1 results
Conditioned Limit Theorems for the Difference of Waiting Time and Queue Length
- Part of
-
- Journal:
- Advances in Applied Probability / Volume 26 / Issue 1 / March 1994
- Published online by Cambridge University Press:
- 01 July 2016, pp. 242-257
- Print publication:
- March 1994
-
- Article
- Export citation
-
Consider the GI/G/1 queueing system with traffic intensity 1 and let wk and lk denote the actual waiting time of the kth unit and the number of units present in the system at the kth arrival including the kth unit, respectively. Furthermore let τ denote the number of units served during the first busy period and μ the intensity of the service. It is shown that
as k →∞, where a is some known constant, 
, 
, 
and 
are independent, 
is a Brownian meander and 
is a Wiener process. A similar result is also given for the difference of virtual waiting time and queue length processes. These results are also extended to a wider class of queueing systems than GI/G/1 queues and a scheme of series of queues.
as 
, 
, 
and 
are independent, 
is a Brownian meander and 
is a Wiener process. A similar result is also given for the difference of virtual waiting time and queue length processes. These results are also extended to a wider class of queueing systems than 