Queueing Theory

3. (25 points) Janet is planning to open a small car-wash operation. She must decide how much space to provide for waiting cars. Janet estimates that customer arrivals follow a Poisson process at a rate of 1 every 4 minutes, unless the waiting area is full, in which case the arriving customers would take their cars elsewhere. The time that can be attributed to washing one car has an exponential distribution with a mean of 3 minutes. Compare the expected fraction of potential customers that will be lost because of inadequate waiting space if (a) (8 points) 0 space (not including the car being washed) or (b) (8 points) 2 spaces (not including the car being washed) or (c) (9 points) 4 (not including the car being washed) or were provided