Probabilistic Programming Models for Response Vehicle Dispatching and Resource Allocation in Traffic Incident Management

This paper proposes mathematical programming models with probabilistic constraints in order to address incident response and resource allocation problems for traffic incident management. In incident response problems, we introduce the concept of quality of service during a potential incident to give the operator the flexibility to determine the optimal dispatching policy in response to various situations. A mixedinteger programming (MIP) model with probabilistic constraints is proposed to address the dispatching problem with consideration given to the stochastic resource requirements at the sites of the potential incidents. For the resource allocation problem, assuming that the stochastic distribution of incidents over a network is given, we introduce a mathematical model to determine the number of service vehicles allocated to each depot to meet the requirements of the potential incidents by taking into account the stochastic nature of the resource requirement and incident occurrence probabilities. For completeness, relevant concepts and solution algorithms in stochastic programming are also presented. Several examples are included to demonstrate the applications of these models to real-world problems. This paper concludes with a summary of results and recommendations for future research.