Blue Sky Airlines 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 5.123 customers per minute (believed to follow a Poisson process). Moreover, Caitlin has determined that on average, it takes 0.1815 minutes to serve a customer, service times follow a continuous uniform distribution with minimum possible service time 0.09. The COO has asked Caitlin to estimate the average number of customers waiting and the average customer waiting time.
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!
Blue Sky Airlines 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 5.123 customers per minute (believed to follow a Poisson process). Moreover, Caitlin has determined that on average, it takes 0.1815 minutes to serve a customer, service times follow a continuous uniform distribution with minimum possible service time 0.09.
The COO has asked Caitlin to estimate the average number of customers waiting and the average customer waiting time.
Given:
Arrival rate = 5.123 Customers per minute
Service time = 0.1815 minute
Service rate = customer per minute
= 5.5096 customer per minute
Formula Used:
The average number of customers waiting =
Average waiting time =
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