Empirical Estimation of a Macroscopic Fundamental Diagram (MFD) for the City of Cape Town Freeway Network

The City of Cape Town is the most congested city in South Africa, with Johannesburg coming in second. Capetonians are spending 75% more time in traffic because of the congestion during peak hours, thus reducing time spent on leisure and other activities. Due to population growth, increasing car ownership and declining capacity of rail infrastructure, Cape Town's road infrastructure will continue to be under severe pressure if the status quo is maintained. Research shows that congestion levels in urban areas are key factors in determining the effectiveness and productivity of the transport system. Traffic congestion poses a threat to the economy and the environment. Increasing corridors' capacity by increasing the number of lanes does not necessarily solve the problem. Effective urban traffic management and efficient utilization of existing infrastructure are critical in creating sustainable solutions to congestion problems. To achieve this, it is important that appropriate urban-scale models and monitoring strategies are put in place. Effective traffic management and monitoring strategies require accurate characterization of the traffic state of an urban-scale network. Several approaches, including kinetic wave theory and cell transmission models or macroscopic traffic simulation models, have been proposed and developed to describe the traffic state of an urban-scale network. However, these approaches are limited and require significant amounts of computational time and effort. The application of macroscopic fundamental diagram (herein referred to as MFD) to characterize the state of an urban-scale network has thus far proven to be more effective than other approaches. MFD represents the state of urban traffic by defining the traffic throughput of an area at given traffic densities. It describes the characteristics and dynamics of urban-scale traffic conditions, allowing for improved and sustainable urban scale traffic management and monitoring strategies. Against this backdrop, the existence of MFD for the City of Cape Town (CoCT) urbanscale network is yet to be established and the implications yet to be understood, as in other parts of the world. The main aim of this research was, therefore, to empirically estimate the macroscopic fundamental diagram for the CoCT's freeway network and analyse its observed features. To achieve this, observed data of 5 minutes periods for the month of May 2019 was used to estimate the MFD. The results confirmed that when the chaotic scatter-plots of flow and density from individual fixed loop detectors were aggregated the scatter nearly disappeared and points grouped neatly to form a clearly defined free-flow state, critical state and the formation of hysteresis loops past the critical density corresponding with the network observed maximum flow. Further analysis of the MFDs showed that a single hysteresis loop always forms past the critical density during the evening peak in a weekday MFD. However, it was inconclusive during the morning peak period in weekday MFDs. Lastly, an explicit hysteresis loop seldom appears in a Saturday MFD when the peak of traffic demand is lower than on weekdays. In order to understand the dynamics of the congestion spread, the freeway network was partitioned into penetrating highways network and the ring highway network. The results showed that the maximum flows observed for the two sub-networks were significantly different (943 veh/hr/lane for the penetrating highways network and 1539 veh/hr/lane for the ring highway network). The penetrating highways network's MFD indicated the presence of congestion in the network whereas the ring highway network indicated only the free-flow state (no indication of congestion) during peak periods. The congestion seen on the penetrating highways network was found not to be sufficiently spread on those highways. On the 24th May, congestion on the penetrating highway network was observed during both the morning and evening peak periods, whereas on the 31st May congestion was observed mainly during the evening peak period, with hysteresis-like shape. These observations confirmed that congestion during peak periods is not homogenously spread across the entire network, certain areas are more congested than others, hence the observed formation of hysteresis loops and slight scatters. Lastly, the hysteresis loops observed in the penetrating highways network's MFD was further characterized in terms of their shape and size. First, the results showed that the slight scatter and hysteresis patterns observed in penetrating highways network MFD's vary in size and shape across different days. The shapes of the hysteresis loops observed during both the morning and evening peak periods, were type H2 hysteresis loops, signifying a stable recovery of the network with the average network flow remaining unchanged as average network density decreases during the recovery. Characterization of the size of the observed hysteresis loops showed that the drop of the hysteresis (an indicator of network level of instability during recovery phase) was smaller, signifying a more stable network traffic and homogenous distribution of congestion during the recovery phase