Elsevier

Computer Communications

Volume 31, Issue 14, 5 September 2008, Pages 3242-3249
Computer Communications

A Generalized FAST TCP scheme

https://doi.org/10.1016/j.comcom.2008.05.028Get rights and content

Abstract

FAST TCP has been shown to be promising in terms of system stability, throughput and fairness. However, it requires buffering which increases linearly with the number of flows bottlenecked at a link. This paper proposes a new TCP algorithm that extends FAST TCP to achieve (α,n)-proportional fairness in steady state, yielding buffer requirements which grow only as the nth power of the number of flows. We call the new algorithm Generalized FAST TCP. We prove stability for the case of a single bottleneck link with homogeneous sources in the absence of feedback delay. Simulation results verify that the new scheme is stable in the presence of feedback delay, and that its buffering requirements can be made to scale significantly better than standard FAST TCP.

Introduction

There is much evidence [3] that the loss-based additive increase/multiplicative decrease (AIMD) algorithm used in TCP [5] does not scale well to high capacity networks. Many new improved versions of TCP have been proposed to solve this problem. These include CUBIC [13], H-TCP [14] and FAST TCP [19]. Recent simulation [19] and experimental [8] studies indicate that FAST TCP is a viable alternative to the currently used loss-based TCP versions.

Many modern congestion control algorithms can be understood as algorithms to solve an optimization problem, in which the network seeks to maximize the sum of the users’ “utilities” subject to link capacity constraints. A user’s utility is the benefit it derives from transmitting at a given rate. The equilibrium rates are determined by the objective of the optimization, while the dynamics are determined by the optimization procedure. In this framework, users pay a “price” for transmitting data on a congested link; typically either in terms of loss or queueing delay, and the equilibrium value of this price depends on the users’ utility functions. As these two price mechanisms have adverse effects on users, it is desirable to use a utility function which achieves a fair rate allocation and imposes low (and fair) prices on users. This paper adapts the dynamics of FAST [19] to allow it to optimize a more general form of utility function. This allows a tradeoff to be made between fairness and low queueing delay.

Unlike AIMD-based TCP schemes, FAST TCP uses queueing delay as the congestion indication, or price. Users’ utilities are logarithmic, making the solution to the optimization problem satisfy the proportional fairness criterion [9]. If all users use FAST, the unique equilibrium rate vector is the unique solution of the utility maximization problem. One drawback of this approach is that the queueing delay (and hence buffer requirements) at a node increase in proportion to the number of flows bottlenecked there.

To allow a tradeoff between fairness and network utilization, Mo and Walrand [12] popularized the concept of (α,n)-proportional fairness, which generalizes max-min fairness [1], proportional fairness [9] and minimum potential delay [11]. This corresponds to a simple family of power-law utility functions. We propose an extended version of FAST TCP, termed Generalized FAST TCP, whose equilibrium rates are (α,n)-proportional fair. This is achieved by making a slight change to the window update equation, which implicitly optimizes a suitable utility function. As well as allowing increased fairness, corresponding to n>1, Generalized FAST TCP allows the queueing delay to be reduced at nodes carrying many flows by setting n<1.

Our proposed scheme is a generalization of the existing FAST TCP [19]. Specifically, the behavior of FAST TCP is reproduced by the special case of Generalized FAST with n=1, while other modes of Generalized FAST cannot be achieved simply by tuning FAST TCP parameters. We will show that the new scheme inherits the merits of the current FAST TCP regarding stability and throughput for any value of n and not just for n=1. We also provide stability analysis and prove that Generalized FAST TCP achieves (α,n)-proportional fairness.

The remainder of this paper is organized as follows. In Section 2, we clarify the relationship between the mechanism of FAST TCP and the proportional fairness notion. In Section 3, we describe the new Generalized FAST TCP scheme and discuss the effect of the parameters α1/n and n on buffer occupancy and fairness. In Section 4, we analyze and prove the stability of the new scheme. Section 5 investigates the tradeoff between fairness and the queueing delay experienced by users. In Section 6, we verify by simulations that the new scheme is stable and (α,n)-proportionally fair. Finally, conclusions are drawn in Section 7.

Section snippets

Proportional fairness and FAST TCP

A general network can be described as a set L={1,,M} of links, shared by a set I={1,,N} of flows. Each link lL has capacity cl. Flow iI follows a route Li consisting of a subset of links, i.e., Li={lL|itraversesl}. A link l is shared by a subset Il of flows where Il={iI|itraversesl}. Let xi be the rate of flow i and let x=(xi,iI) be the rate vector. Let A=(Ali,iI,lL) be the routing matrix, where Ali=1 if flow i traverses link l, and 0 otherwise. Throughout this paper, the terms “flow”,

The Generalized FAST TCP

As a generalization of proportional fairness and max–min fairness, the definition of (α,n)-proportional fairness is given by Mo and Walrand in [12], which is described as follows. Note that our notation differs slightly from that of [12], so that it corresponds to its usual meaning in the FAST algorithm. A rate vector x is (α,n)-proportionally fair, if it is feasible, and if for any other feasible vector x,iIαixi-xi(xi)n0,where αi are positive numbers, for iI. Note that (12) reduces to

Stability analyses

We now analyze the stability of Generalized FAST TCP under the dumbbell (single bottleneck) topology with N greedy sources, and with equal propagation delays, d, ignoring feedback delay. Consider the continuous form of the Eq. (14),w˙i(t)=γαi1/n-xi(t)(q(t))1/n,i=1,,N.From wi(t)=xi(t)(d+q(t)), we havew˙i(t)=dx˙i(t)+xi(t)q˙(t)+x˙i(t)q(t).

Substituting (19a) into (19b) gives the implicit equationx˙i(t)=fxi(t),x˙i(t),q(t),q˙(t)=1d-xi(t)q˙(t)-x˙i(t)q(t)+γαi1/n-γxi(t)(q(t))1/n.

We now linearize the

Fairness-scalability tradeoff

The concept of (α,n)-proportional fairness has often been used to investigate the tradeoff between fairness and total throughput (see for example [16]). In the context of Generalized FAST it also provides a tradeoff between fairness and scalability.

In a network with N flows and a single bottleneck running standard FAST, the mean queue size scales linearly with N. Under Generalized FAST, if all flows have the same α, the mean queue size scales as Nn. Specifically, (18) shows that the mean queue

Simulation results

We perform three sets of ns2 [2], [17] simulations. The main objective of the first set of simulations is to verify that the buffer occupancy increases more slowly as the number of flows increases for smaller values of n. It also demonstrates that feedback delay does not effect bandwidth allocation. The second set of simulations quantify the reduction in fairness between flows with different numbers of bottleneck links as n decreases. The third set demonstrate that feedback delay does not

Conclusion

This paper generalizes the current FAST TCP scheme in such a way that the parameter n and α1/n in the new window update equation can be set to achieve (α,n)-proportional fairness and control the rate of buffer increase. We derived a stability condition for a single bottleneck link in the absence of feedback delay, and we have discussed the tradeoff between fairness and buffer increment.

Future research will investigate the performance of networks with general topology and a variety of traffic

Acknowledgements

This research is partially supported by the Program NCET-05-0673, the key Project (No. 108166) from Chinese Ministry of Education and partially by the Australian Research Council (ARC).

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