The reference desk of a university library receives requests for assistance. Ass
ID: 449779 • Letter: T
Question
The reference desk of a university library receives requests for assistance. Assume that a Poisson probability distribution with an arrival rate of 10 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.
What is the probability that no requests for assistance are in the system? If required, round your answer to four decimal places.
P0 =
What is the average number of requests that will be waiting for service? If required, round your answer to four decimal places.
Lq =
What is the average waiting time in minutes before service begins? If required, round your answer to four decimal places.
Wq = hours
What is the average time at the reference desk in minutes (waiting time plus service time)? If required, round your answer to one decimal place.
W = hours
What is the probability that a new arrival has to wait for service? If required, round your answer to four decimal places.
Pw =
Explanation / Answer
What is the probability that no requests for assistance are in the system? If required, round your answer to four decimal places.
P0 = 9.0909%
What is the average number of requests that will be waiting for service? If required, round your answer to four decimal places.
Lq = 9.0909
What is the average waiting time in minutes before service begins? If required, round your answer to four decimal places.
Wq = 0.9091 hours
What is the average time at the reference desk in minutes (waiting time plus service time)? If required, round your answer to one decimal place.
W = 1 hours
What is the probability that a new arrival has to wait for service? If required, round your answer to four decimal places.
Pw = 90.9091 %
Calculations for all questions given below
Arrival rate
=
10
Service rate
=
11
Mean time between arrivals
= 1/
0.100
Mean time per service
= 1/
0.0909
Utilization rate of server
= /
90.9%
Probability of NO customers in system
P0
= 1-
9.1%
Average number of customers in system
L
=/(1-)
10
Average time in system
W
= L/
1.00000
Average time waiting in line
Wq
= W-1/
0.909090909
Average number of customers waiting in line
Lq
= *Wq
9.0909
Probability of waiting time > t
P(t)
=*e(-µ*(1-)*t)
90.9%
Distribution of time in queue
t =
0
Arrival rate
=
10
Service rate
=
11
Mean time between arrivals
= 1/
0.100
Mean time per service
= 1/
0.0909
Utilization rate of server
= /
90.9%
Probability of NO customers in system
P0
= 1-
9.1%
Average number of customers in system
L
=/(1-)
10
Average time in system
W
= L/
1.00000
Average time waiting in line
Wq
= W-1/
0.909090909
Average number of customers waiting in line
Lq
= *Wq
9.0909
Probability of waiting time > t
P(t)
=*e(-µ*(1-)*t)
90.9%
Distribution of time in queue
t =
0
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