Infinite Waiting Space Queue
We note that if a < b then p < q. We have
lim
N®¥ |
r0-1 = 1 + |
a
¾¾
q-p |
= 1 + |
a
¾¾
b-a |
= |
b
¾¾
b-a |
When we let N goes to infinite, it means that there is no rejection of customer as the
number of waiting space is infinite.
The condition a < b means that the probability of having a departure of customer is
greater than the probability of having an arrival of customer in every time interval (i, i+1].
In this case, the long-run probability that the server is idle is given by
| 
