- #1
zzzzz
- 5
- 0
Homework Statement
[/B]Suppose your office telephone has two lines, allowing you to talk with someone and have at most one other person on hold. You receive 10 calls per hour and a conversation takes 2 minutes, on average. Use a Bernoulli single-server queuing process with limited capacity and 1-minute frames to compute the proportion of time you spend using the telephone.
Homework Equations
The Attempt at a Solution
[/B]
Found the transition probability matrix as:
5/6 1/6 0
5/12 1/2 1/12 = [x y z]
0 5/12 7/12
From this matrix, I found the following system of equations
5/6x + 5/12y = x
1/6x +1/2y + 5/12z = y
1/12y + 7/12z = z
Solving the system of equations from this matrix I got
x=25/81
y = 10/27
z = 26/81
I thought that the proportion of time you would spend on the telephone is 56/81, which would be the steady state probabilities of y ( One customer on the phone) and z (One customer on the phone and another one on hold), but that answer is wrong.
I also tried the steady state probability of y = 10/27, but that is also wrong.
Can you please explain what I am doing wrong?
Thank you so much.