The Cove at UP wants to be sure that its customers enjoy a quality service experience. Caitlin Elizabeth is studying a single server queue and has determined that customers arrive at a rate of 5.7013 customers per minute (believed to follow a Poisson process). Moreover, Caitlin has determined that on average, it takes 0.0824 minutes to serve a customer, service times follow a normal distribution, and service time standard deviation is 0.0165 minutes. The COO has asked Caitlin to estimate the average number of customers waiting and the average number of customers in the system. Lq= L=
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The Cove at UP wants to be sure that its customers enjoy a quality service experience. Caitlin Elizabeth is studying a single server queue and has determined that customers arrive at a rate of 5.7013 customers per minute (believed to follow a Poisson process). Moreover, Caitlin has determined that on average, it takes 0.0824 minutes to serve a customer, service times follow a
The COO has asked Caitlin to estimate the average number of customers waiting and the average number of customers in the system.
Lq=
L=
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