![](https://csdnimg.cn/release/download_crawler_static/19644805/bg1.jpg)
J Control Theory Appl 2009 7 (1) 29–34
DOI 10.1007/s11768-009-7112-8
A three-dimensional probabilistic fuzzy control
system for network queue management
Yun ZHANG
1
, Zhi LIU
1
, Yaonan WANG
2
(1.Department of Automation, Guangdong University of Technology, Guangzhou Guangdong 510006, China;
2.Department of Electrical Engineering, Hunan University, Changsha Hunan 410082, China)
Abstract: A novel probabilistic fuzzy control system is proposed to treat the congestion avoidance problem in trans-
mission control protocol (TCP) networks. Studies on traffic measurement of TCP networks have shown that the packet
traffic exhibits long range dependent properties called self-similarity, which degrades the network performance greatly.
The probabilistic fuzzy control (PFC) system is used to handle the complex stochastic features of self-similar traffic and the
modeling uncertainties in the network system. A three-dimensional (3-D) membership function (MF) is embedded in the
PFC to express and describe the stochastic feature of network traffic. The 3-D MF has extended the traditional fuzzy planar
mapping and further provides a spatial mapping among “fuzziness-randomness-state”. The additional stochastic expression
of 3-D MF provides the PFC an additional freedom to handle the stochastic features of self-similar traffic. Simulation ex-
periments show that the proposed control method achieves superior performance compared to traditional control schemes
in a stochastic environment.
Keywords: Probabilistic fuzzy control; Probabilistic fuzzy logic system; Network control
1 Introduction
With the growth of the size, demand and applications on
the Internet, the network congestion control problem has
emerged as a critical issue in TCP networking [1]. With
more real-time network applications being applied on the
Internet, the quality of service (QoS) has become an ex-
tremely important problem for current networks. Active
queue management schemes have been proposed to deliver
congestion notification to the source for congestion avoid-
ance, which is also a hot topic in the current network con-
trol field [2, 3]. The IETF has proposed the deployment of
active queue management techniques such as random early
detection (RED). Random Early Detection (RED) is a pop-
ular congestion avoidance method of the AQM scheme. It
aims to calculate the drop probability using the average
queue length. The router randomly drops the packets be-
fore a queue becomes full, so that end nodes can respond
by adjusting the transmission rate or window size to avoid
network congestion. Although RED is an efficient conges-
tion control method, the optimal sets of RED parameters are
designed by heuristics or simulation methods. The configu-
ration of RED is very sensitive to the specified condition of
the network. Many researchers have studied the optimal pa-
rameter selection for RED [4∼6]. Reference proposes the
dynamic-RED scheme to enhance the control performance
with a proportional control gain. The Random Early Mark-
ing (REM) scheme decouples the equilibrium value of con-
gestion measure to achieve a high performance. Adaptive
Virtual Queue (AVQ) [5], BLUE and SRED are presented to
achieve low-loss, low-delay and high utilization operation
at the link. To design the congestion control system under
a systematic view, a control theory-based AQM scheme is
proposed to study the stability, robustness and adaptability
of the network control system [7, 8]. PID control is designed
for the linear classical network system to enhance the queue
performance. Considered the nonlinearity, time-varying and
uncertainties features of the Internet, many nonlinear con-
trol approaches, such as Hinf control, variable structure con-
trol and fuzzy control method, are used to regulate the actual
queue size to approach the reference one. By this way, they
can make a proper equilibrium between low-loss, delay and
high utilization.
Many of the network analytical models are designed by
assuming the Poisson packet arrivals and the time indepen-
dence [9]. Recently, the study of traffic measurement has
shown that the actual network traffic exhibits self-similar,
fractal or long-range dependence. Thus, the Poisson model
inherited from the telephony world is no longer valid for
the self-similar network traffic. The self-similar and multi-
fractal nature of network traffic can degrade the network
performance greatly due to the heavy-tailed distribution of
transmitted files, high queue buffer overflow rates, large de-
lays and persistent periods of congestion. Therefore, design-
ing congestion control schemes to treat self-similarity net-
work traffic and reducing the effect of self-similarity fea-
tures are the focus of the attention of the networking com-
munity, which is still an open area in the QoS field. In the
design of AQM methods, few studies have reported system-
atic congestion control schemes to treat self-similarity net-
work traffic and to reduce the effect of self-similarity fea-
tures. Note that the stochastic uncertainty is an important
feature in self-similar networks. Therefore, it is interesting
to study the probabilistic fuzzy control system to treat the
network stochastic features. To the best of our knowledge,
Received 23 May 2007; revised 13 May 2008.
This work was supported by the National Natural Science Foundation of China (U0735003, 60604006) and Natural Science Foundation of Guangdong
Province (8351009001000002, 6021452).