 
Summary: Queueing Systems 28 (1998) 191214 191
On the departure process of a leaky bucket system with
longrange dependent input traffic
Socrates Vamvakos and Venkat Anantharam
EECS Department, University of California, Berkeley, CA 94720, USA
Email: sokratis@cory.eecs.berkeley.edu; ananth@vyasa.eecs.berkeley.edu
Due to the strong experimental evidence that the traffic to be offered to future broad
band networks will display longrange dependence, it is important to study the possible
implications that such traffic may have for the design and performance of these networks.
In particular, an important question is whether the offered traffic preserves its longrange
dependent nature after passing through a policing mechanism at the interface of the net
work. One of the proposed solutions for flow control in the context of the emerging ATM
standard is the socalled leaky bucket scheme. In this paper we consider a leaky bucket
system with longrange dependent input traffic. We adopt the following popular model for
longrange dependent traffic: Time is discrete. At each unit time a random number of ses
sions is initiated, having the distribution of a Poisson random variable with mean . Each
of these sessions has a random duration , where the integer random variable has finite
mean, infinite variance, and a regularly varying tail, i.e., P( > k) k
L(k), where
1 < < 2 and L(·) is a slowly varying function. Once a session is initiated, it generates
