Activity Rates with Very Heavy Tails
نویسندگان
چکیده
Consider a data network model in which sources begin to transmit at renewal time points {Sn}. Transmissions proceed for random durations of time {Tn} and transmissions are assumed to proceed at fixed rate unity. We study M(t), the number of active sources at time t, a process we term the activity rate process, since M(t) gives the overall input rate into the network at time t. Under a variety of heavy-tailed assumptions on the inter-renewal times and the duration times, we can give results on asymptotic behavior of M(t) and the cumulative input process A(t) = R t 0 M(s) ds. 1. The model, notation, preliminary results. Consider an ordinary renewal process {Sn, n ≥ 0} such that S0 = 0, Sn = n ∑
منابع مشابه
Self-similar Communication Models and Very Heavy Tails
Several studies of le sizes either being downloaded or stored in the world wide web have commented that tails can be so heavy that not only are variances innnite, but so are means. Motivated by this fact, we study the innnite node Poisson model under the assumption that transmission times are heavy tailed with innnite mean. The model is unstable but we are able to provide growth rates. Self-sim...
متن کاملRunaway Events Dominate the Heavy Tail of Citation Distributions
Statistical distributions with heavy tails are ubiquitous in natural and social phenomena. Since the entries in heavy tail have unproportional significance, the knowledge of its exact shape is very important. Citations of scientific papers form one of the best-known heavy tail distributions. Even in this case there is a considerable debate whether citation distribution follows the log-normal or...
متن کاملVolatility and Asymmetry of Small Firm Growth Rates Over Increasing Time Frames
This report was developed under a contract with the U.S. Small Business Administration, Office of Advocacy, and contains information and analysis that was reviewed and edited by officials of the Office of Advocacy. However, the final conclusions of the report do not necessarily reflect the views of the Office of Advocacy. Arlington, VA. Under contract no. SBAHQ-05-Q-0018 [21] pages. With the em...
متن کاملStatistical Inference in the Presence of Heavy Tails
Income distributions are usually characterised by a heavy right-hand tail. Apart from any ethical considerations raised by the presence among us of the very rich, statistical inference is complicated by the need to consider distributions of which the moments may not exist. In extreme cases, no valid inference about expectations is possible until restrictions are imposed on the class of distribu...
متن کاملPerformance Evaluation with Heavy Tailed Distributions
Over the last decade an important new direction has developed in the performance evaluation of computer systems: the study of heavy-tailed distributions. Loosely speaking, these are distributions whose tails follow a power-law with low exponent, in contrast to traditional distributions (e.g., Gaussian, Exponential, Poisson) whose tails decline exponentially (or faster). In the late '80s and ear...
متن کامل