Question

F6: In a waiting line situation, arrivals occur around the clock at a rate of six per day, and the service occurs at one every three hours. Assume the Poisson and exponential distributions.

Please show your work

a.	What is λ?
b.	What is μ?
c.	Find probability of no units in the system.
d.	Find average number of units in the system.
e.	Find average time in the waiting line.
f.	Find average time in the system.
g.	Find probability that there is one person waiting.
h.	Find probability an arrival will have to wait.

Answer 1

Answer

Given that:

In a waiting line situation, arrivals occur around the clock at a rate of six per day, and the service occurs at one every three hours

Arrival occur at a rate of six per day

Y= service time exp(3) per hour

per hour

per day = per hour

a) What is λ?

per day per hour

b) What is μ?

per hour

c) Find probability of no units in the system.

No unit in the system

d) Find average number of units in the system.

e) Find average time in the waiting line.

time exp() with mean is average time in the waiting line is 1/3

f) Find average time in the system.

The average time in the system =

g) Find probability that there is one person waiting

h)  Find probability that there is one person waiting

Probability that system will busy