Four-Regime Speed–Flow Relationships for Work Zones with Police Patrol and Automated Speed Enforcement

This paper presents the development of a four-regime speed–flow relationship for highway work zones and the effects of police presence (police) and speed photo enforcement (SPE) on the speed–flow relationship and capacity. The base data were collected when signage typical of that shown in the Manual on Uniform Traffic Control Devices for an Interstate highway work zone with no lane reduction was present. Police and SPE data were collected, respectively, when a police patrol car and an SPE van were added to the typical work zone. From each data set, the step-by-step progression from a three-regime model based on least-squares regression to a four-regime speed–flow curve is presented. The four-regime model comprises four equations: (a) horizontal line for free-flow regime that covered the volume levels up to 900 passenger cars per hour per lane, (b) fourth-degree spline for the upper transition part of the speed–flow curve, (c) another fourth-degree spline for the lower transitions part, and (d) equation in the form of power function for the highly congested part of the speed–flow relationship. The speed–flow curve for the base case had a free-flow speed (FFS) of 61.3 mph and a capacity of 1,850 per car per hour per lane (pcphpl). In the police case, however, the FFS and capacity were reduced by 6.3 mph and 50 pcphpl, respectively. For the SPE case, the FFS and capacity were also reduced by 6.8 mph and 100 pcphpl, respectively. The new curves provided the more accurate speed and work zone capacity estimations required for efficient operation.