Abstract
The paper presents a new mathematical model of TCP (Transmission Control Protocol) link functioning in a heterogeneous (wired/wireless) channel. It represents a controllable, partially observable stochastic dynamic system. The system state describes the status of the modeled TCP link and expresses it via an unobservable controllable MJP (Markov jump process) with finite-state space. Observations are formed by low-frequency counting processes of packet losses and timeouts and a high-frequency compound Poisson process of packet acknowledgments. The information transmission through the TCP-equipped channel is considered a stochastic control problem with incomplete information. The main idea to solve it is to impose the separation principle on the problem. The paper proposes a mathematical framework and algorithmic support to implement the solution. It includes a solution to the stochastic control problem with complete information, a diffusion approximation of the high-frequency observations, a solution to the MJP state filtering problem given the observations with multiplicative noises, and a numerical scheme of the filtering algorithm. The paper also contains the results of a comparative study of the proposed state-based congestion control algorithm with the contemporary TCP versions: Illinois, CUBIC, Compound, and BBR (Bottleneck Bandwidth and RTT).
Highlights
Despite its age of almost 50 years, the Transmission Control Protocol (TCP) [1] is still an object of permanent modernization and improvement, and this evolution represents a natural perpetual process
We demonstrate how the proposed mathematical model can describe various contemporary versions of the TCP: Illinois, CUBIC, BBR, and Compound
The probing phase, which is symmetrical to the recovery phase, is too aggressive, and the average throughput would benefit from longer “plateau” periods. Another advantage, which must be mentioned, is the ability to adjust to dramatic changes in the media: in contrast with TCP Illinois, the CUBIC protocol keeps the control at low values throughout the whole period of wireless signal degradation, which results in fewer losses
Summary
Despite its age of almost 50 years, the Transmission Control Protocol (TCP) [1] is still an object of permanent modernization and improvement, and this evolution represents a natural perpetual process. To develop the TCP prototype, we need a substantial mathematical framework, which is introduced in Section 3: Section 3.1 contains the solution to the optimal MJP control problem with instant geometric control constraints and complete information [26], Section 3.2 introduces a diffusion approximation for the high-frequency CPP describing the packet acknowledgment flow [27], Section 3.3 presents a solution to the optimal MJP state filtering problem given both counting and diffusion observations with state-dependent noise [28], Section 3.4 contains a numerical algorithm for the optimal filtering realization [28]. The articles [26,27,28] represent a formal, detailed mathematical background of all applied inferences presented in this paper
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
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 call
