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

Abstract

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 world's 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.