Stuck in Traffic:
Dynamics of Congestion in Cities
Developed by Ragavendran Lakshminarasimhan and Dr. Meead Saberi at University of New South Wales, Sydney.
Thanks to Sajjad Shafiei, Ziyuan Gu, Lucas Martin-King, Serge Rogov, Luis Olmos and Prof. Marta Gonzalez from UC Berkeley for their contributions.
Large cities around the world are facing an increasing challenge in satisfying their needs for mobility and accessibility due to rapid population growth. Melbourne, Australia is not an exception. Despite carrying the “most liveable” city brand for a number of years[1], Melbourne’s peak period congestion has been the fastest growing in the country with 8:30 AM being the busiest time to travel[2]. In 2013, an estimated 12.3 million trips were made on an average weekday in greater Melbourne area.[2] As population increases, the number of daily trips is estimated to increase to near 25 million in 2051. Private car use across Melbourne accounts for 72 per cent of trips, leaving the road network to accommodate for more than 7 million car trips in a day, today[2]. That’s a lot of cars!
Why congestion forms?
Space available to travel in our cities is tightly constrained and is often subject to competition among different modes. When demand for travel exceeds the available capacity in the road network, congestion forms. If demand for travel continues to grow faster than the rate trips are being completed, we start seeing pockets of congestion appearing in different parts of the network. Thankfully, there is a science behind it and it’s called “network traffic flow theory”.
The history of network traffic flow theory goes back to 1960s, in which a number of seminal studies[3-6] explored the macroscopic dynamics and relationships in car traffic in an urban network. More recent scientific explorations[7-10] have shed light on how and why a road network becomes congested and how it can actually be controlled with gating or perimeter control strategies and pricing[11-15]. This is in fact a growing and attractive research subject around the world with many researchers from different countries and universities trying to develop solutions for this world-wide problem.
Simulating Melbourne traffic
Here, we re-tell the story of traffic in Melbourne[16,17] with a little bit of scientific flavour to it to engage public and policy makers with our research. Over the past few years, we have built a dynamic model that simulates Melbourne traffic. We call it DynaMel and it’s open access. DynaMel is a “dynamic traffic assignment” model[18] that estimates the evolution and propagation of congestion through detailed models that capture travel demand, network supply and their complex interactions.
Below, is an example visualisation of the simulated traffic of Melbourne. Note that the simulation includes realistic input for 6:00 AM to 10:00 AM. From 10:00 AM to 2:00 PM, we are letting the network to recover. We’ll describe why below.
Loading and unloading of traffic
The simulation consists of the 4-hour morning peak period from 6:00 AM to 10:00 AM with near 2.1 million simulated cars. When we are dealing with traffic flow in a network, we can describe the system with two states: loading and recovery. Loading is the phase that the network is being loaded with more cars, demand for travel is growing and as a result, streets are becoming more congested. This happens from 6:15 AM until 9:00 AM in Melbourne. After 9:00 AM, when most people have already reached their destination, demand for travel starts decreasing. Therefore, the network goes to a recovery state in which congestion starts dissipating. However, this doesn’t last long enough for the network to fully recover. The network goes under another loading phase at the beginning of the afternoon peak which could be as early as 3:00 PM. To study dynamics of recovery, without being interrupted with a re-loading phase, we have let the simulated network to continue unloading until all trips are completed and everyone in the network has reached their destination.
Network recovery
Network recovery is an interesting phenomenon in traffic. Recovery is often less efficient than loading. In other words, for the same number of cars in the network, if the network is loading we expect to see higher productivity (e.g. higher trip completion rate) while if the network is recovering, the productivity is often less. Remember this is for the same number of cars in the network. That’s why it takes a very short time for congestion to build up but it takes ages to recover. Let’s create an example. How about we focus on the unlucky target group who enters the network between 7:45 AM and 8:45 AM which represents the busiest time of the day? We would like to know how long it actually takes for all those travellers to complete their trip. If they’re lucky and the network isn’t gridlocked, the full recovery is going to take 3 hours so the last traveller in the group finishes its journey. This is identified as an interesting characteristic of urban networks, thanks to a collaborative research with Prof. Marta Gonzalez at UC Berkeley
This makes an interesting case for predictive control of traffic. We don’t want to start controlling traffic too late in the loading phase because it’s simply too late. Congestion has already built up and it’s going to take a long time to recover. A better control strategy is to tackle congestion before it’s forming. It’s easier said than done though.
Reality vs. Computer Simulation
Well, this was all done in a computer simulation. How does this look like in reality? Pretty much the same with more or less congestion here and there. In fact, we have compared our simulation results with travel times from Google Maps and traffic counts from VicRoads’ vehicle counters across the region. We have seen a reasonable match. We actually have a published paper on it[19].
References
1.The Gaurdian. 2. Victorian Integrated Survey of Travel and Activity (VISTA). 3. Smeed, R. J., 1966. Road Capacity of City Centers. Traffic Engineering and Control, Vol. 8, No. 7, 455–458.
4. Wardrop, J. G., 1968. Journey Speed and Flow in Central Urban Areas. Traffic Engineering and Control, Vol. 9, No. 11, 528–532.
5. Godfrey, J. W., 1969. The Mechanism of a Road Network. Traffic Engineering and Control, Vol. 11, No. 7, 323–327.
6. Zahavi, Y., 1972. Traffic Performance Evaluation of Road Networks by the α-Relationship. Parts I and II. Traffic Engineering and Control, Vol. 14, No. 5–6, 228–231 and 292–293.
7. Daganzo, C. F., 2007. Urban Gridlock: Macroscopic Modeling and Mitigation Approaches. Transportation Research Part B, Vol. 41, No. 1, 49–62.
8. Daganzo, C. F., and N. Geroliminis, 2008. Analytical Approximation for the Macroscopic Fundamental Diagram of Urban Traffic. Transportation Research Part B, Vol. 42, No. 9, 771–781.
9. Mahmassani, H.S., Saberi, M., Zockaie, A., 2013. Urban network gridlock: theory, characteristics, and dynamics. Transp. Res. Part C 36, 480–497.
10. Saberi, M., Mahmassani, H.S., Hou, T., Zockaie, A., 2014a. Estimating network fundamental diagram using three-dimensional vehicle trajectories: extending Edie’s definitions of traffic flow variables to networks. Transp. Res. Rec J Transp. Res. Board 2422, 12–20.
11. Ramezani, M., Haddad, J., Geroliminis, N., 2015. Dynamics of heterogeneity in urban networks: aggregated traffic modeling and hierarchical control. Transp. Res. Part B 74, 1–19.
12. Haddad, J., 2017. Optimal perimeter control synthesis for two urban regions with aggregate boundary queue dynamics. Transp. Res. Part B 96, 1–25.
13. Haddad, J., Ramezani, M., Geroliminis, N., 2013. Cooperative traffic control of a mixed network with two urban regions and a freeway. Transp. Res. Part B 54, 17–36.
14. Keyvan-Ekbatani, M., Kouvelas, A., Papamichail, I., Papageorgiou, M., 2012. Exploiting the fundamental diagram of urban networks for feedback-based gating. Transp. Res. Part B 46 (10), 1393–1403.
15. Gu, Z., Shafiei, S., Liu, Z., Saberi, M., 2018. Optimal distance- and time-dependent area-based pricing with the Network Fundamental Diagram. Transp. Res. Part C 95, 1-28.
16. The Age. 17. The Age. 18. UNSW CityX lab. 19. Shafiei, S., Gu, Z., Saberi, M. (2018) Calibration and validation of simulation-based dynamic traffic assignment model for a large-scale congested network. Simulation Modelling Practice and Theory 86, 169-186.