Question

A new shopping mall is considering setting up an information desk manned by one employee. Based upon data obtained from similar information desks, it is believed that people will arrive at the desk at a rate of 15 per hour. It takes an average of 1.5 minutes to answer a question. It is assumed that the arrivals are Poisson and answer times are exponentially distributed.

What is the probability that the service facility will be idle?

What is the average time (hours) a customer spends getting information?

What is the average number of customers in the system?

What is the probability an arriving customer has to wait?

Answer 1

This is M/M/1 queue system with following parameters

Arrival rate, = 15 per hour

Service rate, = 60/1.5 = 40 per hour

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1. What is the probability that the service facility will be idle?

= 1-/

= 1-15/40

= 0.625

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2. What is the average time (hours) a customer spends getting information?

W = 1/(​-)

= 1/(40-15)

= 0.04 hour

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3. What is the average number of customers in the system?

L = W

= 0.04*15

= 0.6

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4. What is the probability an arriving customer has to wait?

= /

= 15/40

= 0.375

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