# A Traffic Breakdown Model Based on Queueing Theory

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## Abstract

In this paper, we propose a queueing model to describe traffic breakdown phenomena caused by perturbations of on-ramp merging vehicles. In congested mainline traffic flow, we assume that a merging vehicle will trigger a jam queue formulation. If this jam queue cannot dissipate before the next vehicle merges into the main road, it could grow into a wide jam and eventually result in traffic breakdown. Different from many existing models that focused on the propagation of jam waves, the proposed model emphasizes the size evolution of a jam queue (local congested vehicle cluster) instead of its spatial evolutions. This new approach reduces analysis difficulties and allows us to directly link microscopic driving behaviors with macroscopic breakdown phenomena. Test results show that the simulated breakdown probability curve (parameter tuning using Next Generation Simulation vehicular trajectories) fits with the empirical breakdown probability curve that is estimated by Performance Measurement System (PeMS) data. This indicates that this new model can account for the probability of breakdown phenomena and help us set an appropriate inflow rate so as to void breakdown and meanwhile maintain a high road capacity.

## Keywords

Traffic breakdown Queueing theory Newell’s simplified model Headway## Notes

### Acknowledgments

This work was supported in part by National Basic Research Program of China (973 Project) 2012CB725405, The National Science and Technology Support Program 2013BAG18B00, National Natural Science Foundation of China 51278280, 51138003.

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