The reference desk of a university library receives requests for assistance. Assume that a Poisson probability distribution with a mean rate of 10 requests per hour can be used to describe the arrival pattern and that service times follow the exponential probability distribution, with a mean service rate of 12 requests per hour.
a)What is the probability that there are no requests for assistance in the system?
b)What is the average number of requests that will be waiting for service?
c)What is the average waiting time in minutes before service begins?
d)What is the average time at the reference desk in minutes (waiting time plus service time)?
e)What is the probability that a new arrival has to wait for service?
f)Suppose that another helper could be hired to join the desk, and she would have the same service rate. Assuming that all patrons wait in a single line, what is the new average waiting time in minutes before service begins?
g)Instead of the change in question f, suppose that a "super" librarian can be hired who can handle 16 requests per hour. Now what is the average waiting time in minutes before service begins?

Question

Quizplus · Accepted Answer

The Answer of The reference desk of a university library receives requests for assistance. Assume that a Poisson probability distribution with a mean rate of 10 requests per hour can be used to describe the arrival pattern and that service times follow the exponential probability distribution, with a mean service rate of 12 requests per hour.
a)What is the probability that there are no requests for assistance in the system?
b)What is the average number of requests that will be waiting for service?
c)What is the average waiting time in minutes before service begins?
d)What is the average time at the reference desk in minutes (waiting time plus service time)?
e)What is the probability that a new arrival has to wait for service?
f)Suppose that another helper could be hired to join the desk, and she would have the same service rate. Assuming that all patrons wait in a single line, what is the new average waiting time in minutes before service begins?
g)Instead of the change in question f, suppose that a "super" librarian can be hired who can handle 16 requests per hour. Now what is the average waiting time in minutes before service begins?

The Reference Desk of a University Library Receives Requests for Assistance