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Gap Acceptance Model for Pedestrians at Traffic Signals

This functionality allows the user to model the behavior of pedestrians at traffic signals during four distinct parts to the signal cycle for pedestrians. It adds a new behavioral model during pedestrian red period and complements the behavior when the pedestrians have the right of way during the green and blackout period.

Schema of signal cycle for pedestrians

  • Before green: time from the departure of last vehicle to the start of the pedestrian green.
  • Green + blackout: the green-man period including blackout
  • After green: when the conflicting traffic is held by red signal and when the red figure is displayed to pedestrians because other vehicular traffic streams are at green.
  • Gap accepting: the period when the conflicting traffic is flowing and pedestrians are seeking gaps in traffic.

The gap acceptance model is based on a discrete choice model for determining if a pedestrian could cross during the red period. This model is represented by the probability of a pedestrian accepting a gap with a binary logit

where utility function

describes site characteristics and traffic state.

The traffic state is characterized by the following explanatory variables:

Variable Name Type Description --------------- ----- ------------------------------------ GAP_SIZE seconds Gap size AVE_WAIT seconds Pedestrian average waiting time in seconds X_WIDTH meters Studs area width AVE_LANE_WIDTH meters Average road lane width LA_CT_1 boolean 1-Lane crossing LA_CT_2 boolean 2-Lane crossing LA_CT_3 boolean 3-Lane crossing VEH_FLO vehicle/15 minutes Vehicle Flow VEH_DIR_1 boolean Traffic entering intersection VEH_DIR_2 boolean Traffic exiting intersection LOOK_RIGHT boolean Pedestrian is looking right LOOK_LEFT boolean Pedestrian is looking left LOOK2WAYS boolean Pedestrian is looking both ways P2P 1 boolean Pavement to pavement crossing P2R 2 boolean Pavement to refuge crossing R2P 3 boolean Refuge to pavement crossing AVE_GRN seconds Average green time PROP_IMPAIRED proportion Proportion of pedestrian being physical impaired PROP_ADULT proportion Proportion of pedestrian aged 18 to 60 PROP_OLD proportion Proportion of pedestrian aged over 60

Gap accepting

Here's the estimated model parameters for the full model for Gap accepting period.

Non-interaction term variable Coefficient Estimated value ------------------------------ ------------ ---------------- CONST a0 -4.366 X_WIDTH a1 -0.2278 AVE_WAIT a2 0.10283 LA_CT_2 a3 1.109 LA_CT_3 a4 0.885 VEH_FLO a5 -0.01056 VEH_DIR_2 a6 1.561 PROP_IMPAIRED a7 -31.6 AVE_GRN a8 -0.02964

Interaction term variable Coefficient Estimated value ------------------------------ ------------ ---------------- CONST b0 -0.179 AVE_WAIT b1 -0.01111 LA_CT_2 b2 0.023 LA_CT_3 b3 -0.0189 VEH_FLO b4 0.001534 VEH_DIR_2 b5 -0.1672 LOOK_RIGHT b6 -0.1063 LOOK2WAYS b7 -0.2868 P2R b8 0.0275 R2P b9 -0.1056 PROP_ADULT b10 0.651 PROP_OLD b11 0.422 PROP_IMPAIRED b12 0.41 AVE_GRN b13 0.00581 X_WIDTH b14 0.00633

After green

The estimated model parameters for the full model for After green period are.

Non-interaction term variable Coefficient Estimated value ------------------------------ ------------ ---------------- CONST a0 0.55 AVE_LANE_WIDTH a1 0.446 X_WIDTH a2 0.6423 AVE_WAIT a3 -0.1778 LA_CT_2 a4 -0.344 LA_CT_3 a5 3.235 VEH_FLO a6 -0.00997 VEH_DIR_2 a7 -0.955 PROP_IMPAIRED a8 -18.6 AVE_GRN a9 0.002

Interaction term variable Coefficient Estimated value ------------------------------ ------------ ---------------- CONST b0 0.68 AVE_WAIT b1 0.00854 LA_CT_2 b2 -0.2346 LA_CT_3 b3 -0.2346 VEH_FLO b4 0.000161 VEH_DIR_2 b5 0.1156 LOOK_RIGHT b6 -0.0077 LOOK2WAYS b7 -0.2277 P2R b8 -0.0308 R2P b9 0.0215 PROP_ADULT b10 0.0109 PROP_OLD b11 0.571 PROP_IMPAIRED b12 2.59 AVE_LANE_WIDTH b13 -0.0828 AVE_GRN b14 -0.00555 X_WIDTH b15 -0.05092