Empirical synchronized flow in oversaturated city traffic

Based on a study of anonymized GPS probe vehicle traces measured by personal navigation devices in vehicles randomly distributed in city traffic, empirical synchronized flow in oversaturated city traffic has been revealed. It turns out that real oversaturated city traffic resulting from speed breakdown in a city in most cases can be considered random spatiotemporal alternations between sequences of moving queues and synchronized flow patterns in which the moving queues do not occur.

Figure 1

Typical city traffic data for speed and flow rate: (a) Scheme of a section of Völklinger Straße with a speed limit of 60 km/h [12]. (b), (c) Average speed (left) and the total flow rate across a two-lane road (right); 1-min average data measured by a road detector [D in (a)] for two different days. TS indicates a traffic signal; the data in (b) and (c) are qualitatively similar to data from previous measurements made in different countries [1, 2].

Figure 2

Comparison of empirical (black points) and theoretical (dashed curves) probabilities of traffic breakdown measured by the detector on (a) 219 days for 06:30–11:00 (mornings) and (b) 60 days for 18:00–20:30 (evenings). Empirical breakdown probabilities as functions of the total flow rate across a two-lane road (black points) are found to be similar to highway bottlenecks [15] as follows: (i) The breakdown is measured at detector D with the use of 1-min data. (ii) the flow rates in free flow (before the breakdown) have been averaged over 15-min intervals. (iii) The flow rate axis is divided into flow rate intervals $(q_k,q_k+\Delta q_k)$ with constant $\Delta q_k=240$ vehicles/h (“$k$-flow rate interval”), $k=1,2,\cdots ,K$, where $K$ is the total number of different $k$-flow rate intervals in free flow. (iv) For each of the $k$-flow rate intervals, the breakdown probability is equal to $n_k/N_k$, where $N_k$ is the number of observed flow rates within the $k$-flow rate interval in 219 data sets for mornings (60 data sets for evenings) and $n_k$ is the number of breakdowns found in the $k$-flow rate interval.

Figure 3

Fragment of typical empirical microscopic spatiotemporal structure of oversaturated city traffic: (a) Vehicle trajectories of probe vehicles on the road section shown in Fig. 1 measured on 5 February 2013. (b) Microscopic (single-vehicle) speeds (black squares) along vehicle trajectories shown by the numbers in (a). Dash-dotted lines show the traffic signal location in (a) and time instances of vehicle passing the signal in (b).

Figure 4

Fragment of a typical empirical microscopic spatiotemporal structure of oversaturated city traffic: (a) Vehicle trajectories of probe vehicles on the street section shown in Fig. 1 measured on 10 April 2013. (b) Microscopic (single-vehicle) speeds (black squares) along vehicle trajectories shown by the numbers in (a). Other details are the same as in Fig. 3.

Figure 5

Explanations of oversaturated traffic in (a), (b) classical theory [1, 2] and (c)–(f) three-phase theory [9]. Simulations of speed in moving queues (b) and SPs (c) are shown. J is line $J$, $q_{\mathrm{sat}}$ is a saturation flow rate, F is free flow, and S is synchronized flow.