B.K. Bhavathrathan

Capacity uncertainty on urban road networks: A critical state and its applicability in resilience quantification

There are many aspects of urban transportation that represent sources of uncertainty in the design of roadways, such as the level of capacity needed to ensure efficient traffic flow. As a result of uncertainty in roadway capacity, an urban road network can be deemed to operate at different capacity levels. Some of these levels will have unused capacity, whereas some others will not be enough to cater traffic from all origins to all destinations. Past models assume knowledge over the pattern of these uncertainties. However, it is difficult to gather such knowledge from field observations, and it is absent for majority of the worlds urban areas. We present an alternative methodology in which the capacities are considered as variables that can take any value from zero to a practically realizable maximum. Using a minimax optimization formulation, we determine bounds on urban roadway capacity levels, below which the traffic demand will go unmet. We call this the critical state, and define it as a state of link capacities which effects in the maximum irreducible operational cost on the network with the demand getting fulfilled. We prove that at a critical state, the total travel time (or cost) of the system will be a unique value; i.e. for a given urban road network and a given traffic demand, there is an associated unique critical travel time. We illustrate that this unique travel time—which is an aggregate value of the travel times from all roads on the network—can be used as a benchmark to create various metrics for the urban road network. As an illustrative example on the applicability of critical state, we compare the unique travel time with the best possible travel time on the network, and develop a metric for network resilience. Network resilience is calculated as a normalized difference of the critical and best operation costs. Two-space genetic algorithm is used to solve the problem formulation. The formulation and the solution methodology are illustrated on test networks and results are presented.

Quantifying resilience using a unique critical cost on road networks subject to recurring capacity disruptions

This paper presents a methodology to quantify resilience of transportation networks that are subject to recurring capacity disruptions. System-optimal total travel time at full-capacities is usually adopted as a performance-benchmark on networks. Capacity degradation results in different capacity combinations, and thus, there can be different travel times. We thus compare the best network performance with an upper bound of network performance—indicating how much disruptions the network can take in before it displaces from a demand-meeting state to a demand-not-meeting state—and construct an index of network resilience. For this, we establish a critical state which is an upper bound of network cost under recurring capacity degradation. We define discrete capacity levels and search for probability values over those levels that would result in a critical state. We formulate the critical state link disruption problem as a minimax optimisation problem, where expected system travel time is maximised with respect to probability of recurrence and minimised with respect to link flow. We prove that the network cost is unique at the critical state, although the critical degradation need not be. We solve the minimax problem using a coevolutionary algorithm. We exemplify the formulation on test networks and quantify the improvement in network resilience by retrofitting the Sioux Falls network.

EFFECT OF TRAFFIC DEMAND VARIATION ON ROAD NETWORK RESILIENCE

Certain capacity degradation levels increase travel times on road networks, while traffic demand remains met. Resilience of a road network is higher, if it can take-in higher levels of degradation without leaving any part of the demand unmet. It is important for planners to quantify this, and it can be obtained as the output of an optimization problem. The resultant measure of resilience is demand-specific. To generalize the resilience measure, its sensitivity to change in demand should be studied. We observe that irrespective of the difference in network size or network topology, resilience decreases with increase in demand. We perform computational experiments on different network topologies to investigate the relationship between network resilience and traffic demand. Based on this, we introduce the area under the demand-resilience curve as a generalized index of resilience (GIR). We compare the GIR with traditional network indicators and find that it is in certain ways, better.

Algorithm to Compute Urban Road Network Resilience

Road network resilience is emerging as a vital planning criterion. Yet, unique and cross-comparable indices for road network resilience are scarce. One of the recent approaches determines resilience as a unique network attribute based on the system travel time at an upper envelope of operable disruptions. This upper envelope represents ‘critical states’ (or tipping points) of capacity disruptions. Critical state gives a bounding capacity degradation vector, beyond which the network cannot wholly cater to the origin–destination demand even under the best possible traffic assignment. However, solving the critical state identification problem (CSP) on real-scale networks has remained a challenge. This paper presents a weighted fictitious play algorithm to fill this gap. CSP has been previously envisaged as a two-player game between a network attacker and a network defender. Here, we make the players play iteratively, and make them learn from the competitor’s past strategies so that they converge to an equilibrium. We illustrate the method on a simple toy network, and solve it on different real-life networks. Resilience of the Anaheim city network was computed in 42.8 min., considerably outperforming—both in problem-size and solution-time—the previous, two-space genetic algorithm.

Red Light Running at Heterogeneous Saturated Intersections in Mumbai, India: On the Existence of Two Regimes and Causal Factors

This paper presents an analysis of red light running (RLR) conducted at saturated intersections in the city of Mumbai, India, where the traffic is highly heterogeneous with respect to vehicle classes and driver behavior. When all vehicles are considered, almost one in 17 drivers is seen to be jumping red signals there. Unlike the RLR behavior that has been previously reported from intersections elsewhere, a peculiarity observed here is that, within a single red phase, two distinguishable segments of RLR behavior exist. The authors classified them into two regimes: Regime 1, just after the onset of red, and Regime 2, just before the onset of the next green. About one-third of RLR events occur in Regime 1 and the rest in Regime 2. The authors fit different distributions on the time distribution of RLR events. The Kolmogorov–Smirnov test suggests that, at all intersections, exponential distribution fits best for RLR behaviors in Regime 1, and extreme value distribution fits for Regime 2. In addition to those two regimes, RLR at a lower rate is observed in the period between those regimes, and normal distribution fits there. To analyze the causal factors of RLR behavior in the two regimes, the authors developed models at a mesoscopic level specific to vehicle class and regime. Although the red-to-green ratio and the presence of policing prove to be relevant factors affecting RLR in both the regimes, the relative time for which the conflict area is free affects RLR in Regime 2 but not in Regime 1.