A Heuristic Method for Connectivity and Capacity Reliability Evaluation in Degradable Urban Transportation Networks

A transportation network, subject to some internal or external events, may be involved in performance degradation and traffic flow instability. The external events mainly include weather conditions and natural disasters like snowfall, ice, hurricane, earthquake and avalanche. Internal degradations are due to traffic related factors such as control systems failure, accidents, and maintenance and construction operations. All aforementioned circumstances can severely decrease links’ capacities, and some of them affect the base demand of the origin-destination pairs; hence, the network cannot perform as well as that in normal situation.When a transportation network or a number of its components (links) is vulnerable pertain to the foregoing incidents or disasters, its performance cannot be evaluated through the conventional methods in which we calculate deterministic measures such as average travel speed, average delay per vehicle and vehicle-kilometer traveled. In such situations the capacity of degraded links has not certain values, and they must be referred to as probability distribution functions; we therefore will face with a probabilistic network whose performance index ought to be assessed in reliability terms. Until now different types of performance reliability have been established to evaluate the reliability of degradable transportation networks. The first one is the connectivity reliability which considers the probability that a special origin-destination (OD) pair of the network remains connected. The other measure addressed frequently in previous studies is travel time reliability, which is defined as the probability that a trip performs successfully between a given OD pair within a specified time interval. Recently, another challenging measure has been introduced in order to estimate that at what level of a certain demand the network can perform accurately. This measure is known as capacity reliability and, in other words, is the probability that a network can accommodate a certain traffic demand at a required service level.This paper presents a heuristic method to calculate the connectivity (terminal) reliability and the capacity reliability. The capacity of each link is assumed to have a normal distribution function that is verified by a proposed method in order that a lower bound and an upper bound can be assigned to the function. Using these modified normal distribution functions the performance reliability of each link is obtained based on the integration of its probability density function from to: where is the traffic volume on link that is computed through the application of user equilibrium assignment with respect to the expected link capacities. and are respectively upper bound and probability density function of capacity of link. Notice the link performance reliability will be zero if the volume exceeds the upper bound of link capacity.Having calculated the links performance reliabilities, the capacity and connectivity reliability of the network are calculated by means of the closed formulas presented in this paper for each type of considered performance reliability measures. Another contribution of this paper is that the presented method has the ability of taking into account a required level of service for each link, namely it would be possible to assess the network performance when there exist especial expectations for maximum volume per capacity ratios (s). Therefore, it might be said that in the proposed method the travel time reliability is considered along with evaluating the two explained performance reliability measures because the travel time of each link is a function of its. Finally, for the sake of comparing the numerical results obtained from proposed method and from the other previous works, we have examined a simple test network employed repeatedly in network reliability analysis, particularly in the case of capacity reliability studies.