|
|
|
|
|
|
|
The equation E.3 is valid for an arbitrary arrival time distribution (i.e., G/G/1). |
|
|
|
|
|
|
|
|
Suppose we now assume a Poisson type arrival distribution; then from chapter 6, section 6.4.1: |
|
|
|
|
|
|
|
|
where ri is the number of arrivals during Ti. The mean of this distribution is E(ri) = lTi and the variance ( ) is also lTi. From probability theory, |
|
|
|
|
|
|
|
|
Taking the expectation over all i, |
|
|
|
|
|
|
|
|
But, from probability theory ( is the variance of Ti): |
|
|
|
|
|
|
|
|
and substituting into equation E.3: |
|
|
|
|
|
|
|
|
Since the coeficient of service variance  |
|
|
|
|
|
|
|
|
Little's result applied to equation E.5 gives the M/G/1 form for Tw as used in chapter 6. |
|
|
|
|
|
