Modeling Freeway Traffic Flow under off-Ramp Congestion Habibollah Nassiri, Ali Khayat Khoie Sharif University of Technology, Civil Engineering Department E-mail: [email protected] Abstract: This paper studies the effects of queue formation in the bottlenecks at off-ramps on the capacity of the freeways. Six expressway exit-ramps throughout the city of Tehran, Iran were selected and their traffic flows were observed in thirty-minute intervals during which the queue formation and queue elimination occurred. Assuming that in the absence of the queue, the traffic flow is in its normal state, the changes in the volume of through vehicles has been modeled as an average estimator of the change in the expressway capacity. The developed models prove that the changes in freeway capacity are due to queue formation at the off-ramp sections. However, the estimated figures are different from those obtained from the theory of freeway capacity. The conclusion is that lane blockage is only one of many factors that affect the freeway capacity while the queue forms. Since it is not possible to quantify all those factors individually, the resulting models are macroscopic estimates of the phenomenon. Keywords: capacity drop, vehicles queue, exit-ramps, modeling. 1- INTRODUCTION 2- LITERATURE REVIEW Due to the rapid development of cities, the Hall et. al studied the freeway capacity drop transportation of goods and passengers has due to queue formation and pointed out become an issue of concern. An important inadequacies of the method presented by issue regarding the traffic management of a Highway Capacity Manual (HCM) to city street network is to alleviate congestion. estimate the capacity of freeways[1]. They A review of the studies in this field reveals pointed out the alterations of the ideal that in spite of the obvious problems of off- capacity in transient state in which the traffic ramp congestions, no comprehensive studies flow is unstable. They concluded that in of its effects on expressway have been done transient state the output on the freeway in Iran. downstream from the congested exit is a better estimator of the freeway capacity, Flow congestion in exit-ramps adversely because it shows more stable patterns. affects the capacity of expressways at the bottlenecks section. Moreover, formation of In other studies, Banks dealt with dual long queues at the off-ramp section and the capacity phenomenon caused by congestion blockage of these sections affect other in freeway and questioned the validity of sections of the expressway, including the shock wave theory in the aforementioned upstream of the bottleneck. Due to this condition sections [2, 3]. Banks notes that the congestion, even those vehicles that do not shock wave theory yields accurate results in want to exit expressway experience long case of a single wave; while in real delays. This sometimes results in a total congestion conditions the results are not breakdown of the flow and blockage of the reliable due to several shock waves resulting expressway. from stop and go. 192 International Journal of Civil Engineering. Vol.3, Nos.3&4 September & December 2005 Moreover, the changes in time and spatial 4.Modarres Expressrway, south bound, off- overheads raised questions regarding the ramp to Motahari Ave. validity of car-following theory in real congestion conditions. Studies have modified 5.Kordestan Expressway, north bound, off- the shock wave and car-following theories so ramp to Tavanir Bridge. the results would be more compatible with observations [4, 5, and 6]. But Trieterer and 6.Chamran Expressway, north bound, off- Mayers noted that the condition in case of ramp to Hemmat Expressway, east bound. congestion is completely non-linear and thus, even the modified theories, due to their linear All these off-ramps are located on 6-lane nature, will fail to yield an accurate freeways with auxiliary deceleration lanes. estimation of the complicated congestion Each of the selected sites was filmed at conditions [7]. Tehran Traffic Control Center for 30-minutes period. Table 1 presents the date and the time Kerner also studied the changes in vehicle which each off-ramp traffic condition was speeds in bottlenecks [8]. He observed the recorded. The periods in which the sites continuous changes in flow and speed of were filmed were chosen in a way that queue vehicles at bottleneck sections and indicated formation was most likely to occur. that the flow-density diagram fails to explain The information that was observed from the the conditions due to non-linear video films is the relative time and space of characteristics of transient flow, which vehicles in queues at certain points of each always exit. He concluded that the bottleneck, volume counts in one-minute application of kinematics’ wave theory is not intervals, and time of queue formations and advisable for these conditions. eliminations at each off-ramp site. To extract the relative time and space of passing vehicles, different sections were selected along each off-ramp section and the 3- DATA COLLECTION time that each vehicle passed the selected sections was measured using a chronometer Preliminary observations of Tehran's street while the video player was playing back the network indicated that although there are film at half of the speed of the film so the real many off-ramp sites, only few sites passing times would be half of the measured experience congestions. Therefore, based on times. This provided more time to observe the consultations with the experts at Tehran the traffic congestion. A sample of this Traffic and Transportation Organization, the information is provided in Table 2. The following six sites were selected: video films were played once again to count the number of passing vehicles separately 1.Modarres Expreesway, south bound, off- and also to extract the state of the queue in ramp to Sadr Expressway, east bound. each one-minute interval. Table 3 shows a sample of this information. 2.Modarres Expressway, south bound, off- ramp to Hemmat Expressway, east bound. 4- STUDY METHOD 3.Modarres Expressway, south bound, off- ramp to Behesthi Ave. The first step is to study the traffic flow in the International Journal of Civil Engineering. Vol.3 Nos.3&4 September & December 2005 193 Table (1) – Date and time of filming at different sites No. Site Week Day Date Beginning End Modarres freeway, south bound, off -ramp to 1 Wednesday 10/8/2003 9:24:50 9:54:50 Sadr freeway, east bound Modarres freew ay, south bound, off -ramp to 2 Monday 10/13/2003 7:48:00 8:18:00 Hemamt freeway, east bound Modarres freeway, south bound, off -ramp to 3 Wednesday 10/15/2003 9:26:05 9:56:05 Behesthi Av. Modarres freeway, south bound, off -ramp to 4 Wednesday 10/15/2003 12:17:45 12:47:45 Motahari Av. Kordestan freeway, north bound, off -ramp to 5 Tuesday 10/14/2003 8:11:30 8:41:30 Tavanir Bridge. Chamran freeway, north bound, off -ramp to 6 Monday 10/13/2004 9:07:00 9:37:00 Hemmat freeway, east bound Table (2) – Sample vehicle passing time and distance information Time to reach Time to reach Time to reach Vehicle # section 1 section 2 section 3 Min. Sec. Real Min. Sec. Real Min. Sec. Real 1 0 12 6.0 0 36 18.0 0 57 28.0 2 0 18 9.0 0 43 21.0 1 4 62.0 3 0 27 13.0 0 55 27.0 1 9 34.0 4 0 35 17.0 1 5 62.0 1 25 42.0 5 1 1 30.0 1 38 49.0 2 2 61.o Table (3) – Vehicle behavior in queue, sample information Beginning End Vehicle Count Queue Queue Queue Queue Passenger Buses Motor in in in in cars trucks bikes storage lane 3RD 2ND 1ST lane lane lane 7:48:00 7:49:00 86 2 4 - - - 7:49:00 7:50:00 87 2 3 - - - 7:50:00 7:51:00 98 2 - - - - - 7:51:00 7:52:00 84 1 1 - - - 7:52:00 7:52:00 83 2 3 - - - 7:53:00 7:54:00 83 1 4 - - - 7:54:00 7:55:00 74 1 6 - - 7:55:00 7:56:00 82 - 3 - - - 7:56:00 7:57:00 75 2 5 - - 194 International Journal of Civil Engineering. Vol.3, Nos.3&4 September & December 2005 freeway during the queue formation. To do each line is the mean speed of the relevant so, time-space diagrams of vehicle vehicle between the two points. As there are movements inside queues at each off-ramp many obvious changes in line slopes, the were plotted using the queue behavior speed changes at all six sites observed are information. As seen in Figures 1 to 6, each unstable. line represents a vehicle moving through the queue at the specified site. Thus, the slope of It is concluded that the flow is in unstable 50 250 40 200 30 150 20 100 Distance (m) Distance Distance (m) 10 50 0 0 0 50 100 150 Time (s) 0 200 400 600 800 Time (s) Figure 1: Vehicles displacement, site 1. Figure 2: Vehicles displacement, site 2. 100 200 80 150 60 100 40 Distance (m) Distance (m) 50 20 0 0 0 100 200 300 400 500 600 0 100 200 300 400 500 Time (s) Time (s) Figure 3: Vehicles displacement, site 3. Figure 4: Vehicles displacement, site 4. 100 160 140 80 120 100 60 80 60 40 Distance (m) 40 Distance (m) 20 20 0 0 100 200 300 400 0 0 100 200 300 400 500 600 Time (s) Time (s) Figure 5: Vehicles displacement, site 5.