SOME MATHEMATICAL ASPECTS OF THE PARKING PROBLEM

ONE OF THE PROBLEMS IN QUEUING THEORY IS DETERMINING THE PROBABILITY AT A GIVEN MOMENT OF TOTAL OCCUPANCY OF A FINITE NUMBER OF POSITIONS IN A FIXED AREA GIVEN RANDOM ARRIVALS AND RANDOM DEPARTURES, THE SO-CALLED "SWITCHBOARD PROBLEM." CHARACTERISTICS OF PARKING IN DOWNTOWN SANTA MONICA WERE STUDIED AT A SINGLE LARGE LOT ON 15 JUNE 1960 TO DETERMINE THE NATURE OF ARRIVALS AND DEPARTURES. THIS INFORMATION IS FIRST USED TO ASSESS A HIGH-YIELD REVENUE STRATEGY FOR THE CITY, AFTER WHICH TWO MODELS---ONE FOR OFF-STREET PARKING AND THE OTHER FOR ON-STREET---ARE DERIVED FROM RELEVANT FEATURES OF QUEUING THEORY TO PREDICT SEARCH TIME AND OTHER PARKING CHARACTERISTICS. THE MODELS DEAL WITH DELAY AT A SINGLE DESIRABLE LOT OR SLOT, OR SERIES THEREOF AT INCREASING DISTANCES FROM THE OBJECTIVE, AND NO ATTEMPT IS MADE TO DEFINE THE BEHAVIOR OF OVERFLOWS.