Customers arrive at random at an average rate of 3 per hour at a health and wellbeing shop. The manager serves all the customers herself; she does not have any assistants. Individual service times are exponentially distributed with mean 12 minutes. (a) Write down the specification of the queue, and calculate the traffic intensity for this queue. (Assume that the patterns of arrivals and departures at the shop attain equilibrium shortly after the shop opens each day.)

A First Course in Probability (10th Edition)
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ISBN:9780134753119
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Chapter1: Combinatorial Analysis
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Customers arrive at random at an average rate of 3 per hour at a
health and wellbeing shop. The manager serves all the customers
herself; she does not have any assistants. Individual service times are
exponentially distributed with mean 12 minutes.
(a) Write down the specification of the queue, and calculate the traffic
intensity for this queue. (Assume that the patterns of arrivals and
departures at the shop attain equilibrium shortly after the shop
opens each day.)
(b)
Calculate the mean equilibrium queue size.
(c) For how long should a customer expect to have to queue
(including the time spent receiving assistance)?
(d) Find the probability that a customer will be in the shop for more
than 30 minutes.
Transcribed Image Text:Customers arrive at random at an average rate of 3 per hour at a health and wellbeing shop. The manager serves all the customers herself; she does not have any assistants. Individual service times are exponentially distributed with mean 12 minutes. (a) Write down the specification of the queue, and calculate the traffic intensity for this queue. (Assume that the patterns of arrivals and departures at the shop attain equilibrium shortly after the shop opens each day.) (b) Calculate the mean equilibrium queue size. (c) For how long should a customer expect to have to queue (including the time spent receiving assistance)? (d) Find the probability that a customer will be in the shop for more than 30 minutes.
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