An office employs several clerks who originate documents and one operator who en
ID: 3264958 • Letter: A
Question
An office employs several clerks who originate documents and one operator who enters the document information in a computer system. The group originates documents at a rate of 15 per hour. The operator can enter the information with average exponentially distributed time of 3 minutes. Assume the population is infinite, arrivals are Poisson, and queue length is infinite with FCFS discipline.
a. Calculate the percentage utilization of the operator. (Round your answer to 2 decimal places.)
Utilization of the operator %
b. Calculate the average number of documents in the system. (Round your answer to 1 decimal place.)
Average number of documents
c. Calculate the average time in the system. (Round your answer to 1 decimal place.)
Average time in system minutes
d. Calculate the probability of four or more documents being in the system. (Round your intermediate calculations to 3 decimal places and final answer to 1 decimal place.
Probability %
Explanation / Answer
: mean rate of arrival = 15 documents per hour
µ: mean service rate = 20 documents per hour
(A)
= /µ for single server queues: utilization of the server; also the probability that the
server is busy or the probability that someone is being served.
= /µ = 15/20 = 0.75
(B)
Number of documents in the queue, Lq = ^2/(1-) = 2.25
Wait in the Queue, Wq = Lq/ = 0.15
Wait in the system, W = Wq + 1/µ = 0.2 hours
Number of documents in the system, L = W = 3
(C)
Average time in the system, W = 0.2 hours
(D)
the probability of four or more documents being in the system = P(X>3) = 0.1055