THE BINOMIAL MODEL OF PEDESTRIAN FLOWS - IMPLICATIONS AND EXPERIMENTS

AN APPROACH IS SUGGESTED TO PEDESTRIAN MOVEMENT THAT FOCUSES ON PATH SELECTION AND ON DISTRIBUTIONS OF PEDESTRIANS OVER STREET NETWORKS. THE CONCERN IS WITH AGGREGATES OF PEDESTRIANS, NOT WITH THE WAY IN WHICH AN INDIVIDUAL BEHAVES WHEN WALKING THROUGH A STREET GRID. ASSUMPTIONS MADE ABOUT THE STREET NETWORK ARE: (1) IT IS A RECTANGULAR, TWO-DIMENSIONAL GRID, AND (2) THERE IS ALWAYS AT LEAST ONE PATH WHICH MINIMIZES TIME-DISTANCE BETWEEN ORIGIN AND DESTINATION. FOUR ASSUMPTIONS ABOUT PEDESTRIANS ARE NECESSARY: (1) TRIPS ARE COMPLETELY PEDESTRIAN; NO TRANSPORTATION MEANS IS USED DURING THE TRIP, (2) TIME- DISTANCE IS MINIMIZED, (3) WHEN MORE THAN ONE PATH LEADS FROM AN INTERSECTION TO THE DESTINATION, A PROBABILITY EQUATION IS USED, AND (4) WHENEVER A PERSON HAS ARRIVED ON A GRID BOUNDARY GOING THROUGH THE DESTINATION, HE CONTINUES HIS PATH ALONG THIS BOUNDARY UNTIL HE REACHES THE DESTINATION EXPRESSED AS A BINOMIAL DISTRIBUTION. USING THESE ASSUMPTIONS AND THE BINOMIAL THEORY, THE FOLLOWING QUESTIONS WILL BE ANSWERED: (1) DOES EQUIPROBABLE CHOICE (RANDOM WALK) IMPLY A UNIFORM DISTRIBUTION OF PROBABILITIES AND PEDESTRIANS? (2) IF A FACILITY SERVES AS AN 0-D IN A MULTIPLE 0-D SITUATION, HOW DOES THE SHIFT OF THIS FACILITY AFFECT THE DISTRIBUTION OF PEDESTRIANS? (3) WHAT IS THE DIFFERENTIAL IMPACT OF THE CLOSURE OR OPENING OF TWO DIFFERENT STREET LINKS AND WHAT ARE THE IMPLICATIONS FOR THE DISTRIBUTION OF PEDESTRIANS IF IT IS HYPOTHESIZED THAT AGGREGATE PATH SELECTION IS INFLUENCED BY ENVIRONMENTAL QUALITY? THE IMPACT IS DISCUSSED OF LOCATION CHANGES ON PEDESTRIAN DISTRIBUTION. A MODEL WHICH PREDICTS PEDESTRIAN DISTRIBUTIONS IS SHOWN TO BE USEFUL IN SEVERAL SITUATIONS.