A multi-state merging based analytical model for an operation design domain of autonomous vehicles in work zones on two-lane highways

As a special application of connected and automated vehicles (CAVs), the Autonomous Truck Mounted Attenuator (ATMA) vehicle system is promoted to reduce fatalities in work zone locations. In this manuscript, we focus on the Operational Design Domain (ODD) problem of two-lane highways, i.e., under what traffic conditions should an ATMA be deployed. Due to the dramatic speed difference between ATMA vehicles and general vehicles, a queue will be formed, leading to a percent-time-spent-following (PTSF) increase during maintenance. General vehicles in the queue will assess a gap on the opposite lane to perform a passing maneuver, which is broken down into multi-stage merging behavior. As such, an analytical model is first made, based on queuing theory in which the arrival rate and service rate are analyzed to estimate the PTSF. In this way, the linkage between annual average daily traffic (AADT) and level of service (LOS) is analytically established. Then, the proposed model is validated by comparing the estimated PTSF with that of the Highway Capacity Manual (HCM) values. The comparison results show that the mean error is 9.58%, and the mean absolute error is 12.36%, which demonstrate that the developed model is able to generate satisfactory results when compared with the HCM model. Numeric analysis also shows that roadway performance is sensitive to the K factor and D factor, as well as the operating speed of an ATMA. If LOS = C is a desirable design objective, a good AADT threshold to use would be around 11,000 vehicles per day.