Design Considerations Based on Stability for a Class of TCP Algorithms

TL;DR

The paper addresses ensuring local stability for a broad class of TCP congestion-control algorithms in networks with heterogeneous delays and multiple bottlenecks. It develops a generalized fluid-dynamics framework and derives sufficient stability conditions for single, tandem, edge-core, and arbitrary-bottleneck topologies under intermediate and small drop-tail buffers. It analyzes the impact of multiple TCP variants (Reno, Compound, Scalable) and delays on stability, and provides design guidelines based on a positive $a_j$ condition. The findings support decentralized, stable operation of TCP in diverse network topologies, with practical implications for buffer sizing and protocol design.

Abstract

Transmission Control Protocol (TCP) continues to be the dominant transport protocol on the Internet. The stability of fluid models has been a key consideration in the design of TCP and the performance evaluation of TCP algorithms. Based on local stability analysis, we formulate some design considerations for a class of TCP algorithms. We begin with deriving sufficient conditions for the local stability of a generalized TCP algorithm in the presence of heterogeneous round-trip delays. Within this generalized model, we consider three specific variants of TCP: TCP Reno, Compound TCP, and Scalable TCP. The sufficient conditions we derive are scalable across network topologies with one, two, and many bottleneck links. We are interested in networks with intermediate and small drop-tail buffers as they offer smaller queuing delays. The small buffer regime is more attractive as the conditions for stability are decentralized. TCP algorithms that follow our design considerations can provide stable operation on any network topology, irrespective of the number of bottleneck links or delays in the network.

Figures (4)

• Figure 1: $n$ sets of flows sharing a single bottleneck link with capacity $C$ and buffer size $B$. Each set is characterized by its window adjustment functions ($i_j(w(t)), d_j(w(t))$), average sending rate ($x_j(t)$) and RTT ($T_j$).
• Figure 2: Nyquist plot of $\frac{e^{-sT}}{sT}$. The Nyquist plot cuts the real axis at $\frac{-2}{\pi}$. An additional gain of $\frac{\pi}{2}$ can be permitted for the system without compromising stability.
• Figure 3: Two bottleneck links in tandem shared by $n$ flows. The links have capacities $C_1$, $C_2$ and associated buffer sizes $B_1$, $B_2$ respectively. Each set of flows is characterized by its average sending rate ($x_j(t)$), window adjustment functions ($i_j(x_j(t)), d_j(x_j(t))$), and RTT ($T_j$).
• Figure 4: Two edge routers feeding into a core router: TCP flows with heterogeneous round-trip delays entering two edge routers with capacities $C_1$ and $C_2$, respectively. Each set is characterized by its window adjustment functions (i.e., $i_j(x_j(t))$ and $d_j(x_j(t))$), RTT ($T_j$) and average sending rate ($x_j(t)$). $B_1$ and $B_2$ are the buffer sizes associated with the edge routers. $C_3$ and $B_3$ respectively denote the link capacity and buffer size associated with the core router.