Performance Approximation for Highway Emergency Rescue Systems

Ensuring prompt responses to spatially uncertain traffic accidents is critical for highway emergency rescue systems, aiming to address emergencies and to prevent network-wide traffic disruptions. This paper develops an approximation model to characterize priority-based rescue systems for RV fleets. By representing each RV's state as either idle or busy, we formulate an approximation model in which the dispatch probability of an RV is dynamically influenced by the utilization of higher-priority RVs and its own availability. The proportionality constant governing this relationship is derived analytically from an M/M/N queuing model, incorporating a random server selection mechanism without replacement until the first available RV is identified. The system of equations is simplified into a tractable set of N linear simultaneous equations, enabling efficient computation of RV workloads. We further propose a solution algorithm to estimate critical performance metrics, including individual RV workloads, system response times, and cross-dispatch frequencies. A practical case study based on the G15 Highway (Sutong Bridge section) in China illustrates the model's applicability in quantifying performance measures such as individual RV response times, cross-regional dispatch ratios, and workload distribution under varying vehicle allocations and priority levels. The proposed model provides a practical and computationally efficient tool to support RV location planning, response section partitioning, and overall performance evaluation in highway emergency services, offering valuable insights for optimizing rescue efficiency and resource allocation.