|Title||Nonlinear Instabilities in Internet Protocols|
In the era of heavy-duty transmission control protocols (TCP), adapted for extremely hi-bandwidth data-centers; the fundamental question of stable interaction with either proposed/customized active queue management(AQM) or popularly discussed Random Early Detection (RED) remains a hotly debated issue. While there are claims of “oscillation” only dynamical behavior, there are equally large number of claims which demonstrate the chaotic nature of different flavors of TCP and their AQM interaction. In this work, we provide a sound and analytical mathematical model of TCP/DTCP/D2TCP/Incast and study their interaction with threshold based packet marking policy. Similar processes are unfolded in Kelly's optimization based framework for understanding resource allocation for internet protocols once one allows the operation beyond stability regimes in the presence of arbitrarily large delays. What we show is that there is emergence of a special type of periodic orbit known as "Slowly oscillating periodic (SOP)" orbit and chaos can appear if saturation of capacity and buffers can be modeled. Our work shows that for a simple scenario this interaction is chaotic in nature and has large variability in dynamical behavior over orders of magnitude changes in parameter range as demonstrated by bifurcation diagrams and emergence of slowly oscillating periodic orbits. We conclude with numerical simulation evidence that chaotic behavior of protocols is inherent in their design which they inherit from their early vanilla TCP days, and it has serious implications for data-center throughput, load batching and collapse in Incast kind of scenario. Future directions will be outlined for rate control on dynamic networks and appearance and disappearance of ghost like temporal flows which is our current research direction. We shall also lead young researchers towards a spatio-temporal theory of communication processes on dynamic networks which is in development with current students, colleagues and lab-wizards. We believe that a sound theory of such processes will provide deeper insights and help us build truly scalable protocols on dynamic networks despite of their inherent disruptive nature.
Priya Ranjan (M’1997) graduated from IIT Kharagpur (EE, 1997), West Bengal, India and earned his advanced degrees of MS (EE) and Ph.D. (ECE) at the University of Maryland, College Park, USA in 1999 and 2003 respectively. He has contributed towards modern science and engineering at the Institute of Systems Research (ISR/UMD), the Intelligent Automation Inc., Rockville, Maryland, IIT Kanpur etc. His special fields of interest include hi-quality computer/telecom networking, capacity enhancement, stability in the presence of arbitrary delays, distributed robotics, sensor networks (INDRION, Raspberry-Pi), nonlinear dynamics of internet protocols, communication on dynamic networks, robotics in the presence of limited sensory immersion, sensors for mining and environment, bio inspired sensors and robotics, advanced power electronics etc. He has received many large project awards from some of the most reputed agencies like National Science Foundation (NSF), DARPA (Credited with development of the Internet), Delhi University etc. He has been currently thinking about processes on dynamic networks and sheaf theory to integrate local and global information in a consistent fashion. He has authored more than fifty research articles in different international conferences around the world, many heavily cited journal papers and many book chapters in heavily cited books published by IEEE and Springer Press. He believes that information, communication and visualization technology (ICVT) has a huge role to play in making traditional societies more and more transparent in their decision making and providing new capabilities hitherto denied to women and children. His collaboration with many NGOs working in India and abroad has brought deprived communities closer to ICVT and provided them rather affordable forum for airing their side of situation in complex decision making processes of global development.