The statistical properties of freeway traffic

Variations in urban traffic

“…In any case, mirroring real-world traffic dynamics in this setting is very challenging compared to freeways. For example, the arrival events on freeways were shown to approximately follow a renewal process under low-to-moderate flows (Breiman et al, 1977;Luttinen, 1996), and can thus be modeled using solely an inter-arrival or headway distribution (Ha et al, 2012;Hoogendoorn, 2005). In an urban context, under all conditions, one should study events in conjunction with other processes mainly at intersections, e.g., the inter-relations between arrival and departure processes and signal dynamics (Luttinen, 1996;Zheng et al, 2017).…”

“…Despite the strong interest for the statistical properties of noise in image and signal processing (e.g., Foi et al, 2008;Liu et al, 2014), relatively few studies (Chen et al, 2008;Ghosh et al, 2010;Guo et al, 2015;Guo & Williams, 2012;Huang et al, 2018;Thomas et al, 2008;Tsekeris & Stathopoulos, 2006) investigate the noise properties and volatility in traffic measurements. Although there is evidence that the amount of random variation depends on the underlying (systematic) flow (e.g., Breiman et al, 1977;Chen et al, 2012;Chen et al, 2008;Luttinen, 1996;Thomas et al, 2010), many estimation and prediction methods (e.g., Wang & Papageorgiou, 2005) assume white Gaussian noise. We cite some exceptions: Li and Rose (2011), Thomas et al (2010), Wagner-Muns et al (2018 on traffic volumes, and Nantes et al (2015), Tang et al (2018), andYang et al (2010) on travel times.…”

“…This rate is slowly changing compared to fluctuations in the inter-arrival times of the individual vehicles under regular conditions. Typically, a location-dependent 24h pattern is used to express the non-stationarity in the demand -thereby incorporating that 'normal' or random fluctuations naturally exist even under stationary demand (Breiman et al, 1977;Breiman & Lawrence, 1973;Sparks, 1976). Very short-term fluctuations, in the order of tenths of seconds, roughly describe the non-predictable (random) fluctuations in the arrival events (Dion et al, 2004;Gwiggner & Nagaoka, 2014).…”