Question 3 [15]

3.1 What are the three main components of any queuing system? (3)

3.2 Why is it important to consider arrival characteristics in a queuing system? (1)

3.3 What is the difference between single-phase and multi-phase in the service facilities phase? (2)

3.4 Suppose that the owner of a car wash estimates that dirty cars arrive at the rate of 10 per hour all day Saturday. With a crew working the wash line, the owner figures that car can be cleaned at the rate of one every 5 minutes. One car at the time is cleaned (i.e. singlechannel waiting line). Assuming Poisson arrivals and exponential service time, find the following:

a) Average number of cars in line. (2)

b) Average time a car waits before it is washed. (2)

c) Average time a car spends in the service system. (2)

d) Utilization rate of the car wash. (2)

e) Probability that no cars are in the system. (1)