Definition and Validity of the FS Paradigm

A paradigm for congestion control is a model used to devise new congestion control proto-cols. A paradigm makes assumptions and under these assumptions we can devise compatible congestion control protocols; compatible means that the protocols have a same set of proper-ties. Therefore, to define a new paradigm, we must clearly express the assumptions made and the properties guaranteed by the paradigm. To be viable in the Internet, the paradigm must be compliant with the end-to-end argument [78]. Mainly, the congestion control protocols de-vised with the paradigm have to be end-to-end and should not have to rely on specific network support. These issues are addressed in this section.

We first define the notion of Fair Scheduler policy.

Definition 2 (Fair Scheduler policy) A Fair Scheduler policy is a per-packet approximation of a fluid GPS scheduling policy [65] with longest queue drop buffer management.

We note that there are many approximations of the GPS scheduling policy (see [65], [20], and [4] for some examples). The better the approximation, the better the properties guaranteed by the FS paradigm. The WF²Q scheduling policy [3] is a good approximation of the GPS fluid model that perfectly suits our paradigm.

For sake of simplicity, we make a distinction between the assumption that involves the network support, which we call that the Network Part of the paradigm (NP), and the assumptions that involve the end systems, which we call that the End System Part of the paradigm (ESP).

The assumptions required for our new paradigm are:

For the NP of the paradigm we assume a Fair Scheduler network, i.e. a network where every router implements a Fair Scheduler policy;

For the ESP, the end users are assumed to be selfish and non-collaborative. This is a sufficient but not a necessary condition. In particular, collaboration among the users is possible if that increases their satisfaction.

B.2. THE FS PARADIGM 93 We call this paradigm the Fair Scheduler (FS) paradigm¹. With the TCP-friendly paradigm, the equation B.1 guarantees efficiency, stability, and fairness, however not in the sense as these three properties were defined for an ideal congestion control protocol in section B.2.2. Since TCP guarantees efficiency, stability, and fairness by only one mechanism at the end system, compromises between the three properties are unavoidable. The idea of the FS paradigm is to rely on the support of the network to guarantee the properties required for an ideal congestion control protocol, and to let the protocol at the end system only address the application needs.

We note that the FS paradigm, unlike the TCP-friendly paradigm, does not make any assump-tions on the mechanism used at the end systems. The FS paradigm assumes full freedom when devising a congestion control protocol. This characteristic of the paradigm is very appealing but may lead to a high diversity of the congestion control mechanisms used. Therefore, one may ask the question about the set of properties enforced by the FS paradigm. If the FS paradigm enforces fewer properties than the TCP-friendly paradigm, the FS paradigm does not make any sense. We show, in the following, that our simple FS paradigm enforces almost all the prop-erties of an ideal congestion control protocol and consequently outperforms the TCP-friendly paradigm.

Stability Under the NP and ESP hypothesis, the existence and uniqueness of a Nash equilib-rium is assured (see [79]). The congestion control protocols devised with the FS paradigm therefore meet the condition of stability.

Efficiency Under the NP and ESP hypothesis, even a simple optimization algorithm (like a hill climbing algorithm) converges fast to the Nash equilibrium. However, the Nash equi-librium is not Pareto optimal in the general case. If all the users have the same utility function, the Nash equilibrium is Pareto optimal. One can point out that ideal efficiency can be achieved with full collaboration of the users (see [79]). However, it is contrary to the ESP assumptions. The congestion control scheme devised with our new paradigm does not have necessarily ideal efficiency.

Fairness Every Fair Scheduler policy achieves max-min fairness. Moreover, as a Fair Sched-uler policy is implemented in every network node, every flow achieves its max-min fair-ness rate on the long term average (see [36]). Our NP assumption enforces fairfair-ness.

Robustness Using a Fair Scheduler enforces that the network is protected against malicious, misbehaving, and greedy users (see [20]). While a user by opening multiple connections can increase its share of the bottleneck, we do not expect this multiple connections effect

1Like the TCP-friendly paradigm, we compose the name of our new paradigm using the name of the funda-mental mechanism involved in the paradigm, namely the Fair Scheduler policy.

to be a significant weakness of the robustness property, as the number of connections that a single user can open is limited in practice.

Scalability According to the ESP assumption, selfish and non-collaborative end users is a suf-ficient condition. Unlike the TCP-friendly paradigm, the designer has a great flexibility to devise scalable end-to-end congestion control protocols with the FS paradigm.

Feasibility A Fair Scheduler policy (HPFQ [4]) can be implemented today in Gigabit routers (see [45]). So the practical application of the NP assumption is no longer an issue (see section B.3.2 for a discussion on the practical deployment of Fair Schedulers policy in the Internet). Moreover, even a simple algorithm will lead to an efficient congestion control protocol. The protocol will be easier to devise and easier to evaluate.

We see that the FS paradigm does not allow to devise an ideal efficient congestion control protocol, because the Nash equilibrium can not be guaranteed to be Pareto optimal. The simple case that consists in considering the user satisfaction of everyone using the same linear function of the bandwidth seen leads to ideal efficiency, as every user has the same utility function.

However, in the general case ideal efficiency is not achieved. According to the NP assumption, every network node implements a Fair Scheduler policy, so we can manage the tradeoff among the three main performance parameters: bandwidth, delay, and loss (see [65]). This tradeoff can not be made with the TCP-friendly paradigm, therefore our paradigm leads to a significantly higher efficiency, in the sense of the satisfaction of end users, than the TCP-friendly paradigm.

We have given the assumptions made and the properties enforced by the FS paradigm. The NP contains only the Fair Scheduler assumption. As this mechanism is of broad utility – we will show in section B.3.1 that a Fair Scheduler has a positive impact on TCP flows – it does not violate the end-to-end argument [71]. The issues related to the practical introduction of the paradigm are studied in section B.3.

The FS paradigm, like the TCP-friendly paradigm, applies for both unicast and multicast since the paradigm does not make any assumption on the transmission mode. Moreover, the FS paradigm enforces properties of great benefits for multicast flows (see section B.3.3).

In conclusion, we have defined a simple paradigm for end-to-end congestion control, called FS paradigm, that relies on a Fair Scheduler network and only makes the assumption that the end users are selfish and non-collaborative. We note that the FS paradigm is less restrictive than the TCP-friendly paradigm, as it does not make any assumptions on the mechanism used by the end users. Whereas the benefits of the FS paradigm with respect to flow isolation are commonly agreed on by the research community, its benefits for congestion control have been less clear since the congestion control properties are often not clearly defined. We showed that the FS paradigm allows to devise end-to-end congestion control protocols that meet almost all the properties of an ideal congestion control protocol. The remarkable point is that simply

B.3. PRACTICAL ASPECTS OF THE FS PARADIGM 95