This exam covers customer queuing systems including arrival rates, Poisson processes, probability density functions, steady states, operator utilisation, machine efficiency, and exponentially distributed service times.

a) This question can be solved using Bayes' Theorem. The theorem states that, given f(x|y) (the conditional density function of x given y) and the density function f(y),

inf.
f(x) = integral f(x|y)f(y)dy
y=0

Let's see how to use this theorem to solve this problem. We are asked to find the probability function of the number of customers that arrive during an interval t of time, where t is a random variable with density function f(t). Since customers arrive according to a Poisson process, we have that, given t,

(that's the Poisson probability function) This would be the f(x|y) in Bayes' Theorem. Since we know that t follows the distribution f(t) then, using the theorem, we arrive at:

Service station cars arive randomly at a rate of 1 car every 30 min. the average time to change oil on a car is 20 min. both the time between arrivals and service time can be modeled using the negative exponential Poisson distribution. This shop only has one garage and one oil change person on duty at any given time.
a) On

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Queueing Theory Question 1
An average of 10 people per hour arrive (inter-arrival times are exponential) intending to swim laps at the local YMCA. Each intends to swim an average of 30 minutes. The YMCA has 3 lanes open for lap swimming. If one swimmer is in a lane, he or she swims up and down the right side of the lane.

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1) WAITING LINE MODELS -AMC Movie Theatre has only one box office clerk. For the movie theatre's normal offerings, customers arrive at the average rate of 3 per minute. On the average, each customer who comes to see a movie can be sold a ticket at the rate of 6 per minute. Assume arrivals follow the Poisson distribution and ser

A) What are 2 possible ways to improve the service rate of a waiting line operation?
B) Briefly describe how simulation could be used to assist decision makers in regards to new product development?
C) Give an example of how Decision analysis could be used to determine an optimal strategy? Briefly describe several decisio