Page 536. Problem 5 with different numbers. The reference desk arrival rate of 2
ID: 366388 • Letter: P
Question
Page 536. Problem 5 with different numbers. The reference desk arrival rate of 20 requests per hour can be used to describe the arrival pattern and that service times follow an exponential probability of a university library receives requests for assistance. Assume that a Poisson probability distribution with an distribution with a service rate of 30 requests per hour. a. What is the probability that no requests for assistance are 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?Explanation / Answer
We have,
Arrival rate = 20 requests per hour
Service rate µ = 30 requests per hour
And waiting line has a single server
A. The probability that no requests for assistance are in the system
P0 = 1- ( /µ) = 1-(20/30) = 0.33
B. The average number of requests that will be waiting for service
Lq = ^2 / [µ (µ-)]
Lq = 20^2 / [30 *(30-20)]
Lq = 400 / (30 *10)
= 1.33 requests
C. The average time in minutes before service begins
Wq= /µ * (µ - ) = 20 / 30 * (30 -20) =20/30*10 =20/300 =0.0667 hours or 4 minutes
D. The average time at the reference desk in minutes (waiting time plus service time)
W = Wq + 1/µ
= 0.0667 +1/30
= 0.1 hours or 6 minutes
E. The probability that a new arrival has to wait for service
Pw = /µ = 20/30 = 0.6667
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