Temporal dynamics of the impact of land use on modal disparity in commuting efficiency

Abstract   Urban land use is known to affect commuting efficiency according to the excess commuting framework. However, most studies do not include temporal dynamics, and those that do, focus on decadal, yearly, or daily temporal resolutions. However, commuting is not a stationary spatial process. Since people leave home and start their jobs at different times of the day and since traffic congestion varies throughout the day, neglecting hourly dynamics can misestimate commuting efficiency in a region and lead to erroneous policy implications. Another important issue often overlooked in the past is the modal disparity in commuting efficiency and how it evolves during the day. To overcome these limitations, this research examines the commuting efficiency variation by car and public transport by six one-hour periods between 5 AM and 11 AM in Warsaw, Poland, using travel survey data and travel times generated from GPS-based big data for cars and from GTFS for public transport. We develop four different groups of modeling scenarios: no disaggregation, disaggregation by time, disaggregation by mode, and disaggregation by time and mode. Therefore, excess commuting and modal disparity metrics are applied for a total of 21 specific time and mode combinations. The results suggest that commuting efficiency is worst during the 8–9 AM period for both modes, and that public transport users are more efficient after 7 AM. Hourly variations in the excess commuting metrics imply that policy makers should examine ways to encourage flexible work hours to distribute work starts and to increase public transport frequencies in the off-peak.

section_content: Excess commuting, also known as wasteful commuting when first introduced by Hamilton (1982), is a metric that reflects to what extent the actual commuting length in a city, such as distance or time, deviates from the theoretical minimum value. Mathematically, it is defined as the proportion of the observed commute that is over the minimum commute suggested by the existing spatial distribution of housing and jobs (Horner, 2002; Hu and Wang, 2019; White, 1988). In essence, this metric captures a city's overall commuting efficiency by quantifying the potential for a city to reduce the overall commuting length to an expected lower bound without changing the existing urban form. Therefore, it is often used as a planning tool to evaluate the performance of urban form, such as the jobs-housing balance. As the minimum commuting length describes the average shortest distance or time, that is, spatial separation, between jobs and households in a given city, it can be interpreted as a proximity-based measure of jobshousing balance (Horner, 2008; Niedzielski, 2006). A lower minimum commute indicates a greater intermixing of employment and housing and thus a more balanced configuration of jobs and housing. 

Since the invention of the excess commuting metric, many studies have raised concerns that the way to measure it-either by the classic monocentric urban model (Hamilton, 1982) or the widely-accepted linear programming approach (White, 1988 )-could lead to biased and misleading estimates and policy implications. Many attempts have been made to fine-tune this metric both methodologically and conceptually. For example, one line of research is focused on taking into account heterogeneity of households and jobs, instead of treating every household or job equal, when solving the minimum commute. These efforts include, among others, the consideration of the number of workers in a household, occupation type, neighborhood attributes, and worker mobility levels (Buliung and Kanaroglou, 2002; Cropper and Gordon, 1991; Kim, 1995; Thurston and Yezer, 1991). As the calculation of excess commuting relies on using census data at a level of aggregation, some researchers examined the modifiable areal unit problem (MAUP), showing how estimates of excess commuting vary by level of aggregation (Horner and Murray, 2002; Niedzielski et al., 2013), and proposed simulation approaches to mitigate such scale effect (Hu and Wang, 2015). Conceptually, the minimum commute defines only the lower bound of a city's commute. One could not grasp the whole picture of the commute behavior in a city by examining the minimum commute alone. In this regard, some other metrics about commuting length that characterize the upper bound of a city's commute, including the theoretical maximum commute (Horner, 2002) and random commute (Charron, 2007), have been developed. Despite these substantial efforts, many existing studies have omitted the temporal dynamics, particularly short-term, of excess commuting by calculating this metric for a region over a period of one year or longer. Nonetheless, the commuting metrics, including minimum, maximum, random, and actual commute, are subject to change in reality. For instance, the number of workers leaving home or arriving at work could vary significantly during the day. In addition, the traffic on the road network is not stationary over time but rather has peak and off-peak hours (Hu and Downs, 2019). Thus, omitting such temporal (short-term) dynamics in excess Using the 2015 Warsaw Traffic Survey (WTS) (Kostelecka, 2015) data collected in Warsaw, Poland, this research aims to measure the hourly temporal dynamics of excess commuting. It is unique from existing studies in several aspects. First, to the best of our knowledge, no studies have ever looked at such a fine temporal resolution before. Second, it addresses the aforementioned issues of modal disparity in excess commuting by adapting the modal accessibility gap indicator developed in Kwok and Yeh (2004) to systematically reveal the commuting efficiency modal disparity and its short-term (hourly) dynamic patterns. Moreover, this research contributes to the literature by analyzing a much less studied European city and new big data sources.
section_name: Introduction

section_name: Background

section_content: The theoretical minimum commute (Tmin) is the lower bound of commuting in a city. In essence, it represents the commute when all workers, on average, relocate to existing housing that is closest to their jobs. This is achieved by a linear programming problem that rearranges the journey-to-work flow pattern between zones until the lowest system cost (e. g., distance or time) is found (White, 1988). Mathematically, it can be defined as:

where xij is the optimal number of commuters living in zone i while working in zone j and it is nonnegative, dij is the travel distance (or time) between zones i and j, Wi is the total number of workers residing in zone i, Jj is the total number of jobs in zone j, m is the total number of residential zones, n is the total number of employment zones, and N is the total number of workers in the region. The objective function minimizes the average commute and the model constraints ensure that all workers leave home and arrive at work. 

The theoretical maximum commute (Tmax) is proposed by Horner (2002). As opposed to Tmin, it represents the upper bound of a city's commute where all workers, on average, relocate to housing that is the farthest from their workplace. Therefore, Tmin and Tmax represent a city's most efficient and least efficient commute, respectively, and together they define a city's possible commuting range or capacity. Because Tmax is exactly the opposite scenario of Tmin, it is equivalent to the minimization problem of negative Tmin:

where the notations and constraints are the same as previously defined. 

Some studies (Charron, 2007; Murphy and Killen, 2011) criticized Tmax for being an unreasonable upper limit of a city's commute as the scenario where all individual workers relocate their residences in a way to maximize their commute is not likely to happen. In response, they proposed the theoretical random commute (Trnd) as a more appropriate upper limit of a city's commute. Trnd represents a travel pattern in which individual workers are insensitive to commuting costs when selecting a residence and workplace. In other words, any existing home has an equal chance of being matched to any existing job during the spatial reassignment of workers between homes and jobs. Therefore, Trnd lies between the lower limit of a city's commute Tmin and the upper limit Tmax. There exist two approaches to measure Trnd. The first one is to generate a large random sample of commuting trips for a given city and calculate the average commuting costs. This approach has been implemented by a Markov Chain Monte Carlo method in Murphy and Killen (2011). An alternative approach, which is much less computationally demanding but can still produce highly consistent estimates, was proposed by Charron (2007) and has the following formulation:

where the notations are the same as previously stated.
section_name: Commuting metrics

section_content: The excess commuting (Tex) metric (Hamilton, 1982) measures the difference between Tmin and the observed commute (Tobs). It can be formulated as:

Tex represents the extent to which a city can optimize its commute without altering the existing jobs-housing distribution, and a greater value indicates higher commute saving potential and thus lower commuting efficiency. Although all these excess commute metrics reflect the commuting efficiency level in a city, it is reported that no single metric can fully capture the city's commuting profile alone (Kanaroglou et al. 2015). Tex, Tpu, and Tce are complimentary because they explain different aspects of commuting behavior. For example, in a hypothetical city, Tmin = 5, Tobs = 8, Trnd = 12, and Tmax = 15. Then Tex = 37. 5%, Tpu = 30% and Tce = 57. 1%. If we consider the full commuting capacity, people are relatively more efficient than when the Trnd -Tmin range is used. Therefore, it is suggested that these metrics should be examined together.
section_name: Excess commuting metrics

section_name: By replacing

section_name: Methodology

section_content: Warsaw, the capital of Poland, and its metropolitan area includes suburban cities such as Łomianki and Legionowo in the north, Marki, Wołomin, Sulejówek in the east, Otwock and Piaseczno in the south, and Piastów and Pruszków in the west (Fig. 1 ). There were 2,733,840 people living in the metropolitan area in 2015 (Zegar, 2016), of which 895,505 were workers including 702,030 workers commuting by the two modes studied in this paper, cars and public transport, which includes buses, trams, and subway (Kostelecka, 2015). These two modes combine for 78. 4% of commute trips in the metropolitan area. Of all the car and public transport workers, 71. 07% commute within the city boundary, 2. 96% commute from the city to the suburbs, 11. 4% commute from the suburbs to the city and 14. 57% commute within the suburbs. 

Warsaw's labor market reflects its role as a capital city and an alpha city in the Global and World Cities (GaWC) 2018 list (The World According to GaWC 2018, 2018). Table 1 shows that the single largest share of jobs in the city, 15. 9%, is in administration, though producer services (finance, insurance, real estate, professional, information) combined account for 29. 9% of all jobs in the city. Spatially jobs tend to follow major roads and railroads as shown in Figure 1. 

Three major job centers that emerged after 1990, are highlighted to show the impact of the restoration of property rights during the post-1990 economic transformation. Two of these, Wola and South Służewiec, are major centers of finance, insurance and information sector jobs, which emerged in former factory areas because of their regulated property rights (Górczyńska et al., 2019).
section_name: Study area

section_content: Three major sources of data are used in this research. First, the WTS (Kostelecka, 2015), obtained from the Warsaw municipal government, provides hourly journey-to-work flows and the origin and destination totals for 895 zones in the metropolitan area. The zones average 1. 98 km 2 in size for the whole study area, 0. 62 km 2 within the city and 13. 4 km 2 in the suburbs (see Figure 1 ). Second, car travel times are sourced from TomTom Speed Profiles data which provided traffic patterns in five-minute intervals. Third, public transport travel times are computed using the General Transit Feed Specification (GTFS). The road transport network contained in the WTS was used as the source of the pedestrian network for public transport travel times calculations. 

Looking at the hourly frequency distribution of commuting trips in Figure 2, it is obvious that the majority of trips, regardless of where they start (either in the city or the suburb), peaks at 5-11AM. To be specific, the total percentages of commuting trips starting in the city and suburbs during this 6-hour range are respectively 91% and 93%. Therefore, this research examines the temporal dynamics of excess commuting and the modal disparity only within this time range, instead of the entire 24 hours. Certainly, the proposed framework, including the data sources and analytical methods, can be readily applied to other time periods of choosing.
section_name: Data sources

section_content: The study design consists of four major steps. The first step involves extracting the hourly journey-to-work flow matrices and subsequently the origin and destination totals. The second step is to calculate congested travel times for car and public transport travel for each one-hour period. Third, the various commuting metrics and excess commuting indicators described in section 2 are calculated for each of the two modes-cars and public transport-and for each hourly group. Finally, the modal commuting efficiency disparity is quantified by measuring the modal disparity gap indicator (MDG) that is detailed in section 3. 5.
section_name: Study design

section_content: The calculation of travel time is a critical step in the measurement of hourly variations in The intrazonal time, dii, is set equal to 60% of the travel time from a zone to its closest neighbor (Horner, 2010). The observed average commute distance is computed the following way:

where fij is the observed number of commuters living in zone i and working in zone j, with other notation as previously defined.
section_name: Travel time calculation

section_content: As stated, straightforward 1-on-1 comparisons being made on a variety of excess commuting metrics between users of car and public transport could be problematic, because of a lack of a consistent scale that could lead to misinterpretation of the results. As a result, this research defines a modal disparity gap (MDG) index for systematically measuring the modal disparity in excess commuting. The MDG is adapted from the modal accessibility gap index that was developed by Kwok and Yeh (2004) to quantify the difference between the accessibility of private and public transport. The MDG is expressed as a ratio and is defined as:

where T P represents the public transport excess commuting metrics and T C describes the car metrics. The MDG is a standardized ratio ranging between -1 and 1. It has a value of -1 when T P reaches 0 and T C equals any nonzero value. Take Tex as an example, this scenario happens when Tobs reaches the optimal commute Tmin for public transport while Tobs is inconsistent with Tmin for car users in a city. On the contrary, the MDG becomes 1 when T C is 0 and T P has any nonzero
section_name: Modal disparity

section_content: In order to more fully understand the short-term temporal dynamics and modal disparity of Looking at results in scenario 1, it is found that Warsaw's current jobs-housing distribution could lead to an average commuting time of 16. 79 minutes, (i. e., Tmin) if no one made trips longer than required. The reality is far from the optimal case, however. In fact, an average worker is found to spend 34. 56 minutes (i. e., Tobs) commuting, a value remarkably greater than the required one. 

That said, about 51. 42% (i. e., Tex) of the observed commute in Warsaw is more than necessary. 

Conversely, the upper limit of Warsaw's commute, Tmax, is 53. 18 The foregoing results make sense in relation to the urban form of Warsaw. The jobs-housing balance of Warsaw (Figure 1 ) suggests a stark juxtaposition of housing-rich and jobs-rich areas with little intermixing. Most areas of the city are either housing estates (with service jobs) or office complexes (with some communist era housing especially in the central area). This means that if jobs and housing were more intermixed, then the minimum commute could be shorter. 

The minimum commute is also higher due to the peripheral suburban areas that contain mostly housing from which workers have to commute inward. However, the lack of job decentralization means that the maximum commute, at 53. 18 minutes, is relatively short when compared to US cities, such as Los Angeles with a 92-minute Tmax (Zhou et al., 2018). The spatial structure of the city also means that workers can find jobs without using most of the available commuting range, because either they live adjacent to jobs or they can find jobs in the central area without having to cross commute. Therefore, commuting efficiency is not as bad as it could be, again compared to Los Angeles, where Tex = 75% and Tce = 7%. These temporal variations are shown in Figure 5 (only the car pattern is shown; the pattern for public transport is similar). Temporal variations in commute origins drive the metric value variations. The hourly changing patterns imply that jobs are, on average, the furthest from homes at 5-6AM during the 6-hour time window. Put another way, the intermixing of available employment and housing is the worst at 5-6AM. The first row of Figure 5 shows that this is because most workers leaving home during this period live in the suburbs and they travel to jobs in the suburbs and in the central city leading to the highest Tmin value. While Table 2 shows that the number of available jobs increases substantially-an increase of 198% is observed from 5-6AM to 6-7AM and a 79% increase is noted from 6-7AM to 7-8AM, Tmin declines. The second to last column of Figure 5 shows that the relative number of workers leaving home and arriving at work located at more than 15km from the central point of the city is decreasing over time (from 5 to 8AM). The last column shows that as more workers wake up and start their jobs within Warsaw and its central area, the jobs-housing balance is improving after 5-6 AM. The greatest proximity between jobs and housing appears at 8-9 AM, because this period is dominated by commuting between homes and jobs located within the city boundary (Figure 5, third column). After this period, the number of jobs drops considerably by about 60% towards 9-10AM (Table 2 ; Figure 5, fourth column). Understandably, these jobs tend to shrink over space and concentrate at certain job centers. This gives rise to increasing average job-home distance from 8-9AM to 9-10AM (Table 2 ; Figure 5, fourth column). From 9-10AM to 10-11AM, the number of jobs further drops by 52% and the average job-home distance declines slightly (Table 2 ). Tobs increases after 9AM because jobs and housing are becoming imbalanced. A similar fluctuation pattern is also perceived for Trnd and Tmax-the values peak at 5-6AM and drop afterwards until 8-9AM, then rise again (9-10AM) and finally decline (10-11AM). An Unlike these theoretical commute limits, the actual commute Tobs has an exactly contrasting fluctuation curve between 5 and 11AM. Specifically, it is the lowest (29. 28 minutes) at 5-6-AM, peaks at 8-9AM (39. 54 minutes), then declines towards 9-10AM and slightly bounces back at 10-11AM. This pattern makes sense, because at 8-9AM, when jobs and housing have the best spatial proximity, work-and nonwork-related traffic is the worst during the 6-hour period. All these activities during this traffic peak hour make roads the most congested and result in the greatest Tobs at the time when jobs and housing are overall the closest to one another. On the contrary, the traffic at 5-6AM is the best within the 6-hour range and hence leads to the lowest Tobs, even though the average distance between jobs and housing is the greatest in this period. 

Note that the above finding is opposite to some previous studies focusing on U. S. cities. For instance, some have suggested improving the proximity between jobs and housing-i. e., promoting jobs-housing balance-could arguably lead to a reduction in actual commute (Horner, 2002; Hu and Wang, 2016). However, this policy relation does not seem to apply to Warsaw. 

Another factor that may contribute to the contrasting finding is that these studies examined the long-term changing patterns of commuting whereas the present study looks at the short-term dynamics instead. The findings, perhaps, suggest that it would be beneficial to take nonwork travel into account in the measurement of excess commuting, such as supermarkets stops after work (Niedzielski and Kucharski, 2019). 

In terms of the 6-hour excess commuting dynamics, the three relevant metrics-Tex, Tpu, and Tce-are in agreement. Table 2 and Figure 4G show that the Tex and Tpu values increase from 5-6AM, peak at 8-9AM, drop towards 9-10AM, and slightly rise at 10-11AM. This indicates that excess commuting in Warsaw, when measured by the Tobs-Tmin deviation or by how much commuting capacity has been consumed, starts the lowest at 5-6AM and gradually increases and becomes the greatest at the traffic peak hour 8-9AM. The percent increases are highly noticeable-60% for Tex and 137% for Tpu. After then, Warsaw's commute becomes moderately more efficient at 9-10AM and then slightly inefficient again at 10-11AM. In the same vein, the commuting economy captured by Tce has the highest value at 5-6AM, indicating the greatest commute efficiency in this period, then dropping toward the worst efficiency at 8-9AM. The commute becomes more economized at 9-10AM but less efficient at 10-11AM. indicating an increasing degree of inefficiency in commute from 5 to 9AM for both travel modes. 

To better illustrate the dynamics of excess commute modal disparity, the MDG values for the three excess commuting metrics, are plotted against the time (Figure 4C ). Clearly, commute efficiency modal disparity is not stationary, but rather has distinct peaks and pits. The Tex curve shows that public transport users are consistently less efficient in their commutes. However, the disparity between the two modes narrows greatly (about 45% decrease) from 5AM until 9AM

and then increases afterwards. The closing modal disparity gap is driven by the greater increasing rate (76%) in car commuting inefficiency (Tex) than that of public transport (45%) from 5 to 9AM. As expected, Tpu and Tce MDGs return a different shifting pattern compared to

Tex, but are more realist because they are based on the full commuting capacity. Note that the opposing curve pattern between Tpu and Tce is because of the exactly opposite interpretations of their values as explained in section 3. 5. Between 5 and 7AM, public transport because they are based on the full commuting capacity appear to commute less efficiently than their car counterparts, based on Tex. However, after 7AM, the disparity is reversed, as car users are inefficient commuters. The results and findings from above suggest significant temporal dynamics in commuting patterns and efficiency as well as modal disparity, which would have not been possible by existing methods and datasets.
section_name: Results and discussion

section_content: Using Second, public transport users are more efficient in their commutes after 7 AM showing that public transport schedules impact commute efficiency: higher frequency between 7 and 9 AM leads to less waiting time for public transport and shorter travel times. These hourly variations imply that policy makers should examine ways to encourage flexible work hours to distribute work starts and to increase public transport frequencies in the off-peak (before 7 AM and after 9 AM). 

There are several directions for future research. First, smaller temporal resolutions, such as 15 or 30 minutes, should be considered to explore the sensitivity of modal disparity in commuting efficiency to various levels of temporal aggregation. Second, how the temporal dynamics of commuting efficiency vary spatially within the city should be explored. Third, how the hourly impact of land use on commuting varies by different population groups, such as education, job skills, and race/ethnicity should also be explored. Fourth, these findings are unique to Warsaw, Poland, so an international comparison of the temporal dynamics of modal disparity in commuting efficiency is warranted.
section_name: Conclusions

section_name: National Employment Section

section_name: Acknowledgements

section_content: M. Niedzielski acknowledges the support of the Polish National Science Centre, within the POLONEZ programme, allocated on the basis of the decision no. UMO-2015/19/P/HS4/04067, which received funding from the European Union 's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 665778. The views and
section_name: Acknowledgements