This paper develops an agent gap acceptance based algorithm for modelling opportunistic agent behaviour and safer crossing behaviour at crossings using the Urban Analytics Framework (UAF). The UAF software combines the Quadstone Paramics traffic micro-simulation model and crowd/pedestrian algorithms developed by Crowd Dynamics International Limited. Unique algorithms fuse these two parts, allowing the individual vehicles and agents to interact. This allows many different geometries and behaviours to be modelled, including pedestrian crossings, shared space, pedestrian presence at signalised junctions and pedestrians who do not comply with signals and cross against a red man or ‚Don‘t Walk‘ signal. However, there are also many unmanaged crossings in urban environments, where pedestrians must make a decision as to when a sufficient gap in traffic exists so that it is safe to cross. This paper will identify methods that allow this gap acceptance behaviour to be modelled in a flexible manner.
The methods developed to model pedestrian gap acceptance use the concept of scan areas. Each vehicle is assigned two polygonal shapes. The primary scan area will be the area where a vehicle will be able to see pedestrians and to slow down for them. The secondary scan area will be an area that will allow any agent inside it to consider whether to cross in front of the vehicle depending on combined gap acceptance criteria defined for the agent, vehicle and location . Both scan areas take into account individual vehicle kinematics and agent attributes. This would allow agent behaviour at unmanaged marked and refuge crossings and median strip environments to be modelled more realistically with more flexibility on defining the behaviours. The primary scan area instructs vehicles to slow down for an agent who is within a specified area. The primary scan area is an irregular hexagon that adjoins the front of the vehicle. It is defined using four measurements: End Width (EW), Start Width (SW), Start Length (SL) and End Length (EL). EW is based on the total number of lanes that the link on which the vehicle travelling has on both sides of the road. EW has an additional 1m width on either side of the road to ensure that agents approaching a crossing point will be seen. EL is based on the additional buffer time set in the location of the crossing. SW is based on the width of the vehicle, but can be extended up to the end width (EW) by a percentage. This allows behaviour to be altered by allowing the vehicle to wait for agents that are at a wide angle of view from the driver, as if the driver were looking left and right; or to allow the vehicle to continue moving in a more aggressive style of behaviour; or some arbitrary parameter between the two. SL is based on the vehicle‘s minimum desired stopping distance. This is taken from the secondary scan area determines whether an agent can safely enter the crossing by performing gap acceptance checks against conflicting vehicles. The shape is a trapezium that adjoins the front of the vehicle. The dimensions of this scan area are defined by four points using three measurements: Width (W), Near side Length (NSL) and Additional Length (AL). W is based on the EW of the Primary Scan Area, which covers the whole road width with a 1m buffer to ensure approaching agents are included in the calculations. NSL is the length of secondary scan area when the vehicle is in the lane next to the kerbline. This is the shortest length of the dimensions because it would take an agent less time to travel past the vehicle than it would if the vehicle was in any other lane. AL is added on for each lane the vehicle is away from the kerbline. This is controlled as a percentage of the NSL and is added on for each lane that the vehicle is away from the kerbline. The AL is added on to both the nearside of the vehicle and the far side depending on which lane the vehicle is in. Agents will wait whenever they are inside a secondary scan area and approaching gap finding space. This is extremely useful for defining behaviours in a specific area allowing all agents to take similar gaps. However, the above method does not allow for differing behaviours in agents. For example a faster moving agent may be more likely to take a smaller gap than a slower moving agent. Therefore, an additional algorithm can be used to allow the model to vary the gap choice for different agents. This is done by calculating the time taken by a vehicle to reach a theoretical collision point.
Each agent has a buffer zone which is based on the maximum walking speed of an agent. The buffer zone is the additional time which needs to be taken by an agent to cross before a vehicle arrives at the collision point. The collision point is calculated using the current line of sight of an agent. This allows any direction of movement to be taken into account. The agent will look along the line of direction the agent is facing until an available walking area is found. This distance is used to assess if an agent is able to cross the road before the vehicle passes the collision point. This variable approach allows different agent behaviours to be modelled in the same location.
In the paper, the above approaches are developed in detail. The limitations of the algorithms with regards to type and style of crossing behaviour are identified and where possible, these are overcome by allowing a dynamic alteration of the scan area shapes.