PhD Thesis

  • Advisor: Dr. Gaurav Raina, Department of Electrical Engineering, IIT Madras
  • Title: Stability and Performance of Some Queue Management Policies with Transport Protocols in High-Speed Networks
  • Highlights:
    • Motivated by the problem of increasing queueing delays in the Internet, we studied the Random Early Detection (RED) and Proportional Integral (PI) policies for queue management at routers, in conjunction with Compound TCP (Windows OS).
    • Using control- and bifurcation-theoretic tools, we outlined some limitations of the two queue policies, and proposed a simple threshold-based queue policy that can mitigate queueing delays.
    • The threshold-based queue policy is shown to outperform both RED and PI using a simulation-based performance evaluation.
    • A detailed study of FAST TCP (a new proposal for delay-based TCP) suggests that, the threshold-based queue policy would yield stable performance with FAST TCP as well.
  • Abstract: Click here to read.

Other Work

  • Advisor: Dr. Gaurav Raina, Department of Electrical Engineering, IIT Madras
  • Highlights:
    • Population Dynamics: Analysis of first-order and second-order systems with single and multiple time delays, to exhibit the existence of interesting non-linear phenomenon such as bifurcation, limit cycles, chaos, stability switches, etc. We also developed an analog oscillator circuit inspired from a first-order time-delayed model proposed to capture the population of blow flies (known as the Perez Malta Coutinho equation). The voltage level was seen to exhibit chaotic phenomenon predicted by the numerical simulations performed on the mathematical model.
    • Human Physiology: We studied non-linear models proposed to capture haematopoietic and erythropoietic processes in humans; namely Mackey-Glass and Lasota equations. Control- and bifurcation-theoretic analyses of these models reveal the emergence of oscillations, thus predicting the onset of dynamical diseases. Stability conditions that yield design guidelines were derived.
    • Economics: Mathematical models that capture the change in Gross Domestic Product (GDP) and capital stock in an economy were studied to understand the impact of time delays. Our study reveals that the time taken to make the investment decisions impacts the GDP. Some design guidelines are provided to ensure convergence of the GDP to a stable equilibrium.