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 19 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 in %:

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 in 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 in %:

Solution and Explanation:

In this system, population is infinite, arrivals are poisson distributed, service time is exponentially distributed, queue length is infinite with FCFS discipline. Therefore M/M/1 model fits.

Arrival rate, λ = 19 customers per hour

Service rate, μ = 1 / service time =20 customers per hour

a). Percentage utilization of the operator, = 95.00%

b). Average number of documents in the system, = 19.00

c). Average time in system in minutes,  = 1 hour = 60 minutes

d). Probability of four or more documents being in the system = 1 - (probability of 0 document in the system + probability of 1 document in the system + probability of 2 documents in the system + probability of 3 documents in the system)

= .8145 or 81.5%

answer; /// the above statement is (true);

a recipe serves 8 people, and calls for 5 lbs of apples and 2 cups of flour. you want to prepare it for 24 people. divide 24 by 8 to get 3, and then multiply your ingredients by 3.

so for 24 people, you'll need 15 lbs of apples, and 6 cups of flour.