Modelling Emergency Rescue System on Highways: A Queueing Approach

The emergency rescue systems on highways can reduce direct and indirect economic losses and casualties within the shortest response time. This paper aims to formulate the performances of emergency services operations for rescuing vehicle locations and responding to district planning on highways. First, a highway rescue vehicle scheduling strategy considering the equilibrium probability of rescue vehicle state is established based on the idle or busy state of rescue vehicles. Then, the equilibrium equation of the working intensity of rescue vehicles (the time proportion of rescue vehicles in the rescue state) is proposed on the basis of the theory of stochastic birth and death process, conditional probability theory and probability multiplication formula. The equilibrium equations are linear and easy to be solved iteratively. From the working intensities of the rescue vehicles, several rescue performances of emergency rescue systems are derived, such as the rescue response time of systems, districts and rescue vehicles, as well as the fraction of rescue vehicles inter-district, etc. Finally, the numerical experiments from the Su-Tong Yangtze River Bridge on the G15 highway are implemented to verify the proposed model and algorithm. These rescue performances could provide support for decision-making on the reasonable number of rescue vehicles and location of the emergency stations.