arXiv:1212.6907v1 [cs.NI] 31 Dec 2012 Nonlinear Instabilities of D2TCP-II Abhisek Mukhopadhyay 1 Priya Ranjan 2 Abstract— 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 DTCP/D2TCP and study their interaction with threshold based packet marking policy. 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. 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. I. I NTRODUCTION In the era of record breaking memory to memory through- put, dynamical behavior of Internet protocols has become key to achieving predictability, optimal utilization of resources and dynamic stability in throughput allocation among partic- ipating agents/devices/entities. With the recent proposals of DCTCP, D2TCP, CTCP, D3 etc, a new research area of super- optimal and dynamically oscillating behavior of transport protocols has been forging itself. We based our analysis and discrete time models in contrast to the early claims of periodic only behavior in DCTCP and its different relatives and derivatives. We show again that discrete time models are the right framework to think about next generation successors of TCP and chaos remains a dominant phenomenon in the case of wildly fluctuating parameter ranges. In particular, we compare its dynamical behavior with switched power electronic circuits and impact oscillators. II. OBJECTIVE OF THE STUDY The objectives of our study are as follows: 1) Build a discrete time mathematical model of DCTCP- AQM interaction. 2) Use techniques from discrete time maps to analyze their behavior. 1 A.Mukhopadhyay is with the department of Electronics and Commu- nication Engineering, National Institute of Technology, Durgapur, West Bengal, India-71320.E-Mail- abhisekmukhopadhyay[at]gmail. com 2 P. Ranjan is with the department of Electronics and Communication Engineering, Templecity Institute of Technology and Engineering, Khurda, Orissa, India-752057. E-mail-pranjan[at]gmail. com 3) Simulate and demonstrate chaotic behavior. III. DCTCP CONGESTION CONTROL ALGORITHM:AN OVERVIEW In this section we describe qualitatively the DCTCP algorithm[1] with its major algorithmic details so as to lay a foundation for our discrete modeling. We also describe the fact that D2TCP [2] can be built upon DCTCP through certain specific changes and we also argue that D2TCP is more general and that DCTCP forms a special case of D2TCP. A. A simple active queue management scheme at the Switch: The marking scheme involves the use of only a single parameter K. An arriving packet is marked with its CE (Congestion Experienced) bit set to 1 iff upon its arrival the instantaneous queue size is greater than K. B. ECN Echo at receiver A difference between conventional TCP receivers and DCTCP receiver is in the way the status of the incoming CE bits are conveyed back to the sender. For the DCTCP receiver ACKs (ACK- Acknowledgment Packet) every single incom- ing packet and its ECN(External Congestion Notification)- Echo flag bit set to 1 when a marked packet (CE=1) is received. DCTCP tries to convey the exact sequence of the received code points. This is accomplished by sending a delayed ACK (1 cumulative ACK for a set of m received packets) which contains the sequence of ECN- Echo flag based on last m incoming packets. Thus the controller at the sender can make out the congestion status in the queue upon reception of the delayed ACK. C. Controller at the sender The sender maintains a running estimate of the fraction of packets that are marked. Called α , Which is updated in everyRTT (Round Trip Time) as follows: α ←- (1 - g) · α + g · F (1) g here is the weight associated to the marked fraction. F is the fraction of packets marked and is given by the drop probability in the current window. Given the fact that the sender receives Marks for every packet sent when the queue length is higher than the threshold and does not receive any marks when the queue length is below threshold K thus (9) implies that α estimates the probability that the queue size is greater than K. Essentially, α close to 0 implies low levels of congestion and when close to 1 implies high levels of congestion.