Variations in Urban Traffic
Oskar Eikenbroek is a PhD student in the department Transport Engineering and Management. (Co)Supervisors are prof.dr.ir. E.C. van Berkum from the faculty of Engineering Technology and prof.dr.ir. M.R.K. Mes from the faculty of Behavioural, Management and Social Sciences.
In many urban areas, the traffic network is operating close to capacity. In such networks, unexpected and small fluctuations in traffic flow can result in a disruption in the level of service (LOS), e.g., travel speeds, delays and travel times. In fact, accumulated local and short-term fluctuations pose a serious risk to actors operating in the urban traffic domain who aim for decisions with stable performance under all conditions. Robust decisions anticipate the uncertainty in the sense that the potential effects of local, yet natural fluctuations are incorporated during the decision-making process. Albeit the increase in available traffic data sources, still very little is known about the dynamics and the uncertainty in urban traffic networks compared to freeways. In this thesis, we therefore investigate urban traffic variations on different scales and explore the potential of information regarding the variations on anticipatory decision making.
We distinguish three illustrative actors using urban traffic information during their decision-making processes: logistics service providers (LSPs), urban traffic managers, and individual road users. LSPs concerned with home delivery use, e.g., travel time predictions with different time horizons to construct robust offline route plans that can be dynamically refined over time. Urban traffic managers mainly use typical volume patterns based on historical data for policy making and use near real-time data to trigger management scenarios. Individual road users employ advanced traveler information systems (ATIS), e.g., navigation devices, to support them in their travel decisions before departure and while being en route. These decision-making processes benefit from information regarding the development of the urban traffic conditions. Estimates about the accompanying dynamics in the uncertainty are often not considered but are also important for anticipatory decision making and the limitations thereof. Hence, the inter-relations between the systematic (predictable) variability in traffic and the uncertainty on various spatio-temporal scales should be understood and quantified.
In this thesis, we use historical data to get a grip on the systematic and random variations in urban traffic measurements. Since the conditions that occur in an urban network are for a major share determined by the dynamics near signalized intersections, we particularly focus on the variations there. Estimates regarding future travel times and delays are typically of interest for the actors under consideration and traffic volumes (or: flows, counts) throughout the network are an important source for explaining and predicting driving times and delays. Urban volume fluctuations are typically monitored and analyzed using measurements in the order of minutes but express only a share of the actual variations. Hence, volume fluctuations need to be studied on various scales to not only account for the spatio-temporal variability in network usage, but also to incorporate the dynamics on a detailed level that introduce uncertainty on an aggregated scale.
In Chapter 2, we examine urban traffic volume time series that explain a share of the dynamics occurring in an urban network. By eye, these time series show clear patterns, many of which are recurrent and can therefore in principle be predicted. Apart from systematic variations, a portion of the fluctuations in the measurements shows no pattern and should therefore not be predicted (noise). For monitoring purposes, it is important to separate the systematic from the random variability in the volumes to recognize changing conditions in a situation where high-frequency fluctuations occur in parallel.
24h traffic volume time series show systematic differences within a day and between days, and time of day and day of week are important predictors for network usage. We examine the changes in the 24h volume time series over the days, thereby considering the variability in volumes within the day but also the changing time-of-day volumes over the days. This simultaneous consideration supports one in revealing trends in the width and height of the peak and to accurately assess the impact of shorter-term systematic variations such as events and incidents. The short-term deviations provide valuable information for management decisions but are more variable in their frequency of occurrence and the accompanying magnitude.
24h time series at a single point in the network basically consist of a combination of underlying recurrent temporal patterns or profiles. Distinct time series look different since they exist of latent profiles that are subject to small transformations changing over time. Extracting the underlying profiles is a challenging task since the profiles are not known in advance and the measurements are corrupted by noise. Moreover, what is considered systematic depends on a priori assumptions regarding the random variation and vice versa. In any case, many of the systematic variations are recurrent and, therefore, we develop a neural network architecture that infers long and short-term profiles together with a noise level estimate. Longer-term profiles express a volume shape occurring on a 24h scale, while short-term profiles represent the systematic differences compared to an underlying intra-day pattern. The random variation is captured using a so-called noise level function, expressing the probabilistic character of the fluctuations around a deterministic systematic pattern. The generic relation between the variance of the random variation and the underlying pattern allows for a full density characterization of the natural stochastic fluctuations.
Using two years of volume data collected throughout the Enschede traffic network, we show that only a few recurrent and physically-meaningful profiles are needed to express almost all systematic variations. Hence, 24h volume time series show a high degree of systematic variability - even in the case of events with variable starting times - only revealed when assessing variations over various timescales. It was estimated that the variance of the noise is linearly dependent on the underlying systemic volume with slight overdispersion compared to Poisson noise. In fact, the noise distribution widens when volumes grow and decision making occurs in an increasingly uncertain environment when network usage increases.
In Chapter 3, we study urban arrival processes at signalized intersections. In fact, a large share of the fluctuations in the delays at signalized intersections can be traced back to the arrivals of vehicles at the approaches. Because of the importance of the dynamics in the delays for decision makers, there is a range of models and simulation methods that aim to capture the interactions at intersections. We use millions of recorded arrival events to statistically characterize arrival patterns and thereby assess the empirical consistency of the existing models.
Changes in the arrival patterns on a fixed location can be measured on different temporal scales. The underlying demand or arrival rate is assumed to be slowly varying and to change on timescales exceeding 5-10 minutes. Very short-term fluctuations, in the order of tenths of seconds, describe the stochastic (random) fluctuations in the actual arrival events. However, the two timescales are related and the point process describing the random occurrences of events over time is typically aggregated for monitoring and prediction purposes. Although on a 10min level arrival volumes show strong similarities with a Poisson or a renewal process, the latter processes fail to reflect the true structure in the arrivals. In fact, a stochastic arrival model in an urban setting should capture the non-stationarity in the demand over time and space, the marginal distribution of inter-arrival times accounting for both physical interactions as well as excess probabilities due to traffic signal control, and the periodicities in the arrival events because of upstream interruptions and platoon formation. In general, arrivals show bursts: periods with many arrivals alternate with periods in which no arrivals occur.
We develop a statistical framework to study arrivals as both a sequence of inter-arrival times as well as a counting process using a time-domain and a frequency-domain approach. When considering the distribution of the inter-arrival times, there is an excess probability of medium and high inter-arrival times, introduced by traffic lights upstream, statistically reflecting a combination of variable cycle times and the interaction with arrival events upstream. While consecutive inter-arrival times show only a weak serial correlation coefficient, this effect accumulates to a significant level when looking at a multitude of vehicles. The Bartlett power spectrum corresponding to the sequence of arrival events reveals dominant frequencies corresponding to the periodicities in the traffic signal cycles upstream. These dominant frequencies introduce dispersion in the counts using lower aggregation levels. Nonetheless, different arrival processes are indistinguishable when aggregation levels increase beyond 4-5min.
In a simulation setting, real-world mirroring arrival processes were shown to influence the variability in delays compared to the Poisson process. With vehicle-actuated traffic signal control, delay estimates obtained using a Poisson process overestimate both the mean as well as the variability in the delay particularly under lower volume occasions. The regularity in the real-world arrivals can be used to optimize vehicle-actuated signal control settings since arrivals contain predictive information about future events - in some cases even up to minutes in advance. In any case, not accounting for the interrupted characteristics of urban arrivals for the benefit of tractability overestimates the variations in delays while underestimating variations in volumes in the short-term, and thereby impacts decision-making processes.
Volume predictions support the decision-making processes of the considered actors. Many decisions of the actors operating in the traffic domain face decision problems characterized by uncertainty covering longer timescales, conflicting with the fact that most existing prediction methods consider short-term point forecasts. Therefore, we develop in Chapter 4 a volume forecasting method that (i) offers reliable forecasts for different urban network conditions, (ii) provides predictions for both the long and short term and (iii) incorporates uncertainty in predictions in the form of probabilistic forecasts.
Traffic volume time series were shown to have a high degree of regularity, which can be well-expressed using latent profiles of different temporal scales. We use these flexible profiles for our prediction method since almost all systematic variability within a day and between days can be explained by using a few profiles. We constructed a prediction method to forecast systematic variations. The 24h forecast provides a prediction for a full day before the start of the day and the remaining-day prediction gives at any time of day a forecast for the volumes for the remainder of the day. Short-term predictions cover the next 15min to 1.5h. Since not all systematic variations can be expressed using basic exogenous variables only, we update initial forecasts based on the systematic differences in the residuals over various timescales. The inferred noise-level function is used to construct full density forecasts and to update the prediction based on the error of previous predictions relative to the inherent variability. Updating the prediction is rather difficult since noise makes it difficult to recognize changing conditions. Therefore, we apply smoothing by means of error aggregation and state-space filtering.
The quality of predictions is tested relative to the predictability of the system - and this difference is the true prediction error. The prediction error is expressed using a relative error based on the point prediction and using the coverage difference - reflecting the difference between the expected and true coverage of a density forecast. Considering 15min predictions, we found a point prediction error of 10-15% suggesting that systematic variations for a major share can be predicted. A large share of these variations was possible to predict well in advance, at the beginning of the day when accounting for day-dependent characteristics. Although predictions are improved over the course of the day, many variations are systematic over timescales longer than hours. The density forecasts anticipating natural fluctuations are accurate and have an absolute coverage difference of 2-3%. Traffic management measures such as rerouting under higher penetration levels suffer from feedback effects in the sense that current decisions influence future developments. Forecasts need to anticipate the emergent behavior of travelers so that intended outcomes are achieved. In Chapter 5, we investigate the potential and complexity of anticipatory traffic management by means of a social rerouting strategy.
Various traffic management measures have been proposed to reroute drivers towards socially desired paths. The main goal of these measures is to achieve the system optimum: the traffic state with minimum total travel time. The behavioral response to route advice needs to be anticipated since drivers are likely to ignore advice if the strategy reroutes them onto substantially longer paths for the system’s benefit. In essence, any social routing strategy should anticipate user responses and persuade travelers to comply with socially oriented advice.
We propose a social routing strategy that explicitly anticipates the behavioral responses to a routing service so that an upper bound on the realized detour can be guaranteed. Compliance can be expected to be much higher when the advised route is only slightly longer than the shortest route. However, the realized travel time depends on the responses with respect to route choice that may occur from travelers that comply with the advice but also from those that do not comply but are now confronted with altered travel times on routes because of behavioral changes by others. The developed social routing strategy steers the traffic network towards an efficient but also fair, and therefore achievable and maintainable, traffic state. We show that the best possible paths with explicit a posteriori detour bounds to be proposed by a social routing service can be found by solving a bilevel optimization problem. A critical issue in solving the bilevel problem is that the lower-level optimal solution is not unique. We use techniques from parametric optimization to show that the directional derivative of the lower-level link flow nonetheless exists. This generalized derivative is used in a descent method and can be efficiently found as a solution of a quadratic optimization problem but requires a suitable route flow solution as parameter. Numerical experiments show that a social routing system is a potential powerful measure to improve efficiency and preserve fairness at the same time. Even if only a small portion of travelers can be rerouted onto social routes, the resulting traffic state shows a major improvement in total travel time compared to the user equilibrium. In fact, only about 12% of the drivers need to take a small detour to obtain 2.4% of the maximum-possible 3.8% total travel time improvement.