On the self-similar nature of Ethernet traffic (extended version)
IEEE/ACM Transactions on Networking (TON)
Wide area traffic: the failure of Poisson modeling
IEEE/ACM Transactions on Networking (TON)
Activity periods of an infinite server queue and performance of certain heavy tailed fluid queues
Queueing Systems: Theory and Applications
Scheduling strategies and long-range dependence
Queueing Systems: Theory and Applications
The departure process of discrete-time queueing systems with Markovian type inputs
Queueing Systems: Theory and Applications
Performance of a Leaky Bucket System with Long-Range Dependent Input Traffic
Queueing Systems: Theory and Applications
Characterization of long-range dependent traffic regulated by leaky-bucket policers and shapers
Computer Communications
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Due to the strong experimental evidence that the traffic to be offered to future broadband networks will display long-range 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 long-range dependent nature after passing through a policing mechanism at the interface of the network. One of the proposed solutions for flow control in the context of the emerging ATM standard is the so-called leaky bucket scheme. In this paper we consider a leaky bucket system with long-range dependent input traffic. We adopt the following popular model for long-range dependent traffic: Time is discrete. At each unit time a random number of sessions is initiated, having the distribution of a Poisson random variable with mean \lambda. Each of these sessions has a random duration \tau, where the integer random variable \tau has finite mean, infinite variance, and a regularly varying tail, i.e., P(\tau k) \sim k^{-\alpha}L(k), where 1 and L(\cdot) is a slowly varying function. Once a session is initiated, it generates one cell at each unit of time until its termination. We examine the departure process of the leaky bucket policing mechanism driven by such an arrival process, and show that it too is long-range dependent for any token buffer size and any – finite or infinite – cell buffer size. Moreover, upper and lower bounds for the covariance sequence of the output process are established. The above results demonstrate that long-range dependence cannot be removed by the kinds of flow control schemes that are currently being envisioned for broadband networks.