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In: Statistics and Probability

Customers arrive at a two pump system at Poisson rate two per hour. An arrival finding...

Customers arrive at a two pump system at Poisson rate two per hour. An arrival finding the system empty is equally likely to enter service with either pump. An arrival finding one customer in the system will enter service with the idle pump. An arrival finding two others in the system will wait in line for the first free pump. An arrival finding three in the system will not enter. Two service times are exponential with rates one per hour and two per hour, respectively. Once a customer is served by either pump, he will depart the system.
(a) What is the average number of customers in the system?
(b) What is the average time an entering customer spends in the system.

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Solution:-

Given that

Customers arrive at a two pump system at Poisson rate two per hour. An arrival finding the system empty is equally likely to enter service with either pump. An arrival finding one customer in the system will enter service with the idle pump. An arrival finding two others in the system will wait in line for the first free pump. An arrival finding three in the system will not enter. Two service times are exponential with rates one per hour and two per hour, respectively. Once a customer is served by either pump, he will depart the system.

Take

a) What is the average number of customers in the system?

Average number of customers in the system (L) = 1.33

b) What is the average time an entering customer spends in the system?

Average time spent by a customer from arrival until fully served (W) = 0.66 hr

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orchestra answered 2 years ago
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