Reliability Based Resource Allocation for Transportation Network

Transportation networks are highly vulnerable to natural disasters such as earthquake. However, they are expected to perform properly in all circumstances. They are expected to connect different parts of the network and provide these connections with a proper level of service. Since transportation networks today are undividable sections of modern lives, being equipped with a sustainable and reliable network is a vital requirement of each society. Transportation authorities are always concerning about the improvement of the network influenced by the external effects as well as its the repair and maintenance due to the stochastic environment encompassing the network. However, their permanent constraint is the limitation of budget available. As a result, to get closer to the subject of improving the network’s performance, it is necessary to allocate resources to the network components in an optimized manner. During the occurrence of a disaster, the basic necessity for the injured is to receive emergency services which are directly dependent on serviceability of the network. Clearly the services are effective and savior if only they are offered in a predefined time threshold. It means that not only the network should provide at least one route between different population centers, but also it should provide a proper serviceability for each route. “Proper serviceability” here means providing complete service to demand in a pre-determined threshold of travel time. As this serviceabilityis uncertain, the reliability term is engaged which has become important parameters for planners and authorities recently. Hence, as connection and travel time are both necessary, under uncertain conditions, their respective reliability indicators are chosen as proper performance measures of the network. It is to be mentioned that the proposed reliability approximation method shows some sorts of limitations through several usage of the method in different networks. For example, increasing the dimension of network leads to a great sudden increase in required probable states to provide a proper coverage. Although the number of required states considerably less that the number of whole probable states, it is still a huge number which makes the algorithm very time consuming.The same problem will occur if the probabilities of the modes of each link are very close to each other. For example sign the algorithm for a link with the set of mode probabilities of (40, 30, 30) is inappropriate while the same algorithm is very efficient and useful for a link with probability set of (8, 7, 85). The provision of emergency services after a disaster is the most important factor to survive the wounded. This issue directly depends on serviceability of the network, which is highly vulnerable to natural disasters. In this paper, a resource allocation model was proposed for degradable transportation networks. In the proposed model, the network travel time reliability and the connectivity reliability of each OD of the network were chosen as two important performance measures under the effect of different type of disasters, e.g. earthquake. Although applying the reliability approximation method will make the challengeable procedure of reliabilityapproximation more efficient, it is does not show the same efficiency in larger or more variable probable state for links. However it can be applied in small size networks, as shown in the numerical example of this paper. For further studies, it is suggested to develop a model for networks with continuous performance function,assuming more than 1 level of investment allowed for each link, or continuous travel time functions which are affected by flow. These changes would lead to more real network studies. In addition the proposed idea can be developed for daily or slight fluctuation of capacity produced by events such as accidents or road maintenance activities.