Empirical Measurement of Freeway Oscillation Characteristics: An International Comparison

The objective of this paper is to conduct a country specific analysis of freeway traffic oscillations. Toward this end, loop detector data from sites in the United States, Germany and the United Kingdom was analyzed. By using a method applied in previous work, traffic oscillations were identified in all three countries. Calculation of the cross–correlation coefficient reveals that they travel upstream at speeds of about 19–20 km/h at the site in the US, 16 km/h at the German site and 14 km/h on the UK freeway. Similar magnitudes were found in the literature verifying the hypothesis that they propagate faster in the US than in Germany. Furthermore, an oscillation frequency was identified by calculation of the data’s autocorrelation. However, since the oscillation frequency is likely to be site specific, conclusions regarding general differences between the frequencies measured in different countries cannot yet be made. For the sites analyzed, it was found that oscillations appear every 8–12 min on the M4 (UK site), 10– 30 minutes on the A9 (German site) and every 3–6 minutes on OR 217 (US site). Even though the magnitudes of the latter two countries are supported by the literature, further empirical research on several different sites should be pursued in order to draw final conclusions. INTRODUCTION In order to maintain and increase the safety, predictability and efficiency of the transportation system, major investments were made in the past leading to the construction of additional road infrastructure. Nowadays economic and political reasons limit the possibility of building new facilities. Instead, more “intelligent” operations (e.g. ramp metering, travel time estimation, traffic state prediction, adaptive cruise control) are the focus. Since their development and deployment requires a thorough understanding of traffic flow phenomena, research has been performed resulting in various traffic models. One of them is the Lighthill Whitham Richards (LWR) model. The LWR model is based on a fundamental diagram (1) and can describe the propagation of perturbations in the flow. Sometimes such perturbations appear regularly, commonly referred to as traffic oscillations. It has been found that oscillations can grow in amplitude while propagating upstream, a feature that cannot be described by the LWR fundamental diagram (2). This is one factor that has led to new modeling approaches. However, these are still not completely satisfactory, since further inconsistencies exist (2). As traffic oscillations are a main driver for criticizing the LWR approach and hence developing new models, they require special focus. Thus a better understanding of traffic oscillations might help resolve some of the remaining questions. Different countries have different standards for infrastructure, vehicle mix and driving rules; driver behavior may also vary. As a result, traffic flow might exhibit different characteristics. Since traffic models aim at describing the traffic flow features, country specific differences might require different calibration of the traffic models. They might even require the use of different models. Since it is not yet clear whether traffic flow features differ from country to country, it is still uncertain whether models developed in one country can be adapted for use in another country. Therefore this paper is a first step toward identifying country-specific differences in traffic flow. More detailed information on this research is available (3). Therefore interested readers are encouraged to contact the authors for further information. BACKGROUND A traffic oscillation is usually defined as stop-and-go or slow-and-go conditions. For this paper, a pattern in traffic flow will be referred to as a traffic oscillation if three conditions hold: • The space–mean speed measured on a short freeway section drops, rises and drops again over time. More information is available in (1, 4) including a definition of space–mean speed, also referred to as traffic speed in this paper. • The traffic is congested. More information is available in (5) about the definition of congestion, also referred to as jammed or queued traffic in this paper. • The observed pattern propagates upstream against the direction of travel. In addition, for this paper, the amplitude of an oscillation will be defined as one half of the difference between the maximum observed speed and the minimum observed speed: 1⁄2(vmax−vmin). Zielke, Bertini and Treiber 3 Causes of Oscillations Previous research has investigated possible reasons for traffic oscillations. Two related explanations are presented in the available literature that describe the possible origin of traffic oscillations. Some researchers have tried to explain traffic oscillations due to car-following behavior. In this regard, microscopic car-following models are often used to explain traffic oscillations (4, 6, 7, 8). Using those models, oscillations form just upstream of a bottleneck and increase in amplitude due to drivers’ large reaction times and their overreactions while they are propagating against the direction of travel. Other related research shows that traffic oscillations are caused by lane changing. In (9) lane changing is identified as the primary factor for traffic oscillations. Accordingly oscillations can form and increase in amplitude if a vehicle merges between two other vehicles and these vehicles are following closely. More empirical research is needed to build on and verify these findings on an array of facilities. Characteristics of Traffic Oscillations Previous research and this paper will consider three main characteristics of traffic oscillations that are relevant for empirical measurements and also for modeling purposes: • Amplitude • Propagation velocity • Frequency The first feature to be considered is the amplitude of oscillations in freeway traffic. When considering the amplitude of oscillations previous research has also attempted to determine conclusively whether oscillations grow or shrink in amplitude as they travel through the traffic stream. Car-following models (4, 6, 7, 8) and some empirical observations (9) have shown that oscillations do increase in amplitude while propagating upstream. (In (9) a measure other than amplitude was used. However, a relation between this measure and amplitude seems intuitively correct and therefore is assumed for this and the following statement.) Real freeways are heterogeneous with changes in cross-section, merges and diverges. If it is assumed that oscillations can increase in amplitude, it is possible to examine possible effects of onand off-ramps on the amplitude of oscillations. In (9) it is found that on-ramps do have an effect on the amplitude of traffic oscillation by a “pumping effect.” As a result, it was shown that oscillations do decrease in amplitude when propagating upstream past on-ramps. Similarly, it can be assumed that oscillations may increase in amplitude when passing off-ramps. However, no validation has been performed for the latter case in (9), and further empirical research is needed in this area. A second feature to be considered is the longitudinal propagation velocity of oscillations in freeway traffic. Since oscillations are perturbations in the flow of congested traffic, various studies (2, 5, 9, 10, 11, 13, 14, 15) have suggested that they travel upstream at a characteristic velocity of about 16 km/h in Germany and about 20 km/h in the United States. Some past analysis of lateral propagation of oscillations has shown that oscillations appear in adjacent lanes shortly after they were first detected (9). The third feature to be measured is the frequency of oscillations. It has been shown that oscillations often occur regularly (2). Therefore they can be characterized by their frequency; its reciprocal value will be referred to as period. Table 1 shows the results of a literature review on the oscillation period. TABLE 1 Oscillation Period of Traffic Oscillations According to Literature Study Period (min) Study site Data Year Comment (13) 3 US (Holland Tunnel) NA Frequency directly upstream of the bottleneck (high frequencies might fade out upstream as explained in the text) (9) 4–8 US (I–80) 2003 Frequency analysis was not object of analysis. Results were obtained by looking at the plots (15) 4 US (J.C. Lodge Freeway) 1966 None Zielke, Bertini and Treiber 4 (12) 6–8 Canada (Queen Elizabeth Way) 1998 Frequency analysis was not object of analysis. Results were obtained by looking at the plots (10) ca. 20 Germany (A5) 2001 Frequency analysis was not object of analysis. Results were obtained by looking at the plots (7) 5.5/7.5/15/16 Germany (A5) NA Oscillations were not chosen arbitrarily, They were chosen to demonstrate the effect of different periods on the amplitude, hence they might not show typical values In (9, 10, 12) a frequency analysis was not objective of the analysis. The values were obtained by visual analysis of the graphs presented in the studies and hence they lack precision and objectivity. Furthermore, it is possible that the methodology applied in these works amplifies certain frequencies and suppresses others (the applied methodology is explained later). Further, according to (2), the oscillation period is dependent on flow. It has also been reported that oscillations do not exist in very low traffic flow conditions (2, 12). Since flow is restricted by site-specific bottlenecks, different sites are expected to show different characteristic oscillation frequencies. The final observation regarding frequency comes from a car-following model described in (16). The model reveals that oscillations with small frequencies would fade out whereas those with low frequencies would grow in amplitude as they propagate upstream. One final issue relating two oscillation features has been addressed in previous research. A relation between amplitude and frequency is described in (7). That publication states that long periods are accompanied by large oscillation amplitudes, and high frequencies result in low amplitudes. Maximum Flow Reported by Capacity Manuals The idea of comparing traffic features between countries is not new and has led to interesting results in the past. In the context of freeway capacity, The US Highway Capacity Manual (HCM) (17) serves as a guide for the design and operation of transportation facilities and infrastructure in the US and other countries. The “Handbuch für die Bemessung von Straßenverkehrsanlagen” (HBS) (18) is the German equivalent of the HCM. Both manuals use level of service (LOS) concepts to quantify how well a facility is operating. A comparison for freeway traffic with a truck percentage of 10% has been performed (22) and has found that the thresholds for the same LOS are associated with higher per lane flows in the HCM than in the HBS. In addition, the maximum per lane flow (threshold for transition from LOS E to LOS F) is higher in the HCM than in the HBS. Hence, a comparison of the manuals indicates that the assumed capacity of a US freeway may be higher than that of a German Autobahn. It is not clear precisely how the LOS thresholds have been determined and if they really refer to the same quality standard. Therefore further site-specific research is needed to verify whether a difference in capacity really exists. DESCRIPTION OF THE DATA In order to draw comparisons between reproducible characteristics of traffic oscillations, freeway loop detector data from three sites was analyzed for this study. Data was available from sites in the US, Germany, and the UK. The main characteristics of the data are summarized below and site maps are presented in Figure 1. The US site is located on OR 217, a freeway southwest of Portland, Oregon. Data (velocity, count and occupancy) was available for the whole section (11.2 km) in 20 s aggregates. The data includes all freeway lanes and on-ramps. Sensors on off-ramps were not installed. The data was available for download from PORTAL (19), an online data archive for the Portland metropolitan area (data in PORTAL is provided by the Oregon Department of Transportation). Analysis was done for the southbound direction for six days in March, April and September, 2005. The PORTAL data was provided by double loop detectors. However, there was uncertainty whether the velocity was directly measured by these detectors or if other information such as flow and occupancy was used to identify the traffic speed. A ramp metering system is active on every on-ramp of this site. It was running on a fixedtime basis for the analyzed days (since 2006 it has been operating on a systemwide adaptive basis). The German site is located on northbound Autobahn A9 north of Munich. Data (velocity and count) from the A9 was available from double loop detectors between km 528.2 and km 513.3 in one minute aggregates and was provided by the Autobahndirektion Südbayern. Five days in June and July, 2002 were analyzed for this study. These data are available by lane, are segregated by autos and trucks, and are available on most onand off-ramps as shown in Figure 1. The freeway is equipped with variable message signs, a variable speed limit system and no ramp meters. Zielke, Bertini and Treiber 5 The UK site is an eastbound motorway M4 near London. Data from double loop detectors was available for the section between km 23.2 and km 16.2 for seven days in November 1998 and was provided by the UK Highways Agency and the Transport Research Laboratory. The data consist of individual vehicle arrival times and velocities for each lane. There were no ramps on the motorway, and data were collected before a bus lane was installed at the site. For the M4 data, since the analysis pursued is based on a macroscopic approach, aggregation was necessary. It was done arbitrarily for 10 s intervals.