On the self-similar nature of Ethernet traffic
ACM SIGCOMM Computer Communication Review - Special twenty-fifth anniversary issue. Highlights from 25 years of the Computer Communication Review
Self-similarity in World Wide Web traffic: evidence and possible causes
IEEE/ACM Transactions on Networking (TON)
On power-law relationships of the Internet topology
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
The structural cause of file size distributions
Proceedings of the 2001 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
On the origin of power laws in Internet topologies
ACM SIGCOMM Computer Communication Review
Stochastic models for the Web graph
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
On unreliable computing systems when heavy-tails appear as a result of the recovery procedure
ACM SIGMETRICS Performance Evaluation Review - Special issue on the workshop on MAthematical performance Modeling And Analysis (MAMA 2005)
Computer Networks: The International Journal of Computer and Telecommunications Networking - Special issue: Long range dependent trafic
Is ALOHA causing power law delays?
ITC20'07 Proceedings of the 20th international teletraffic conference on Managing traffic performance in converged networks
The effect of multiple time scales and subexponentiality in MPEG video streams on queueing behavior
IEEE Journal on Selected Areas in Communications
Retransmissions over correlated channels
ACM SIGMETRICS Performance Evaluation Review - Special issue on the 31st international symposium on computer performance, modeling, measurements and evaluation (IFIPWG 7.3 Performance 2013)
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Power law distributions have been repeatedly observed in a wide variety of socioeconomic, biological, and technological areas. In many of the observations, e.g., city populations and sizes of living organisms, the objects of interest evolve because of the replication of their many independent components, e.g., births and deaths of individuals and replications of cells. Furthermore, the rates of replications are often controlled by exogenous parameters causing periods of expansion and contraction, e.g., baby booms and busts, economic booms and recessions, etc. In addition, the sizes of these objects often have reflective lower boundaries, e.g., cities do not fall below a certain size, low-income individuals are subsidized by the government, companies are protected by bankruptcy laws, etc. Hence, it is natural to propose reflected modulated branching processes as generic models for many of the preceding observations. Indeed, our main results show that the proposed mathematical models result in power law distributions under quite general polynomial Gärtner-Ellis conditions, the generality of which could explain the ubiquitous nature of power law distributions. In addition, on a logarithmic scale, we establish an asymptotic equivalence between the reflected branching processes and the corresponding multiplicative ones. The latter, as recognized by Goldie [Goldie, C. M. 1991. Implicit renewal theory and tails of solutions of random equations. Ann. Appl. Probab.1(1) 126--166], is known to be dual to queueing/additive processes. We emphasize this duality further in the generality of stationary and ergodic processes.