Question

The reference desk of a university library receives requests for assistance. Assume that a Poisson probability distribution with an arrival rate of 9 requests per hour can be used to describe the arrival pattern and that service times follow an exponential probability distribution with a service rate of 11 requests per hour.

1. What is the probability that no requests for assistance are in the system? If required, round your answer to four decimal places.
   
   P₀ =
   
2. What is the average number of requests that will be waiting for service? If required, round your answer to four decimal places.
   
   L_q =
   
3. What is the average waiting time in minutes before service begins? If required, round your answer to nearest whole number.
   
   W_q = _______min
   
4. What is the average time at the reference desk in minutes (waiting time plus service time)? If required, round your answer to nearest whole number.
   
   W = __________ min
   
5. What is the probability that a new arrival has to wait for service? If required, round your answer to four decimal places.
   
   P_w =

Answer 1

= 9 requests per hour

= 11 requests per hour

Utilization rate = / = 9/11 = 0.82

a.

Probability of no requests in the system = 1 - = 1 - 0.82 = 0.18

b.

Lq = / (- ) = 0.82 * 9 / (11 - 9) = 3.69

c.

Wq = / (- ) = 0.82 / (11 - 9) = 0.41 hr = 0.41 * 60 min = 24.6 min

d.

W = 1 / (- ) = 1 / (11 - 9) = 1/2 hr = (1/2) * 60 min = 30 min

e.

Pw = Probability that new arrival has to wait for service = Probability that there is atleast one requests in the system = = 0.82