ISSN:
1572-9443
Keywords:
finite capacity network
;
blocking probabilities
;
loss network
;
semimartingale reflecting Brownian motion
;
RBM
;
heavy traffic
;
limit theorems
;
oscillation estimates
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
Notes:
Abstract We consider a queueing network of d single server stations. Each station has a finite capacity waiting buffer, and all customers served at a station are homogeneous in terms of service requirements and routing. The routing is assumed to be deterministic and hence feedforward. A server stops working when the downstream buffer is full. We show that a properly normalized d-dimensional queue length process converges in distribution to a fd-dimensional semimartingale reflecting Brownian motion (RBM) in a d-dimensional box under a heavy traffic condition. The conventional continuous mapping approach does not apply here because the solution to our Skorohod problem may not be unique. Our proof relies heavily on a uniform oscillation result for solutions to a family of Skorohod problems. The oscillation result is proved in a general form that may be of independent interest. It has the potential to be used as an important ingredient in establishing heavy traffic limit theorems for general finite buffer networks.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1019178802391
