Abstract
In this paper, the nonsmooth compound transmission control protocol (TCP) with the gentle random early detection (GRED) system with the state-dependent round-trip delay is investigated in detail. Uniqueness of the positive equilibrium is proved firstly. Then, the closed approximate periodic solutions in this state-dependent delayed nonsmooth compound TCP with the GRED model are obtained by employing the harmonic balance and alternating frequency/time domain (HB-AFT) method. Then, we compare the results generated by numerical simulations with those of the closed approximate expressions obtained by HB-AFT. It indicates that HB-AFT is simple, correct, and powerful for state-dependent delayed nonsmooth dynamical systems. Finally, we find the complicated dynamic: chaos. It is a grazing chaos with a hybrid property, i.e., where usually w oscillates at a very low frequency and q oscillates at a very high frequency. And, the route to chaos is a very rare route, i.e., the instantaneous and local transition of stable equilibrium to chaos. So, to the end of stability and good performance, we should adjust the parameters carefully to avoid the periodic and chaotic oscillations.
Highlights
With the rapid growth of applications, network congestion is becoming more and more serious
The whole congestion control system is a combination of the end-toend transmission control protocol (TCP) congestion control mechanism at the source and the active queue management (AQM) mechanism at routers
We will present the compound TCP-gentle RED (GRED) model. e standard TCP adjusts the data flow in the way of additive increase and multiplicative decrease, that is, the sending window size increases by one packet per round-trip time (RTT) and reduces to half of the current window size every time packet loss is detected
Summary
With the rapid growth of applications, network congestion is becoming more and more serious. Us, it is important to consider the periodic solutions and complicated dynamics of the compound TCP with GRED congestion control systems in detail. It is our motivation to research the rich dynamics and the closed approximate periodic solutions of the compound TCP with the GRED system. In the process of solving the periodic solution, the HB-AFT method sets both the state variable and the nonlinear function as harmonic solution and establishes the relationship between harmonic coefficients according to the discrete time-frequency characteristics of the system It does not need integration and series expansion for complex nonlinear terms. We derive the closed approximate periodic solutions for the state-dependent delayed nonsmooth compound TCP with GRED system by HB-AFT successfully.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
