On the impact of obstructions on the capacity of nearby signalised intersections

Abstract

Various obstructions exist that can impede maximum vehicle flow through signalised intersections. Examples include buses or freight vehicles dwelling at loading areas near the intersection, stalled vehicles, pre-signals that temporarily block car traffic to provide bus priority, on-street parking manoeuvres and permanent road fixtures. If the effects of these obstructions are not recognised or accounted for, vehicle discharge capacities at these critical locations can be overestimated, leading to ineffective traffic management strategies. This paper examines the capacity of an isolated signalised intersection when a nearby roadway obstruction is present in either the upstream or downstream direction. To quantify the loss of capacity caused by an obstruction, the paper applies the variational theory of kinematic waves in a moving-time coordinate system, which simplifies the traditional variational theory by reducing the number of local path costs that must be considered. The result is a simple recipe that requires few calculations and can be used to gain insights into signal operations when obstructions are present. Capacity formulae for general cases are also developed from the recipe. The results, recipe and formulae can be used to guide policies on the location of obstructions that can be controlled, like bus stops, pre-signals or permanent road fixtures and to develop strategies to mitigate the effects of obstructions that can be identified in real time. As an example, a simple adaptive signal control scheme is created using this methodology to more efficiently allocate green time between competing directions when an obstruction is present.

Keywords:

• signalised intersection capacity
• obstructions
• variational theory
• moving-time coordinate system

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Weihua Gu http://orcid.org/0000-0003-3848-4840

Notes

1. By isolated, we mean that signals upstream and downstream are sufficiently far away as to not interact with the intersection of interest. Although simple, this scenario can serve as a building block for more complicated situations in the future. Furthermore, recent studies have focused on a similar scenario to quantify queue lengths and delays due to obstructions (Gu et al. 2013, 2014).

2. Note that this cost function actually provides a cost rate. However, we use the term cost function to be consistent with the literature.

3. Note that we will drop the use of to denote parameters measured in the moving-time coordinate system for notational simplicity, since the remainder of the paper uses a moving-time coordinate system.

4. We assume here that this reduced capacity incorporates any capacity lost due to vehicles merging at the location of the obstruction.

5. The reader can confirm that the obstruction cannot be used to create any shorter paths than these two.

6. Here, we consider cases in which one lane of a multi-lane intersection approach is blocked by the obstruction (i.e. ) and .

7. A similar equation can be developed for a downstream obstruction, but this is omitted for brevity.

8. Additional signal timing strategies could be developed using flexible cycle lengths. However, for simplicity, we maintain this assumption here.

Additional information

Funding

The research was partially supported by a start-up fund provided by the Hong Kong Polytechnic University.