4.7 Planning for a large parking garage A parking garage is planned for a large airport which is wholly owned by a city. This garage will serve the needs of "park-and-fly" passengers at one major section of the airport. it has been decided that the garage's capacity will be geared to the peak season of the airport, which consists of about five consecutive months. The planners believe that the demand (i.e., the number of cars seeking a parking spot at that section of the airport) can be reasonably modeled as a Poisson process with a mean, lambda.gif (179 bytes), of about 2,500 cars per day. The time during which any given parking spot is occupied by a car is assumed to be a random variable with some arbitrary pdf, a mean (1/mu.gif (189 bytes)) = 30 hours, and finite variance. It has been decided, after much debate, to provide sufficient capacity at the garage so that "a motorist will be able to find a free space there 98 percent of the time"-with a new system planned to direct motorists to areas with free parking spaces. Assuming that drivers who are informed, at the time when they seek entry, that the garage is full will become discouraged and go somewhere else:

a. Estimate approximately how many parking spaces should be provided at the garage. Justify your reasoning, possibly with reference to some queueing theory model.

b. Based on your analysis for part (a)-and provided that all other assumptions in the model are reasonable-discuss which is more important in planning for the size of the garage: the accuracy of the estimated values of lambda.gif (179 bytes) and 1/mu.gif (189 bytes), or the probability of parking availability sought (e.g., 98 percent)?