Students arrive at the Administrative Services Office at an average of one every 20 minutes, and their requests take on average 15 minutes to be processed. The service counter is staffed by only one clerk, Judy gumshoes, who works eight hours per day. Assume Poisson arrivals and exponential service times. A. What percentage of time is Judy idle?

B. How much time, on average, does a student spend waiting in line?

C. How long is the waiting line on average? D. What is the probability that an arriving student will find at least one other student waiting in line?

Question

Mathematics

Tanner

17 May, 17:06

Students arrive at the Administrative Services Office at an average of one every 20 minutes, and their requests take on average 15 minutes to be processed. The service counter is staffed by only one clerk, Judy gumshoes, who works eight hours per day. Assume Poisson arrivals and exponential service times. A. What percentage of time is Judy idle?

B. How much time, on average, does a student spend waiting in line?

C. How long is the waiting line on average? D. What is the probability that an arriving student will find at least one other student waiting in line?

+5

Answers (1)

Know the Answer?

Melody Holt · Answer 1

A. 33.33%

B. 1/3 hours or 20 min.

c. 4/3 customers

d. 4/9, or 0.44

Step-by-step explanation:

a. m/m/1 system

=4 customers/hour

=6 customers/hour

1 - / = 33.33%

b. Wq = / (-)

=1/3 hours or 20 min

C. Lq = Wq

= 4/3 customers

D.

=1-p0-p1

=1 - (1 - / ) - / (1 - / )

=4/9, or 0.44