Properties of Vehicle-Actuated Signals: I. One-Way Streets

Fluid and diffusion queuing approximations are used to analyze the behavior of vehicle-actuated signals at the intersection of two one-way streets at which there is no turning traffic. The arriving traffic is assumed to be a stationary stochastic process with a flow rate just slightly below that which saturates the intersection. Certain qualitative properties of the queues suggests that to minimize delay the signal should (in most cases) switch as soon as the queue vanishes, defined roughly as the time when the expected flow rate across the intersection drops below the discharge rate of a queue. The mean and variance of the cycle time and the mean delay are evaluated for this strategy. The average delay per car is shown to be less than for a fixed-cycle signal by about a factor of 3. The distribution of cycle time is shown to have approximately a Γ distribution.