Question

The reference desk of a university library receives requests for assistance. Assume that a Poisson probability distribution with an arrival rate of 8 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

Given data:

Arrival rate λ = 8 requests per hour

Service rate µ = 11 requests per hour

This is a single server model. Technical notation for this model is M/M/1

(a) Probability of no request

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(b) Average number of requests waiting for the service

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(c) Average waiting time in minutes

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(d) Average waiting time in system

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(e) Probability that new arrival has to wait for the service

Pw = 1 – P0 = 1 – 0.2727 = 0.72727273 = 0.7273

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