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Numerical comparisons of several expressions for the average delay to traffic passing a fixed time traffic signal have been made for a wide range of values of the arrival rate, saturation flow, cycle time, proportion of the cycle effectively green, and variance-to-mean ratio of the number of arrivals per cycle (I-ratio). The values of average delay given by Miller's, Newell's, and Webster's simplified expressions, and by a new modification of the last incorporating the I-ratio are compared with the value given by Webster's full expression. The differences are not usually more than 10 per cent when I = 1, but the importance of the I-ratio is shown by the differences reaching about 50 percent at high degrees of saturation when I = 1.5. The differences between the values of the various expressions are also compared with the effects on the value of Webster's full expression of given errors in the parameters. These effects are found to be large enough to make it difficult to distinguish experimentally between the various expressions when the I -ratio is near to 1 except by extensive measurements. Because of this the choice between expressions is often a matter of convenience of computation, and this choice is briefly discussed. [ABSTRACT FROM AUTHOR]

The various theoretical analyses that have been made of delay to traffic at a fixed time traffic signal are critically reviewed. The more practicably applicable expressions for the average delay per vehicle, especially those derived by Webster, Miller, and Newell, are examined in some detail, and this paper provides an introduction to numerical comparisons to be reported by Hutchinson in the sequel. [ABSTRACT FROM AUTHOR]

Circuit constraints on the phasing of fixed-time synchronized signal networks are defined. A method, based on a graph-theoretic approach, for deriving a fundamental set of equations characterizing these constraints is presented. [ABSTRACT FROM AUTHOR]

This paper concerns itself with the kinematic analysis of traffic flow on a signalized one-way artery. Using as mathematical model the continuum flow theory of LIGHTHILL -WHITHAM-RICHAJWS, the flow pattern is carefully investigated under the assumptions of parabolic volume-density diagram and constant flow on the artery. The interesting symmetry existing between fluid and congested regimes is noted and used in proving various results. The delay caused by an interruption of arbitrary regimes is analyzed as a function of space and time. It is shown that an interruption of an arbitrary regime is equivalent to a particular interruption of a corresponding uniform regime: this provides a very simple and general method for delay computation. The delay caused by a periodic interruption (traffic signal) is bounded by and is asymptotically equal to the duration of the red signal; more- over, both the maximum and the average delay at fixed distance from the signalized intersection are increasing functions of the cycle time. It is further shown that the results concerning the delay function apply to all convex volume-density diagrams. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Delay formulas are derived for vehicles at an isolated intersection at which the vehicle arrivals are supposed generated by a binomial process, the departure rates are assumed constant, and the control strategy is to switch the lights when the favored queue empties. The mean delay is calculated using a discrete analog of the method used by Darroch, Morris, and Newell for the case of random arrivals. Later a probability generating function for delay is developed yielding, in particular, the variance of the delay. [ABSTRACT FROM AUTHOR]