Abstract
This paper contributes to the modeling and analysis of unsignalized intersections. In classical gap acceptance models vehicles on the minor road accept any gap greater than the critical gap, and reject gaps below this threshold, where the gap is the time between two subsequent vehicles on the major road. The main contribution of this paper is to develop a series of generalizations of existing models, thus increasing the model’s practical applicability significantly. First, we incorporate driver impatience behavior while allowing for a realistic merging behavior; we do so by distinguishing between the critical gap and the merging time, thus allowing multiple vehicles to use a sufficiently large gap. Incorporating this feature is particularly challenging in models with driver impatience. Secondly, we allow for multiple classes of gap acceptance behavior, enabling us to distinguish between different driver types and/or different vehicle types. Thirdly, we use the novel M^X/SM2/1 queueing model, which has batch arrivals, dependent service times, and a different service-time distribution for vehicles arriving in an empty queue on the minor road (where ‘service time’ refers to the time required to find a sufficiently large gap). This setup facilitates the analysis of the service-time distribution of an arbitrary vehicle on the minor road and of the queue length on the minor road. In particular, we can compute the mean service time, thus enabling the evaluation of the capacity for the minor road vehicles.
Highlights
In this era of rapidly emerging new technologies for urban traffic control, the vast majority of urban traffic intersections are still priority-based unsignalized intersections, in which the major roads have priority over the minor roads
In classical gap acceptance models vehicles on the minor road accept any gap greater than the critical gap, and reject gaps below this threshold, where the gap is defined as the time between two subsequent vehicles on the major road
We have presented a gap acceptance model for unsignalized intersections that considerably generalizes the existing models
Summary
In this era of rapidly emerging new technologies for urban traffic control, the vast majority of urban traffic intersections are still priority-based unsignalized intersections, in which the major roads have priority over the minor roads. Heidemann and Wegmann (1997) give an excellent overview of the earlier existing literature They add a stochastic dependence between the critical gap and the merging (move-up) time, and study the minor road as an M/G2/1 queue, to determine the queue length, the delay and the capacity on the minor road. They distinguish between three types of driver behavior. We distinguish between the critical gap and the merging time, allowing multiple vehicles to use a sufficiently large gap Incorporating this feature is challenging in models with driver impatience.
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