Question

1. A new shopping mall is considering setting up a car wash manned by six employees. From past data, Regal Car Wash estimates that dirty cars arrive at the rate of 10 per hour all day Saturday. With a crew working the wash line, Regal figures that cars can be cleaned at the rate of one every 5 minutes. One car at a time is cleaned in this example of a single-channel waiting line. It is assumed that arrivals are Poisson and service times are exponentially distributed. (a) Find the average number of cars in line. (b) Find the average time a car waits before it is washed. o find the average time a car spends in the service system. (d) Find the utilization rate of the car wash. (e) Find the probability that no cars are in the system. (f) What approaches do supermarkets use to offset variation customer wait in a single in line, as is now being done in banks, and post offices, rather than multiple lines. (g) Why do waiting lines form even though a service system is underloaded?

Answer 1

lambda= 10/hour

mu = 60/5 = 12 /hour

a)

Lq = 4.1667

b)

Wq = 0.4167

c)

Ws = 0.50

d)

utilization = lambda/mu = 10/12 = 5/6 = 0.8333

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