How incidents impact congestion on roadways: A queuing network approach

Motivated by the need for transportation infrastructure and incident management planning, we study traffic density under non-recurrent congestion. This paper provides an analytical solution approximating the stationary distribution of traffic density in roadways where deterioration of service occurs unpredictably. The proposed solution generalizes a queuing model discussed in the literature to long segments that are not space-homogeneous. We compare single and tandem queuing approaches to segments of different lengths and verify whether each model is appropriate. A single-queue approach works sufficiently well in segments with similar traffic behavior across space. In contrast, a tandem-queue approach more appropriately describes the density behavior for long segments with sections having distinct traffic characteristics. These models have a comparable fit to the ones generated using a lognormal distribution. However, they also have interpretable parameters, directly connecting the distribution of congestion to the dynamics of roadway behavior. The proposed models are general, adaptable, and tractable, thus being instrumental in infrastructure and incident management.