In: Statistics and Probability
An office employs several clerks who create documents, and one
operator who enters the document information in a computer system.
The group creates documents at a rate of 14 per hour. The operator
can enter the information with an average exponentially distributed
time of 3 minutes. Assume the population is infinite, arrivals are
Poisson, and queue length is infinite with the FCFS
discipline.
a. Calculate the percentage utilization of the
operator. (Round your answer to 2 decimal
places.)
b. Calculate the average number of documents in the system. (Round your answer to 1 decimal place.)
c. Calculate the average time in the system. (Round your answer to 1 decimal place.)
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.
Answer :
Given that :
No.of documents per hour = = 14
Let us take
Time t = 3
a)The percentage utilization of the operator is = P
= 14 / 21
= 0.6667
= 66.67%
b)The average number of documents in the system is =
= 14 / (21 - 14)
= 2
So,the documents in system = 2
c)The avg time in system =
= 2 / 21
= 0.0952 hrs
= 5.714 minutes
= 6 minutes
d)Probability of 4 or more documents = 0,1,2,3
0 = 66.67
1 = 66.67 * 66.67% = 44.45
2 = 44.45 * 66.67 % = 29.63
3 = 29.63 * 66.67 % = 19.75
Finally the probability of 4 or more documents = 19.75