In patrol surveys, patrolling observers check the parking area every δ minutes (i.e., at fixed time intervals) and record the plate number of the car occupying each stall. To find the average parking duration, an estimated value is obtained by averaging the parking duration of each car observed. Although the results are biased because of known reasons (i.e., short duration parkers are under sampled; and the parking duration of the observed vehicles are only approximations), the survey accuracy remains unknown even after the survey. Very often, a trade-off between survey accuracy and survey cost must be made. By analyzing the relation between the error and relative labor cost, we provide several suggestions to practitioners to help them obtain high quality results from the patrol survey while keeping costs to a minimum.
By defining three dimensionless variables: survey intensity X , survey error Y, and relative cost Z, the relation between those three key elements can be further analyzed. Evidently, the more intensive the survey is, the more it costs, but the lower error it has. Data from two parking areas (Max-Bill-Platz in Zurich, Switzerland, 60 stalls; and Ballston Garage in U.S.A., 2800 stalls) were used to validate the model. Given that the parking duration follow a gamma distribution, the real data matched the theoretical curves quite well.
Below is a brief summary of the findings and how they could be useful in real surveys:
- The distribution of arrival times is not highly relevant to the relation between X, Y and Z when the quantity of parked vehicles is reasonable (i.e., enough to be representative of the distribution).
- The survey intensity X and relative cost Z can be chosen as the quality criteria of any patrol survey; the survey error Y directly depends on them.
- The survey result is typically an overestimate for average parking durations obeying uniform, gamma or hyper-exponential distributions (the most common types of distributions observed).
- A higher value of X may be required to guarantee the accuracy when the parking area includes parkers with different parking purposes (especially if the sizes of the different sub-populations of parkers are very different).
Based on the findings, knowing the general shape of the duration distribution and some basic assumptions, we are now able to recommend the minimum budget to guarantee results with predictable accuracy. Furthermore, we developed a method to reduce the survey error Y without the need for additional labor. After obtaining the range of possible errors for a given X (the value of X can be found based on the survey), we can now correct the results to achieve higher accuracy. In the case of Max-bill-platz, it is possible to keep the survey error at 6% with a budget of only 109 using our method (only need to assume a lower bound of ), while a budget of 150 would generate an error of 18% when using the traditional method.