6)	40	39.4 (14.0)	40	41.4 (13.1)	37
Daily trips	3.5 (2)	3	3.5 (1.8)	3	4.3 (2.4)	4	3.7 (2.0)	3
Trip duration (minutes)	27.3 (15.8)	24.5	27.7 (13.5)	25	20.8 (18.5)	19	25.7 (15.8)	21
Home–work distance (in miles)	13.8 (13.3)	10.1	10.7 (9.5)	8.7	7.5 (6.9)	5.8	10.2 (9.6)	7.9
Density¹	5.04 (5.03)	4.3	5.98 (8.89)	5.17	6.58 (9.11)	5.54	6.06 (8.67)	5.22
Diversity (Entropy)²	0.41 (0.20)	0.44	0.44 (0.19)	0.46	0.46 (0.18)	0.5	0.44 (0.19)	0.47

Note: SD = standard deviation.

Density = (population + employment)/square miles, in 1,000s.

$Entropy = - \sum_{k} {P_{i}}^{*} \ln (P_{i}) / \ln k$

$P_{i} = proportion of landuse activities; k = number of landuse activities$

Figure 1.

Departure time distribution over the course of a day.

The trip data was further matched with Austin’s traffic analysis zones (TAZ) to obtain land use information. Two land use variables are derived from TAZ data: density and entropy. Density represents how intensively the land is being used for different activities such as housing, employment, and other purposes. In this study, activity density of TAZ trip origin was measured using the sum of population and employment normalized by the area of the TAZ. The entropy index shows the diversity of land use, that is, how different activities are distributed across the space. The index is normalized by the number of distinct activities (natural log), to be bounded between 0 and 1 ( 31 ). An entropy index close to 1 means perfect balance, that is, different activities are uniformly distributed, whereas an index value close to 0 means the balance is not proportionate, that is, a single type of activity is dominating the land use.

Model Specification

Previous studies have used a discrete choice approach for modeling departure time choice ( 11 , 17 , 18 ). However, the fundamental limitation of this approach is the discrete portioning of time in large bins (e.g., peak, off-peak, morning, evening). Different time intervals and resolutions can largely affect model outcomes. Two neighboring time points might fall into different time intervals but may intuitively have the same effect on choice. For example, if we define the peak period as 6:00 to 9:00 a.m., then two spaced time points (e.g., 8:55 a.m. and 9:05 a.m.) will fall into two distinct alternatives (8:55 a.m. as peak and 9:05 a.m. as off-peak), but decisions made at both those instances may be the same.

Continuous cross-nested logit models for departure time choice have been widely used in previous studies to account for the correlation between two bins ( 32 ). Recently, the activity-based approach has become common in travel demand modeling. Unlike the trip-based, four-step model, activity-based models consider work start time, duration, and the interrelationship between these and other activity decisions at more disaggregate levels ( 33 , 34 ). A hazard duration model can also address the continuous nature of trip timing and trip duration ( 35 – 37 ). Bhat and Steed ( 38 ) proposed a continuous-time hazard duration model, which accommodates time-varying coefficients, time-varying covariates, and unobserved heterogeneity in departure time choice. This approach splits the entire day into smaller grouped intervals in which the baseline hazard rate is assumed to be constant, and the coefficients vary in the pre-defined intervals. This frequentist approach helped overcome limitations in logit-based choices while respecting the continuous aspect of time.

In this paper, a Bayesian equivalent of the time-varying continuous-time hazard duration model ( 38 ) is pursued. The Bayesian approach provides flexibility in specification while continuing to allow for uncertainty quantification. Traditional hazard models, such as the semiparametric Cox proportional hazards model, assume that the effect of a covariate on the hazard rate is constant at all points of time. This is limiting, because travelers can make different choices depending on the time of day when controlling for other factors. The value of travel time is potentially perceived differently at different times of the day. This is especially true when travelers have flexibility in their work times or have the option to telecommute. There may be a delayed departure from home in such situations without compromising on daily work activities such that the effect size is higher later in the day. Travelers with such flexibility may make essential personal trips, such as taking children to school or running an errand, before traveling to work, or may choose to travel once peak-hour congestion has passed. Similarly, other variables that do not vary across time may still exhibit a differential effect at different times of the day, and some others may have a constant effect throughout the day. The variation in decision-making for all factors $G$ across the day is captured by including time-varying coefficients, $β (t)$ , in the model. Finally, some other factors, $X$ , may provide a constant time-invariant effect, $α$ , and are also included in the model.

An individual’s departure time $T$ , representing the duration from midnight until departure, has the hazard, $λ (t)$ , at any time $t$ less than $T$ . This hazard rate is the instantaneous probability that the traveler will depart in a small time interval $Δ t$ after time $t$ , given that departure has not occurred until time $t$ . The definition of hazard with regard to probability can be expressed as follows:

λ (t) = lim_{Δ t \to 0} \frac{P (t < T < t + Δ t | T 〉 t)}{Δ t}

This formula makes it possible to calculate the cumulative distribution function for departure at time $t$ , $F (t)$ , and the survival function, denoting the cumulative probability of not departing until time $t$ , $S (t)$ , as shown in the following expression:

\begin{matrix} λ (t) = \frac{f (t)}{S (t)} = - \frac{\frac{dS (t)}{dt}}{S (t)} = - \frac{d}{dt} lnS (t) \\ S (t) = P (T > t) = 1 - F (t) = \exp (- \int_{0}^{t} λ (x) dx) \end{matrix}

This definition of hazard rate is transformed to accommodate time-varying, time-invariant, and unobserved heterogeneity effects. The following equation denotes the use of the time-varying hazard rate $λ (t)$ , estimated in bins of departure. It is expected that the proportional effect of a covariate remains constant in smaller buckets of time during the morning peak, and may remain constant over midday. Therefore, these bins of departure are allowed to vary in size across the day, with a finer granularity of 15 min in the morning peak, and larger bins of 120 and 240 min depending on anticipated departures in the data at those times of day. As shown below, $λ (t)$ is estimated by using a nonparametric time-varying baseline hazard rate $λ_{0} (t)$ , the zero lower-bounded exponent consisting of observed covariates X and G, corresponding coefficients $α$ and $β (t)$ , and unobserved component $ω_{i}$ for each individual $i$ . Therefore, an individual’s hazard at time $t$ (after dropping subscript $i$ for the individual) is given by:

λ (t) = λ_{0} (t) \exp (α X + β (t) \times G (t)) ω

The parameters available for $G$ are exploded for each time the bin is used in the model. The Bayesian hierarchical model is set up to estimate the hazard rate from the data. Observed departure times need to be discretized into bins corresponding to the bins used for the time-varying $β$ (t). A variable, $d_{ij}$ , is created to identify whether an individual $i$ departed during the bin $j$ . Correspondingly, survival time is computed as $t_{ij}$ , which denotes the time in the bin $j$ that individual $i$ survived or did not depart. A convenient Poisson approximation for $d_{ij}$ allows for estimating the hazard rate when the mean of the Poisson is $t_{ij}$ times the hazard rate in bin $j$ ( 42 ). The resulting Bayesian hierarchical model used is as follows:

\begin{matrix} d_{ij} ~ Poisson (t_{ij} \times λ_{ij}) \\ λ_{ij} \leftarrow λ_{0 j} \times \exp (α X_{i} + β_{j} G_{ij}) ω_{i} \\ α ~ Normal (0, σ_{k}^{2}) \\ β_{1} ~ Normal (0, σ_{k}^{2}) \\ β_{j} ~ Normal (β_{j - 1}, σ_{k}^{2}) \\ ω_{i} ~ Gamma (a_{0}, a_{0}) \end{matrix}

The variance of the parameters was based on bin size, with each bin size variance ( $σ_{k}^{2}$ ) estimated through a series of hierarchical priors where $σ_{k}^{2}$ is distributed Gamma (b₀, b₀) and b₀ is distributed Gamma (0.1, 0.1). Because all parameters used were normalized, the expected variance from the priors alone was selected such that it was 1. The time-varying parameter is expected to be correlated between bins, so a random walk is assumed, in which the prior imposes a mean based on the $β$ in the previous time bin. The unobserved heterogeneity is also expected to have a mean of 1 if all heterogeneity is accounted for, so the Gamma prior with the same parameters allows for mean 1, with variance allowed to be dictated by a hierarchical prior Gamma (1, 0.1). It is difficult to determine the baseline hazard rate beforehand, so an uninformative prior Gamma (0.001,0.001) is chosen.

Results

The Bayesian model discussed above was implemented using a Markov-Chain-Monte-Carlo Sampler called Just Another Gibbs Sampler (or JAGS) through its interface in R ( 39 , 40 ). Three chains were simulated in parallel with a 2,000 iteration burn-in, and 1,000 iterations were analyzed for estimates and 95% credible intervals.

Baseline Hazard

Figure 2 shows the baseline hazard for the estimated model. The baseline hazard captures the differential baseline hazard across different departure times for the average person. There is a general positive time dependency as expected, meaning that the longer a commuter waits to depart, the higher his/her probability of departure in the next time period. The baseline hazard is small until 6:00 a.m., larger during peak hours, and eventually fades after 8:00 a.m. This is expected because, on average, the preference is for the majority of work trips with or without flextime to depart during the morning hours.

Figure 2.

Baseline hazard function.

Flextime Effect

The time-varying effect of flextime on commuters’ departure time choice is captured by the corresponding coefficient estimates in β(t). A negative value of β(t), at any time t, suggests that flexible work hours decrease a commuter’s propensity to leave at that time t. The coefficient values decline sharply starting at 6:00 a.m., reach a maximum negative value at 7:45 a.m., and then shift back to 0 after 8:30 a.m. (Figure 3). The hazard multipliers represent the magnitude of the covariate effect, determined by exp (β). The percentage change in the hazard can be further derived by {exp (β)−1} ×100. Thus, the effect of flextime can be interpreted at any instantaneous point of time with regard to the percentage change in the hazard rate. Accordingly, flextime decreases the hazard rate or the propensity to depart at 6:00 a.m. by 40.3%. The effect increases as time progresses until it reaches its peak at 7:45 a.m. with a 53.1% decrease in hazard rate. The time-varying effect of β(t) clearly shows that the effect of flextime on departure time is not constant, but varies significantly throughout the day. Most importantly, the effect of flextime is predominant in deterring morning peak departures. Although the credible intervals of many coefficients estimated at off-peak hours include 0, the large deterrence in morning peak departures is quite significant.

Figure 3.

Time-varying coefficients of flextime.

The effect of flextime can be further illustrated by cumulative hazards plots for two groups: commuters with and without flextime (Figure 4). The slopes of these lines indicate the instantaneous probability of departure. During the early morning hours before 5:00 a.m., the hazards are nearly 0, which means probability of departure is very low. Starting at 6:00 a.m., probability continues to increase, indicating more departures during peak hours. However, the slope declines after 10:00 a.m. because departure rate falls after peak hours. For commuters with flextime, the hazard rate grows slowly over time before being indistinguishable from nonflextime commuters, implying that during peak hours they are more likely to depart later than commuters without flextime.

Figure 4.

Estimated cumulative hazard function.

The survival function, which is actually the exponential of the negative cumulative hazard function, provides a better interpretation of the results (Figure 5). A closer look at the slopes shows a clear difference between the two commuter groups in relation to survival and the likelihood of not departing. Commuters without a flextime option show a higher probability of early departures, explained by the steep slope at the beginning and then the gradual decline after the peak hours. On the other hand, commuters having a flextime option prefer later departure as shown by a less steep slope during the early morning hours. Survival probabilities from the curves can be extracted into exact numeric values for any instantaneous time. The difference between cumulative survivals at the end of two time periods provides the probability of departure during that time interval. The predicted shares of departures of the two commuter groups at an aggregate level are presented in Table 2. Accordingly, 89.3% of commuters without flextime are expected to leave before 9:00 a.m., whereas this value falls to 76.0% for commuters with a flextime option. Flextime commuters show 8.2% less probability of departing during peak hours compared with their counterparts without flextime. The difference is more evident in post-peak hours: having a flextime option increases the probability of post-peak departure from 8.0% to 18.4%.

Table 2.

Predicted Percentage of Departures in each Time Period for an Average Traveler

Time of day	Commuters without flextime (%)	Commuters with flextime (%)
Pre-peak (before 6:00 a.m.)	16.8	11.7
Morning peak (6:00–9:00 a.m.)	72.5	64.3
Post-peak until midday (9:00–12:00 noon)	8.0	18.4
After midday (after 12:00 noon)	2.7	5.6

Figure 5.

Estimated survival function.

Other Covariate Effects

Job category variables were found to be the strongest predictors of departure time choice. Workers in the industrial sector tend to depart earlier compared with those who are in managerial/professional jobs. The opposite is true for service and retail sector workers. The time-varying coefficients of industrial jobs show positive values during the early morning hours starting at 5:00 a.m., then a steep increase until 7:30 a.m., with a decline following afterwards (Figure 6). Early departure of industrial workers is consistent with labor economics: certain industries demand temporal agglomeration, follow rigid working hours, and require their workers to arrive early at the workplace. By contrast, workers in the service and retail sectors are much more likely to have departure times at later hours. The coefficients of the service sector do not show significant values until 8:30 a.m., but negative values afterwards suggest more departures during those hours. The same is true for the retail sector; however, an important difference is that the coefficients of the retail sector are spread more evenly throughout the entire day. This is expected, because morning shift retail workers depart early in the morning, whereas those who work afternoon and evening shifts depart later on.

Figure 6.

Time-varying effects of the covariates.

The number of daily activities can also influence departure time choice. In this study, the number of trips was used as a proxy variable for the number of activities performed during the travel day. Commuters who make a higher number of trips during their travel day are more likely to avoid peak hours, especially because there is a higher probability they will depart in post-peak hours. The time-varying coefficients show increasing negative values during the latter part of the day. This finding suggests that workers whose daily schedule is constrained by more activities tend to choose afternoon or evening shifts. Mandatory activities (e.g., taking children to school, grocery shopping, medical appointments, etc.) usually discourage travelers from leaving before and during the peak hours.

An overall positive sign of the trip duration coefficient suggests that trip duration increases the hazard rate, which implies that commuters with longer trip durations are more likely to depart earlier. The time-varying effect shows that the early morning hours have a higher hazard rate, which declines as the day progresses (Figure 6). This is expected because commuters try to avoid the uncertainty of longer travel and penalty of late arrival by departing at this time.

Demographic variables such as age, gender, ethnicity, and household income were included in the model. The effects of age and ethnicity were not found to be significant at 95% credible interval. The effect of gender was found to be significant, but only in pre-peak hours, suggesting that female commuters are less likely to depart very early in the morning (before 6:00 a.m.), compared with their male counterparts. Previous studies, however, showed a mixed effect of gender on departure time choice ( 17 , 18 , 41 ). Some studies attributed the effect of gender to trip distance. Long-distance commuters are more likely to be male and, therefore, tend to depart earlier ( 26 ). Among other variables, household income (annual income $75,000+) was found to be significant. The coefficient values are negative until 7:00 a.m., and positive in later hours (after 8:00 a.m.), suggesting that people with higher incomes are more likely to avoid departing in the early morning hours.

Among the land use variables, density and entropy were included in the model, but found to be insignificant. One possible explanation is that a dense, diverse built environment does not necessarily mean commuters live close to their workplace. The overall congestion effect depends on the entire network, not only on the origin or destination end of the trip.

The effect of each covariate on cumulative hazards with and without a flextime option was further compared with the baseline. In this way, the practical significance of a flextime option in relation to departure time across all the covariates can be understood. Table 3 shows the probabilities of cumulative hazards by 9:00 a.m., averaged across all commuters. Having a flextime option reduces the departure probability before 9:00 a.m. by 7.3%. Clearly, the effects of flextime on departure probability vary across the covariates. Among different job types, flextime has a more significant impact on the retail and service sectors compared with the industrial sector. Working in the retail sector decreases the probability of departure before 9:00 a.m. by 12.5%. However, working in the retail sector with a flextime option further reduces this probability by 22.1%. A similar effect was also observed for the service sector, but it was less than that of retail. It should be noted that firms in the retail sector usually follow a staggered working hour arrangement; however, some retail employers also offer flexible working schedules to employees. This is not intended to change the entire working schedule of the retail business; instead, it provides flexibility to certain employees, enabling them to balance their work schedule with daily activities. In addition, such temporal rearrangements can provide some travel benefits. For example, employees living a long distance away from their workplace might choose later departure times to avoid congestion, whereas those who live nearby would not mind leaving home during peak hours. Table 3 also shows that a flextime option reduces departure probability for industrial workers, but the effect is less significant. As discussed earlier, manufacturing workers usually start early in the morning, and industrial jobs demand temporal agglomeration. Therefore, the shift in departure time for industrial jobs is not as significant as in other sectors.

Table 3.

Practical Significance of Flextime with regard to Covariates

Variable(s)-specific sensitivity	Cumulative departure by 9:00 a.m. (%)	% Change (baseline effect)
Flextime	74.1	-7.3
Sex (female)	81.2	-0.2
Flextime + Sex (female)	73.9	-7.5
Income < $50,000	80.7	-0.7
Flextime + Income < $50,000	73.1	-8.3
Income($50,000–$75,000)	83.2	1.8
Flextime + Income($50,000–$75,000)	76.4	-4.9
Income $75,000+	82.4	1.0
Flextime+ Income $75,000+	75.6	-5.8
Industrial job	92.5	11.1
Flextime + Industrial job	87.9	6.5
Retail job	68.9	-12.5
Flextime + Retail job	59.3	-22.1
Service job	78.7	-2.7
Flextime + Service job	70.5	-10.8
Trip duration (+1 SD)	86.8	5.4
Flextime + Trip duration (+1 SD)	80.8	-0.6
Trip duration (-1 SD)	75.0	-6.4
Flextime + Trip duration (-1 SD)	66.7	-14.7
Number of daily trips (+1 SD)	76.9	-4.5
Flextime + Number of daily trips (+1 SD)	68.7	-12.7

Note: SD = standard deviation. The percentages in bold show the practical significance of flextime.

Among other variables, trip duration and the number of daily trips also have practical significance. In general, people who have longer journeys are less likely to depart during peak hours, but if they are provided with flextime choice, then they are more likely to utilize the opportunity and depart later. An increase of trip duration by one standard deviation increases the probability of departure before 9:00 a.m. by 5.4%, but having a flextime option reduces this probability by 0.6%. This is expected, because flextime shifts the early morning departure for travelers who have longer trips, but they still need to depart before 9:00 a.m. On the other hand, decreasing trip duration by one standard deviation has a more significant impact than shifting the departure until after 9:00 a.m. Most trips with a long duration originate outside the main city of Austin. In spite of starting their journey early in the morning, long-distance commuters are more likely to experience congestion by the time they arrive at their workplace. With a flextime option, they can avoid congestion by shifting their departure time by an hour or so. In addition, some commuters might have other activity constraints before and after work and, therefore, still prefer to depart no later than 9:00 a.m. Flextime also has a significant impact on those who need to perform more daily activities. An increase in the number of daily activities reduces the probability of early departure, as expected. If these employees are provided with a flextime option, they can utilize the time for mandatory activities (e.g., taking children to school) and avoid early departure.

Conclusions

This paper examines commuters’ departure time choice by using trip data from the Austin Household Travel Survey conducted in 2017 and 2018. A Bayesian continuous-time hazard duration model is established to evaluate the effectiveness of flextime in relation to commuters’ travel outcomes. By using a continuous-time approach, the model overcomes the limitation of discrete time structure, and offers precise prediction of departure times. Another advantage this model has over the commonly used proportional hazard model formulation is that it includes the time-varying effects of covariates on departure time choice. The continuous-time departure model developed in this paper can be used to evaluate the impact of a flexible working schedule at any level of temporal resolution.

The results show that flextime has a significant impact on departure time choice among Austin commuters. Workers with flextime tend to depart later than those without such an option, and have a stronger probability of avoiding morning peak hours. The predicted probabilities show that flextime decreases the share of peak-hour departure from 72.5% to 64.3%. The difference is more evident in post-peak hours: having a flextime option increases the probability of post-peak departure from 8% to 18.4%. The model controlled significant variables affecting departure time choice such as workers’ job type, trip duration, number of trips during the travel day, and household income. Job category variables were found to have the strongest effect on departure time choice among the covariates. Industrial workers show a higher probability of departing in the early morning hours, whereas those in the service and retail sectors tend to depart later. The results also show that the effects of flextime vary across covariates. A flextime option has more practical significance in shifting the departure time for retail and service sector employees, those whose journeys are longer, and for those whose daily schedule is constrained by more activities.

The findings of this study have substantial implications for transportation policy analysis, particularly at a time when employment characteristics, working arrangements, and communication technologies are changing rapidly, and alternative work schedule programs are becoming more prevalent. A flextime policy is relatively cost-effective and more popular compared with other demand management programs. However, it needs careful implementation. Some industries demand temporal agglomeration and have little flexibility to change their core schedule. As shown in the model, industrial workers are more likely to depart early in the morning. Therefore, flextime policies might not be equally effective for all job sectors. Motivation and coordination pose further challenges for flextime implementation. Employers and upper management should be fully aware of the benefits that flextime can bring in both relieving traffic congestion and improving employees’ work–life balance and productivity. Successful implementation requires management and employee cooperation. Flextime is valued more by certain segments of employees than others, yet accessibility to flextime is not equal for all employees. Findings from this study show that employees who face more scheduling constraints because of other daily activities, particularly parents and women especially, are more likely to take advantage of flexible working hours by changing their departure times. Organizations should make flextime information available to all employees, including terms and conditions and coordination plans.

Constructing new infrastructure is expensive and time-intensive. Various demand management strategies such as high occupancy lanes, toll roads, and congestion pricing are being implemented in many cities. The main objective is to alter travel behavior by shifting to alternative modes of transport and departure times. However, success of these strategies largely depends on people’s travel time flexibility and the availability of alternative options. Findings from this study show that people’s travel decisions are constrained by multiple restrictions, including work schedules, commuting distance, household characteristics, and daily activities. Therefore, demand management strategies such as road pricing should be implemented in conjunction with flexible work schedule programs that would allow commuters to overcome these constraints and switch departure times to less congested hours. Regional planning agencies can introduce financial incentives or reward programs to make flextime attractive to employees. As shown by previous studies, targeted implementation along congested corridors with highly peaked traffic flow can bring substantial travel benefits to commuters. A good example is the Metropolitan Washington Council of Governments’ Flextime Reward program, which offers financial incentives to commuters if they choose to travel during off-peak hours along five selected bottleneck corridors.

The significant finding from this paper supports the theory that implementing such policies would ease congestion by staggering travel demand between peak and off-peak hours. In addition, careful implementation of alternative work schedule policies such as flextime can provide multilevel benefits, including reducing pollution, enhancing productivity, and maximizing personal well-being. A limitation of the current study is that it could not incorporate more detailed information on flextime arrangements. The impact of flextime can vary depending on the type of arrangement, and the availability of flextime itself in any form depends on various underlying factors. Additional research is required to understand fully the determinants of flextime availability and the response to alternative forms of flextime arrangements in different employment sectors. Successful implementation of an alternative work schedule policy remains a potential research direction for future studies.

Footnotes

Author Contributions

The authors confirm contribution to the paper as follows: study conception and design: M. Rahman, K.M. Gurumurthy, K. M. Kockelman; data collection: M. Rahman, K.M. Gurumurthy; analysis and interpretation of results: K.M. Gurumurthy, M. Rahman, K. M. Kockelman; draft manuscript preparation: M. Rahman, K.M. Gurumurthy, K. M. Kockelman. All authors reviewed the results and approved the final version of the manuscript.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Mashrur Rahman

Kara M. Kockelman

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