Congestion control in high-speed communication networks using the Smith principle

Abstract

High-speed communication networks are characterized by large bandwidth-delay products. This may have an adverse impact on the stability of closed-loop congestion control algorithms. In this paper, classical control theory and Smith’s principle are proposed as key tools for designing an effective and simple congestion control law for high-speed data networks. Mathematical analysis shows that the proposed control law guarantees stability of network queues and full utilization of network links in a general network topology and traffic scenario during both transient and steady-state condition. In particular, no data loss is guaranteed using buffers with any capacity, whereas full utilization of links is ensured using buffers with capacity at least equal to the bandwidth-delay product. The control law is transformed to a discrete-time form and is applied to ATM networks. Moreover a comparison with the ERICA algorithm is carried out. Finally, the control law is transformed to a window form and is applied to Internet. The resulting control law surprisingly reveals that today's Transmission Control Protocol/Internet Protocol implements a Smith predictor for congestion control. This provides a theoretical insight into the congestion control mechanism of TCP/IP along with a method to modify and improve this mechanism in a way that is backward compatible.

Introduction

Nowadays, communication networks are among the fastest-growing engineering areas and are driving extraordinary developments in communication industry. An increasing amount of research is devoted to the deployment of new communication networks that merge the capabilities of telephone networks and of computer networks in order to transmit multimedia traffic over a fully integrated universal network. These efforts have lead to the introduction of Broadband Integrated Service Digital Networks (B-ISDNs) and the emerging Asynchronous Transfer Mode (ATM) technology has been retained as the transport technology to be used in B-ISDNs (Varaiya & Walrand, 1996).

ATM networks are a class of virtual circuit switching networks conceived to merge the advantages of circuit switched technology (telephone networks) with those of packet switched technology (computer networks). They are connection-oriented in the sense that before two systems on the network can communicate, they should inform all intermediate switches about their service requirements and traffic parameters by establishing a virtual circuit. This is similar to the telephone networks, where an exclusive circuit is set up from the calling party to the called party, with the important difference that, in the case of ATM, many virtual circuits can share network resources via store-and-forward packet switching and statistical multiplexing (Varaiya & Walrand, 1996). The sharing of network resources allows communication costs be drastically reduced and requires sophisticated mechanisms of flow and congestion control to avoid congestion phenomena (Peterson & Davie, 1996). Congestion control is critical in both ATM and Internet networks and it is the most essential aspect of traffic management (Jacobson, 1988; Jain, 1996). Moreover, new control issues are emerging, which aim at ensuring that users get their desired quality of service (QoS). See, for example, Ding (1997), Le Boudec, de Veciana and Walrand (1996), Liew and Chi-yin Tse (1998) and their references.

In the context of ATM networks, the ATM Forum Traffic Management Group defines five service classes to support multimedia traffic, which are the constant bit-rate (CBR) class, the real-time and non-real-time variable bit-rate (VBR) classes, the unspecified bit-rate (UBR) class and the available bit-rate (ABR) class, which is a best-effort class. ABR is the only class that responds to network congestion by means of a feedback control mechanism in order to improve network utilization by minimizing data loss and retransmissions (ATM Forum, 1996; Jain, 1996).

To briefly summarize the algorithms proposed for ABR traffic control, we start by recalling the binary feedback schemes that were first introduced due to their easy implementation (Bonomi, Mitra & Seery, 1995; Fendick, Rodrigues & Weiss, 1992; Ramakrishnan & Jain, 1990; Roberts, 1994; Yin & Hluchyj, 1994). In these schemes, if the queue length in a switch is greater than a threshold, then a binary digit is set in the control management cell. However, they suffer serious problems of stability, exhibit oscillatory dynamics, and require large amount of buffer in order to avoid cell loss. As a consequence, explicit rate algorithms have been largely considered and investigated. See Jain (1996) for an excellent survey. Most of the existing explicit rate schemes lack of two fundamental parts in the feedback control design: (1) the analysis of the closed-loop network dynamics; (2) the interaction with VBR traffic. In Charny, Clark and Jain (1995) and in Jain, Kalyanaraman, Goyal, Fahmy and Viswanathan (1996) an explicit rate algorithm is proposed, which basically computes input rates dividing the measured available bandwidth by the number of active connections. In Zhao, Li and Sigarto (1997), the control design problem is formulated as a standard disturbance rejection problem where the available bandwidth acts as a disturbance for the system. The ABR source rate is adapted to the low-frequency variation of the available bandwidth and H₂ optimal control is applied to design a controller that minimizes the difference between the source input rate and the available bandwidth. A drawback is that the design of the controller depends on the characteristic of the interacting VBR traffic and on the measurements of the available bandwidth, which is difficult to be obtained in practice. In Altman, Basar and Srikant (1998), the problem is formulated as a stochastic control problem where the disturbance is modeled as an autoregressive process. The node has to estimate this process using recursive least squares. In Mascolo (1997), Smith's principle is exploited to derive a controller in case a first in–first out (FIFO) buffering is maintained at output links. The control algorithm is executed at bottleneck node and computes an input rate which is fed back to the source. The advantages are that the bottleneck switch maintains FIFO queuing and measures only the queue and not the available bandwidth; the drawback is that more computational and informational burden is placed at the switch. An analytic method for the design of a congestion controller has been proposed in Benmohamed and Meerkov (1993), where the input rate is computed as a linear combination of the past values of the rates and of the queue levels. The goal is to stabilize the queue level at a given threshold. The algorithm requires a complex on-line tuning of control parameters to ensure stability and to damp queue oscillations under changing traffic condition. Due to the complex closed-loop dynamics, the authors were unable to solve the global stability problem and they investigated it only by simulations. In Izmailov (1995), two linear feedback control algorithms have been proposed for the case of a single connection with a constant service rate, i.e. the interaction with VBR traffic is not considered. Due to the transcendental form of the closed-loop characteristic equations, only the asymptotic properties of the system were analyzed.

In the context of Internet, after the Transmission Control Protocol/Internet protocol (TCP/IP) had become operational, the network was suffering from congestion collapse. TCP/IP congestion control was introduced into the Internet in the late 1980s and has been successful in preventing congestion collapse (Jacobson, 1988). Many improvements have been introduced since that time and intense research activity is going on to improve the efficiency of this control mechanism. See, for example, Floyd and Jacobson (1993), Hahne, Kalmanek and Morgan (1993), Floyd (1994), Villamizar and Song (1995), Brakmo, O'Malley and Peterson (1995), Balakrishnan, Padmanabhan, Seshan and Katz (1996), Jacobson, Braden and Borman (1997), Kalampoukas and Varma (1998), Gerla, Locigno, Mascolo and Weng (1999). Notice that, nowadays, the TCP/IP congestion control algorithm is the only algorithm successfully tested in a real world-wide packet switching network.

In this paper, we address the issue of congestion control in a general packet switching network using classical control theory, that is, transfer functions are used to describe the system to be controlled and to design the controller. The dynamic behavior of each network queue in response to data input is modeled as the cascade of an integrator with a time delay. Since propagation delays play a key role in high-speed communication networks, we choose the Smith principle to design a simple congestion control law that is effective over path with any bandwidth-delay product. The “best effort” available bandwidth is modeled as an unknown and bounded disturbance input since it is difficult to measure it.

The designed control law is applied to control ABR traffic in ATM networks and a comparison with the well-known Explicit Rate Indication Control Algorithm (Jain et al., 1996) is carried out. Moreover, the proposed control law is applied to TCP/IP. This application surprisingly reveals that today's TCP Internet Protocol implements a Smith predictor to control receiver's buffer and network congestion. This result appears extremely interesting because it gives a theoretical basis to the great success of TCP/IP to control congestion and a very useful insight on how to improve its efficiency.

The paper is organized as follows: Section 2 describes the data network model; Section 3 models the controlled data networks using transfer functions; in Section 4 the controller is designed using Smith's principle; in Section 5 transient and steady-state dynamics are evaluated via mathematical analysis; Section 6 describes the application of the proposed control law to ATM networks whereas Section 7 describes the application to Internet; finally, Section 8 draws the conclusions.