1. MEASURING FIRST-IN-FIRST-OUT VIOLATION AMONG VEHICLES Wen-Long Jin, Yu Zhang Institute of Transportation Studies and Civil & Environmental Engineering Department University of California, Irvine Lianyu Chu California Center for Innovative Transportation University of California Berkeley Contact: wjin@uci.edu, yzhang@uci.edu, lchu@berkeley.edu DATE: Wednesday, January 25, 2006 TIME: 9:30am-12:00pm LOCATION: Marriott, Washington SPONSORED BY: Traffic Simulation Models: New Developments and Applications trb06-2903 Poster for TRB 85th Annual Meeting SESSION #640

2. Abastract In reality, First-In-First-Out (FIFO) principle for vehicles on a link or path is often violated due to heterogeneity in drivers’ behavior and traffic conditions on different lanes. It is important to understand how serious such FIFO violation can be, since the assumption of FIFO has been an important foundation for developing many dynamic traffic assignment strategies and traffic flow models. In this paper, we first present a measurement of FIFO violation among vehicles and then theoretically show that this measurement is well defined. We further apply this measurement to study scenarios generated by a microscopic traffic simulator and find that FIFO violation is linear to travel time or distance. This study can serve as a springboard for future studies on FIFO violation in real traffic, and the FIFO violation measurement can be used to calibrate and validate traffic flow models and dynamic traffic assignment models.

3. Introduction First-In-First-Out (FIFO) principle is an important assumption underlying many traffic flow models and dynamic traffic assignment models; In reality, overtaking is often observed to violate FIFO; Understanding how serious FIFO violation can: have important implications on the definitions of dynamic user equilibriums; better validate and improve traffic flow models regarding overtaking behaviors; In this study, a measurement of FIFO violation among vehicles is presented and applied to several simulated scenarios.

4. An Illustration of FIFO Violation Three-stage FIFO violation in Fig 1 (a) & (b): Two cars get closer to each other; White car overtakes black car; Two cars separate from each other; FIFO violation is more serious in (b) than that in (a); Without an order changing, no FIFO violation in (c) and (d); Fig 1. FIFO Violation between Two Cars Causes of FIFO violations: Aggressive drivers actively switching to less congested lanes; Difference in traffic conditions among different lanes; Control devices such as traffic lights;

5. Measurement of FIFO Violation Definition 1. FIFO violation on time among N vehicles in the section from x 1 to x 2 is Where, = time passing x 1 for vehicle n; = ideal FIFO time passing x 2 for vehicle n; Table 1. An Example of FIFO Violation, where J t = 0.8 min Some basic properties: Unit is time; Consists of two parts: forward and backward; Symmetric with respect to locations; An average among all vehicles; Not additive with respect to location.

6. Regulation of FIFO Violation Measurement and Normalized FIFO Violation Theoretical properties: Theorem 2. FIFO Violation equals 0 iff vehicles follow FIFO principles; Theorem 3. Most FIFO Violation occurs in the case of First-In- Last-Out; Theorem 4. FIFO Violation is less than the average travel time of all vehicles between x 1 and x 2. Definition 2. The normalized FIFO violation can be defined as: where, = average travel time of vehicles from x 1 to x 2 ;

7. Simulation Setup Paramics microscopic traffic simulator is used; Basic scenario: 2-lane road of 60 miles with speed limit 50 mph; One O-D pair with demand of 2000 veh/hr; Free flow state; 120 detectors placed, one every half a mile; API plug-in used to record vehicles’ times passing each detector. Other scenarios: A. Market penetration rates of 1%, 2.5%, 5%, 10%, 25%, 50%, 75%, 100%; B. Number of lanes from 1 to 4 with traffic demand proportional; C. Half of vehicles with aggression value of 1, half from 1 to 8; D. Traffic demand levels from 500 veh/hr to 4000 veh/hr with an incremental step of 500 veh/hr.

8. Simulation Results and Analysis Base scenario: Linear relationship between J t (x 1,x 2 ) and locations; Linear relationship between ATT(x 1,x 2 ) and locations; Linear relationship between J t (x 1,x 2 ) and ATT(x 1,x 2 ); Linear relationship between J t (x 1,x 2 ) and std of TT(x 1,x 2 ); Scenario A: No significant differences among normalized FIFO violations as long as the market penetration rate is greater than 5%; Scenario B: The maximum average FIFO violation occurs on the two-lane road, a counter-intuitive result; Scenario C: The larger difference in aggressions between two group of vehicles, the higher FIFO violation; Scenario D: Higher demands cause lower speeds and lower normalized FIFO violation.

9. Conclusion A measurement of FIFO violation among vehicles is proposed and proved to be theoretically well-defined; FIFO violation is studied using a microscopic traffic simulator for different road networks, traffic conditions and drivers’ characteristics; Applications: Measuring the aggregate phenomena of lane-changing or overtaking; Guiding the development of policies on overtaking or lane- changing; Future studies: FIFO violation in real traffic, using vehicle trajectory data from Berkeley Highway Lab or FHWA NGSIM project.