Delay processes at unsignalised junctions: The interrelation between geometric and queueing delay

The interrelation between geometric delay--the delay caused by the need for isolated vehicles to slow down to negotiate a junction--and the queueing delay due to vehicle-vehicle interactions is considered. The delay elements present in measurements of geometric delay are identified, and some overlap is seen with those normally included in the service mechanisms in queueing models. The total delay per vehicle is not, therefore, the sum of the measured geometric delay and the queueing delay. Although the geometric delay can be redefined so as to eliminate the overlap, it is not then measurable. A framework is developed in which the relationships between the "pure" and measured geometric delay and the queueing delay are expressed for the population mean values. Approximate expressions are developed for the elements of delay. The framework is extended to allow queueing delays to be represented by time-dependent functions allowing approximately for non-randomness in arrival and departure patterns and service time differences between queueing and non-queueing vehicles. Numerically, geometric delay elements constitute a significant proportion of total delay except at traffic intensities approaching unity. In this region time-dependent effects dominate the queueing process.