Sufficient Conditions for Functional Limit Theorem Versions of L = λW
P. W. Glynn and W. Whitt
Queueing Systems, Vol. 1, 279-287 (1986)
The familiar queueing principle expressed by the formula L = λW can be interpreted as a relation among strong laws of large numbers. In a previous paper, we showed that this principle can be extended to include relations among other classical limit theorems such as central limit theorems and laws of the iterated logarithm. Here we provide sufficient conditions for these limit theorems using regenerative structure.