CN1874299A - Method for managing active queue of route based on control of slipform variation structure - Google Patents

Abstract

The method features: in term of the predetermined amount of active sessions, target value of queue length, link capacity and length of small queue within the range of round-trip delay, a sliding mode variable structure control system having a sliding mode parameter Omega=2, which adopts a combination of ratio control and constant-value control, are used to control the discarding probability of packet.

Description

Route active queue management method based on sliding mode variable structure control

Technical Field

The invention belongs to the field of router queue management and congestion control.

Background

Congestion control plays a very important role in the network traffic management of the Internet. Traditional congestion control relies primarily on TCP flow control on end systems, but recent studies have shown that: no matter how sophisticated mechanisms are adopted, the role that end systems can play in flow management is ultimately limited, and expanding the functionality of intermediate nodes should be an effective means to enhance end-to-end congestion control. As a mechanism for dropping or marking packets in router queues, Active Queue Management (AQM) is proposed to support end-to-end congestion control over the Internet, which has recently become a research hotspot.

The technical goals of AQM are: (1) the average queue length of the router is reduced, so that the end-to-end delay experienced by the packet is reduced; (2) reducing excessive packet drops due to queue overflow ensures that network link resources are fully utilized. Floyd's proposed RED (random early detection) algorithm meets the technical goals of AQM, so the request for comments document No. 2309 (RFC2309) recommends it as the only candidate algorithm for AQM. However, as the research progresses, people begin to recognize that the RED algorithm itself still has many imperfections, mainly in terms of both stability and fairness. In order to improve and improve the defects of RED, various algorithms of RED have appeared, and more influential are RED-cause (mild RED), stable-RED (stable RED), FRED (flow RED), BLUE, and Self-configuration RED (Self-configuration RED), etc. Most of the methods rely on intuitive heuristic algorithms, partial simulation and experiment under special configuration are the only means for verifying the effectiveness of the algorithms, and theoretical analysis and evaluation of the system are ignored to a certain extent. Once problems occur in practice, the problems are corrected through a large amount of simulation and experiments. Intuitive and heuristic design is not always scientific and reasonable, modeling is the first step in the system's understanding of the Internet, and algorithms designed based on certain models should be more reliable than those relying on intuition. A TCP flow control dynamic nonlinear model elicitation C.V Hollot et al provided in the existing literature designs a PI (proportional integral) controller for AQM, and s.kunniyur and r.srikant also provide an AVQ (adaptive virtual queue) algorithm based on the model. Kelly et al constructs a unified framework for flow control, which translates congestion control into optimization problems, and REM (random index notation) is a typical algorithm under the system. Although the PI controller successfully overcomes some of the limitations of RED, its disadvantages are also apparent, and the adjustment of the probability is so dependent on the size of the buffer that systems with small buffers appear very sluggish. Second, system performance is flat when the reference captain is small, which is very critical to achieving the technical goals of AQM. Moreover, the actual network state is instantaneously changeable, and it is unrealistic to regard the network as a linear constant system in the PI controller design process, so the robustness of the algorithm obtained based on the above assumptions is poor, and the algorithm cannot adapt to a complex and variable network environment.

Disclosure of Invention

The invention aims to provide a route active queue management method based on sliding mode variable structure control, which is very suitable for network time-varying characteristics, has good response performance and is particularly suitable for small queue length.

The invention is characterized in that the method comprises the following steps in sequence:

step (1) a controller of a sliding mode variable structure control system is established in a router, and the controller adopts a control strategy combining the following proportional switching control and constant value control:

<math> <mrow> <mi>p</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>&psi;</mi> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>&psi;</mi> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mi>&alpha;</mi> <mo>,</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mi>&sigma;</mi> <mo>></mo> <mn>0</mn> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>&beta;</mi> <mo>,</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mi>&sigma;</mi> <mo>&lt;</mo> <mn>0</mn> <mo>,</mo> </mtd> </mtr> </mtable> </mfenced> <mo>|</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>|</mo> <mo>&lt;</mo> <mi>M</mi> </mrow> </math>

<math> <mrow> <mi>p</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>&theta;</mi> <mo>,</mo> <mi>&theta;</mi> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mi>M</mi> <mo>,</mo> <mi>&sigma;</mi> <mo>></mo> <mn>0</mn> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>m</mi> <mo>,</mo> <mi>&sigma;</mi> <mo>&lt;</mo> <mn>0</mn> <mo>,</mo> </mtd> </mtr> </mtable> </mfenced> <mo>|</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>|</mo> <mo>></mo> <mi>M</mi> <mo>,</mo> </mrow> </math>

wherein:

p (t) is the packet drop probability, i.e. the amount of control of the controller,

q₀for the queue-length target value to be,

q₁and q is₂Instantaneous sample value of queue length, wherein q₁Is t₁Queue length of time of day, q₂Is t₂Queue length of time, t₂Is the current time, t₂＞t₁，

x₁Is t₂Time queue length and queue length target value q₀The difference between the difference of the two phases,

psi is a proportional control coefficient,

in the sliding mode variable structure controller, the switching line sigma is wx₁+x₂W is a sliding mode parameter,

theta is a constant value control set value,

m is the maximum value of the control quantity p (t), M is 1,

m is the minimum value of the control quantity p (t), m is 0,

in the above formula, when N (t) is 1-300, N (t) is the number of active sessions,

q₀0-300 packets, the default size of a packet is 500 bytes,

c (t) 1250-7500 packets/sec, C (t) link capacity,

r (t) is 0 to 0.4 seconds, R (t) is a round-trip delay,

then: α ═ 0.96, β ═ -0.96, ω ═ 2;

initializing step (2), setting:

t is the sample period of the queue length,

last time is used to record the system time to determine whether the next sampling period is reached, initialized to the current time,

x₂record t₁Time t₂The value of the change in queue length at a time,

z records the value of the switching function, z 2 × x₁+x₂；

Step (3) waiting for a new packet to arrive: if a new packet arrives, judging whether the current time arrives at last _ time + T seconds, if so, executing the step (4), and if not, executing the step (6);

step (4) let x₁＝q₂-q₀，q₂For the current queue length, x₂＝q₂-q₁；

Step (5) assigning last _ time as the current time;

step (6) of judging | x₁If | M is true, if | x₁If the value is greater than M, executing the step (7), otherwise, executing the step (8);

step (7) executing constant value control:

judging whether z is greater than 0.0, if z is greater than 0.0, making p equal to 1.0, otherwise, making p equal to 0.0;

turning to step (9);

step (8) performs proportional control:

judgment of x₁Whether xxz > 0.0 is true, if x₁X z > 0.0, let p be 0.96 x₁Otherwise, let p be-0.96 × x₁；

Step (9) discarding the packet with probability p;

and (5) turning to the step (3) in the step (10), and repeatedly executing the step (3) to the step (9) until the end.

The performance simulation result based on the network simulation platform shows that: the adaptability and robustness of the active route queue management method based on sliding mode variable structure control are stronger than those of a PI controller, and the aim of reducing end-to-end time delay while ensuring higher link utilization rate by AQM is easier to achieve.

Drawings

FIG. 1 is a AQM control block diagram;

FIG. 2 is a typical sliding mode variable structure system;

FIG. 3 is a block flow diagram of a SMVS method;

FIG. 4 simulates a network configuration;

FIG. 5 SMVS controlled queues;

FIG. 6 queue change (FTP + HTTP); -SMVS controller … … PI controller

FIG. 7 queue variation (FTP + UDP); -SMVS controller … … PI controller

FIG. 8 queue Change (SMVS);

fig. 9 queue change (PI).

Detailed Description

The invention designs a robust control method called SMVS for Active Queue Management (AQM) by applying a Sliding Mode Variable Structure (SMVS) theory in a robust control theory, and aims to obtain a new controller with performance superior to PI. Simulation test results show that the controller is insensitive to noise and parameter variation and is very suitable for the time-varying characteristic of the network; the method has good comprehensive performance and good responsiveness, and the robustness is particularly outstanding in the aspect of controlling the small captain.

The prior literature presents a nonlinear model of TCP flow control based on fluid flow theory, which is simplified in the form:

$\left\{\begin{array}{c}\frac{\mathrm{dW}\left(t\right)}{\mathrm{dt}}=\frac{1}{R\left(t\right)}-\frac{W\left(t\right)W(t-R\left(t\right))}{2R\left(t\right)}p(t-R\left(t\right))\\ \frac{\mathrm{dq}\left(t\right)}{\mathrm{dt}}=\frac{N\left(t\right)}{R\left(t\right)}W\left(t\right)-C\left(t\right)\end{array}\right.---(*)$

wherein the physical meanings of the parameters are as follows:

w (t): window size of TCP flow (number of packets), q (t): the queue length (number of packets) of the router,

c (t): link capacity (number of packets/second), n (t): the number of active TCP sessions is,

p (t): the packet drop probability, i.e. the amount of control of the system,

r (t): round Trip Time (RTT) (seconds).

In the prior art, local linearization is carried out on the router at a steady-state working point by using a small signal theory, and a structural block diagram shown in figure 1 is obtained by combining an AQM method acting on the router. The physical meaning of the parameters in fig. 1 is as follows:

q₀: expected queue length (number of packets), e (t): q (t) and q₀The difference between the difference of the two phases,

$K\left(t\right)=\frac{{\left[R\left(t\right)C\left(t\right)\right]}^3}{[2N\left(t\right){]}^2},$ T₁(t)＝R(t)， $T_2\left(t\right)=\frac{R^2\left(t\right)C\left(t\right)}{2N\left(t\right)}.$

figure 1 depicts TCP/AQM as a feedback control system, i.e. a control signal is generated by purposely dropping some packets by the AQM regulator, and the TCP end system responds, eventually keeping the router queue near a desired value. The controller in the figure refers to the AQM method used in the router,is the transfer function of the controlled TCP/AQM system, which describes how the controller affects q (t) by changing the control quantity p (t). The control system depicted in fig. 1 is a second order linear system. A linear constancy system is beneficial for analyzing and interpreting RED stability under some parameter configurations. Nevertheless, we believe that AQM controllers relying on simplified and inaccurate linear constancy models should not be optimal, since real networks vary widely and state parameters are difficult to maintain around constant values for long periods of time. Furthermore, the equation (×) only considers fast retransmissions and fast recovery, neglecting the timeout process due to lack of sufficient repetitive ACKs, which is common in bursty and short-connection traffic. Besides this, there are non-responsive UDP streams in the network in addition to the TCP connections, which are not included in the equation (#). These model mismatch factors must affect the performance of the controller.

In modeling research, some behaviors in a system cannot be described by using a model at all, and some behaviors can be described by using the model but are extremely complex, so that an intuitive and easy-to-process simple model is an effective method for approximating the complex behaviors of an actual system. Thus, it is inevitable that there is a difference between the model and the actual system. From a controller design perspective, an ideal controller should be insensitive to model match errors. Robust control theory works well for the handling of such problems. The sliding mode variable structure control is a branch of robust control, and as the name suggests, in the control process, the structure of the control is not determined but is changed along with the change of the state, so as to constrain the state variable of the system to be always positioned in the neighborhood of a switching function definition curve (or curved surface). Here, a mechanism of the sliding mode variable structure control is briefly described in conjunction with the system shown in fig. 2.

Suppose at t₀The time system is in an initial state A₀Then after the control law u-k₁x₁Under the action of the magnetic field, the magnetic field moves along a certain phase track. When t is₁＞t₀The system reaches and crosses the switching line σ ═ wx₁+x₂(ii) a Subsequently, the control law is switched to u-k₂x₁The system will certainly move along another phase trajectory, once again crossing the straight line σ equal to 0 (i.e. wx)₁＝-x₂) Then, the control law u is k₁x₁Forcing the system to traverse the switch line … … a third time. Thus, the system oscillates along the switching line σ ═ 0 (also called sliding mode line), and finally slides to the origin. Since the sliding mode line can be designed independently of the system itself, and therefore the system motion is also independent of its parameter variations and external disturbances, this is a very useful feature for a transient network. In an actual network, due to factors such as continuous establishment and removal of connections, continuous change of traffic, adjustment of network structure and the like, network characteristic parameters change with time. The conventional control theory is not particularly powerful for processing the time-varying system, but the sliding mode variable structure control forces the system to do small-amplitude and high-frequency oscillating motion along a preset sliding mode track under certain conditions by utilizing the switching characteristic which changes along with time, and the motion per se and the controlled objectThe parameters are irrelevant to the disturbance, so that the method can be well adapted to the change of the parameters and the disturbance of the load, and has strong robustness.

In SMVS method design, let x₁＝e(t)， $x_2=\frac{d}{\mathrm{dt}}e\left(t\right)=\frac{d}{\mathrm{dt}}{x}_1,$ Obtaining a state space representation of the system described in FIG. 1

The formula is as follows:

$\left\{\begin{array}{c}\frac{d{x}_1}{\mathrm{dt}}=x_2\\ \frac{d{x}_2}{\mathrm{dt}}=-a_1\left(t\right)x_1-a_2\left(t\right)x_2-b\left(t\right)p+F\left(t\right)\end{array}\right.---\left(1\right)$

in the formula, $a_1\left(t\right)=\frac{1}{T_1\left(t\right)T_2\left(t\right)},a_2\left(t\right)=\frac{T_1\left(t\right)+T_2\left(t\right)}{T_1\left(t\right)T_2\left(t\right)},b\left(t\right)=\frac{K\left(t\right)}{T_1\left(t\right)T_2\left(t\right)}$

$F\left(t\right)=\frac{1}{T_1\left(t\right)T_2\left(t\right)}{\mathrm{<figure-callout\; id="0"\; label="q"\; filenames="A20061001214100145.png"\; state="\{\{state\}\}">q</figure-callout>}}_0$

treating F (t) in formula (1) as interference. Adopting a proportional switching control strategy:

p＝ψx₁

<math> <mrow> <mi>&psi;</mi> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mi>&alpha;</mi> <mo>,</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mi>&sigma;</mi> <mo>></mo> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>&beta;</mi> <mo>,</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mi>&sigma;</mi> <mo>&lt;</mo> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </math>

wherein, the switching function σ is taken as wx₁+x₂(w is a sliding mode parameter) (3)

The following formula gives the necessary conditions for the existence of a sliding mode line in the above system:

<math> <mrow> <mrow> <mi>&alpha;</mi> <mo>></mo> <munder> <mi>max</mi> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <msub> <mrow> <mo>,</mo> <mi>a</mi> </mrow> <mn>2</mn> </msub> <mo>,</mo> <mi>b</mi> </mrow> </munder> <mo>{</mo> <mo>[</mo> <msub> <mi>wa</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <msup> <mi>w</mi> <mn>2</mn> </msup> <mo>-</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>]</mo> <mo>/</mo> <mi>b</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>}</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <mi>&beta;</mi> <mo>&lt;</mo> <munder> <mi>min</mi> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <msub> <mrow> <mo>,</mo> <mi>a</mi> </mrow> <mn>2</mn> </msub> <mo>,</mo> <mi>b</mi> </mrow> </munder> <mo>{</mo> <mo>[</mo> <msub> <mi>wa</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <msup> <mi>w</mi> <mn>2</mn> </msup> <mo>-</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>]</mo> <mo>/</mo> <mi>b</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>}</mo> </mrow> </math>

to ensure that the system starts from any initial state, the switching line σ must be reached 0 for a limited time, the theorem given in the prior document is quoted:

theorem: a sufficient requirement that the system (1) must be able to reach a switch line σ of 0 at any initial point is that the system's characteristic equation (5) has no non-negative real roots.

<math> <mrow> <msup> <mi>p</mi> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>min</mi> </msub> <mi>p</mi> <mo>+</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>min</mi> </msub> <mo>+</mo> <munder> <mi>inf</mi> <mi>t</mi> </munder> <mo>{</mo> <mi>b</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>&alpha;</mi> <mo>}</mo> <mo>=</mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow> </math>

If only the multiple roots are taken, the following conditions are obtained by the theorem:

α＞{[a₂(t)_min]²-4a₁(t)_min}/4b(t)_min (6)

for a general ideal second-order linear system without zero point and pure lag single-input variable parameters, if the proportional switching control mode (2) meeting the conditions (4) and (6) is adopted, good control performance can be realized; however, for the AQM system, the control quantity p (t) is the packet drop probability, so its range is limited and should be between 0 and 1. For this reason, we adopt a control strategy combining proportional switching control and constant value control:

<math> <mrow> <mi>p</mi> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mi>&psi;</mi> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <mo>|</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>|</mo> <mo>&lt;</mo> <mi>M</mi> </mtd> </mtr> <mtr> <mtd> <mi>&theta;</mi> <mo>,</mo> <mo>|</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>|</mo> <mo>></mo> <mi>M</mi> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow> </math>

wherein, <math> <mrow> <mi>&theta;</mi> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mi>M</mi> <mo>,</mo> <mi>&sigma;</mi> <mo>></mo> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>m</mi> <mo>,</mo> <mi>&sigma;</mi> <mo>&lt;</mo> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow> </math> m, m are the maximum and minimum values of the driving force (i.e., the maximum value 1 and minimum value 0 of the control amount p (t)), respectively, and ψ has the same meaning as in expression (2) (for the sake of simplicity of control implementation, k ═ α > 0 > β ═ k is not allowed). In addition, when the control amount is limited, the sliding mode domain in the phase space has a certain range under certain alpha, beta and w, so the selection of the sliding mode parameter w is also limited, namely, the sliding mode parameter w should be limited <math> <mrow> <mi>w</mi> <mo>&le;</mo> <msub> <mi>w</mi> <mi>max</mi> </msub> <mo>=</mo> <msqrt> <mi>b</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>k</mi> </msqrt> <mo>,</mo> </mrow> </math> Otherwise, the controlled queue will rush out of the sliding mode domain, causing excessive overshoot, generating severe oscillations, affecting the performance of the system.

To design an active queue management method that is suitable for a wide range, we assume here the variation range of each parameter:

N(t)：1～300 q₀: 0 to 300 (number of packets) (default size of 500 bytes)

C (t): 1250 to 7500 (number of packets/sec) R (t): 0 to 0.4 (second)

The parameters in formula (1) are calculated as:

3.8501＝a_2min≤a₂(t)≤a_2max＝1250

0.015＝a_1min≤a₁(t)≤a_1max＝60000 2604.2＝b_min≤b(t)≤b_max＝28125000

let parameter w in switching function (3) be 2, and obtain from sliding mode existence condition (4)

α＞0.958；β＜-0.0021 (8)

The condition (6) is reached by a sliding mode to obtain

α＞0.0015 (9)

By combining (8) and (9), k ═ α ═ β ═ 0.96, and M ═ 1 and M ═ 0 can be taken, and after these parameters are substituted into formula (7), the AQM method based on the sliding mode variable structure can be obtained, which is named SMVS method for convenience of description.

The invention is characterized in that: the active queue management method for congestion control and avoidance sequentially comprises the following steps of:

step (1) a controller of a sliding mode variable structure control system is established in a router, and the controller adopts a control strategy combining the following proportional switching control and constant value control:

<math> <mrow> <mi>p</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>&psi;</mi> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>&psi;</mi> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mi>&alpha;</mi> <mo>,</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mi>&sigma;</mi> <mo>></mo> <mn>0</mn> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>&beta;</mi> <mo>,</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mi>&sigma;</mi> <mo>&lt;</mo> <mn>0</mn> <mo>,</mo> </mtd> </mtr> </mtable> </mfenced> <mo>|</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>|</mo> <mo>&lt;</mo> <mi>M</mi> <mo>,</mo> </mrow> </math>

<math> <mrow> <mi>p</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>&theta;</mi> <mo>,</mo> <mi>&theta;</mi> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mi>M</mi> <mo>,</mo> <mi>&sigma;</mi> <mo>></mo> <mn>0</mn> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>m</mi> <mo>,</mo> <mi>&sigma;</mi> <mo>&lt;</mo> <mn>0</mn> <mo>,</mo> </mtd> </mtr> </mtable> </mfenced> <mo>|</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>|</mo> <mo>></mo> <mi>M</mi> <mo>,</mo> </mrow> </math>

wherein:

p (t) is the packet drop probability, i.e. the amount of control of the controller,

q₀for the queue-length target value to be,

q₁and q is₂Instantaneous sample value of queue length, wherein q₁Is t₁Queue length of time of day, q₂Is t₂Queue length of time, t₂Is the current time, t₂＞t₁，

x₁Is t₂Time queue length and queue length target value q₀The difference between the difference of the two phases,

psi is a proportional control coefficient,

in the sliding mode variable structure controller, the switching line sigma is wx₁+x₂W is a sliding mode parameter,

theta is a constant value control set value,

m is the maximum value of the control quantity p (t), M is 1,

m is the minimum value of the control quantity p (t), m is 0,

in the above formula, when N (t) is 1-300, N (t) is the number of active sessions,

q₀0-300 packets, the default size of a packet is 500 bytes,

c (t) 1250-7500 packets/sec, C (t) link capacity,

r (t) is 0 to 0.4 seconds, R (t) is a round-trip delay,

then: α ═ 0.96, β ═ -0.96, ω ═ 2;

initializing step (2), setting:

t is the sample period of the queue length,

last time is used to record the system time to determine whether the next sampling period is reached, initialized to the current time,

x₂record t₁Time t₂The value of the change in queue length at a time,

z records the value of the switching function, z 2 × x₁+x₂；

Step (3) waiting for a new packet to arrive: if a new packet arrives, judging whether the current time arrives at last _ time + T seconds, if so, executing the step (4), and if not, executing the step (6);

step (4) let x₁＝q₂-q_n，q₂For the current queue length, x₂＝q₂-q₁；

Step (5) assigning last _ time as the current time;

step (6) of judging | x₁If | M is true, if | x₁If the value is greater than M, executing the step (7), otherwise, executing the step (8);

step (7) executing constant value control:

judging whether z is greater than 0.0, if z is greater than 0.0, making p equal to 1.0, otherwise, making p equal to 0.0;

turning to step (9);

step (8) performs proportional control:

judgment of x₁Whether xxz > 0.0 is true, if x₁X z > 0.0, let p be 0.96 x₁Otherwise, let p be-0.96 × x₁；

Step (9) discarding the packet with probability p;

and (5) turning to the step (3) in the step (10), and repeatedly executing the step (3) to the step (9) until the end.

Fig. 3 shows a flow diagram of the SMVS method.

The SMVS method is realized on an NS network simulation platform, and the performance of the SMVS method is tested. NS (network simulator) is a general multi-protocol network simulation software, which is published on the Internet (website: http:// www-mesh. cs. bergelley. edu/NS /), and is widely used by network researchers at present. With the topology shown in fig. 4, except that the queue of node a is SMVS, the other queues are DropTail, and the buffer size of all nodes is 300 packets. Dividing service sources into three groups, wherein the first group consists of N1 persistent FTP (file transfer protocol) sources; the second group comprises N2 bursty HTTP (hypertext transfer protocol) connections, each with 10 session traffic, with an average of 3 pages per session. The third group contains N3 non-responsive UDP (user datagram protocol) sources, all of which follow the ON/OFF model, with idle and burst intervals of 10000ms and 1000ms, respectively, and a traffic generation rate of 40Kbps during the "ON" phase. The link between the service source and node a has the same capacity and broadcast delay (L)₁，τ₁) Parameter pairs (L) for link AB and link BC₂，τ₂) And (L)₃，τ₃) And (4) defining.

To verify whether the SMVS can reach the technical goal of AQM, the simulation network is configured with the most common parameters, given (L)₁，τ₁)＝(10Mbps，15ms)，(L₂，τ₂)＝(15Mbps，15ms)，(L₃，τ₃)＝(45Mbps，15ms)， N₁270, N2, N3, 0, the desired team leader is 75 groups. Fig. 5 depicts the queue length change process, and the queue stabilizes to the desired length through a short adjustment process.

The PI or PID controller is based on a linear model, and because the model has errors, the designed control method is difficult to adapt to a complex and variable network environment, but the SMVS has strong robustness and can adapt to the interferences such as model mismatching, disturbance and the like. To confirm this, the following simulation test was performed. Given N₁＝270，N₂＝400，N₃The queue variation under PI and SMVS control is depicted in fig. 6 at 0, and it is clear that both controllers can stabilize the queue for bursty short connections, since after all the PI controllers also have a certain stability margin. If given N₁＝270，N₂＝0，N₃Observing the effect of the unresponsive UDP flow on the control method 50 results in the results shown in fig. 7, where the PI controller is no longer stable, the queue exhibits large amplitude oscillations, while the SMVS controlled queue operates in a relatively stable state, but the fluctuation amplitude of the queue is increased somewhat compared to the previous case. The above two experiments demonstrate that SMVS is more robust than PI.

Finally, the overall performance of the SMVS controller is analyzed using a relatively realistic network scenario. 270 FTP streams and 30 UDP streams are divided into three groups, and 400 HTTP streams form a group separately. At time 0, the first set of FTP and UDP traffic starts, and after 100 seconds, the second set starts. At 200 seconds, all traffic (including HTTP and third set of FTP, UDP traffic) starts all. And stopping the first group of FTP and UDP flows in 300 seconds, and stopping the second group of FTP and UDP services in 100 seconds. All simulations were completed in 600 seconds. Fig. 8 and 9 show the variation process of the SMVS and PI controlled queues, respectively. It is clear that SMVS is superior to PI, both in transient and in transient performance. Even if the load is greatly suddenly changed, the SMVS controller can control the queue to be close to the expected reference value, and the PI capacity is relatively weak in this respect. That is to say, the adaptability and robustness of the SMVS controller are stronger than those of PI, and the purpose of reducing the end-to-end delay while ensuring higher link utilization by AQM is more easily achieved.

Claims (1)

1. The method for managing the active queue of the route based on the sliding mode variable structure control is characterized by sequentially comprising the following steps of: step (1) a controller of a sliding mode variable structure control system is established in a router, and the controller adopts a control strategy combining the following proportional switching control and constant value control:

p(t)＝ψx₁， <math> <mrow> <mi>&psi;</mi> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mi>&alpha;</mi> <mo>,</mo> </mtd> <mtd> <msub> <mi>x</mi> <mn>1</mn> </msub> <mi>&sigma;</mi> <mo>></mo> <mn>0</mn> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>&beta;</mi> <mo>,</mo> </mtd> <mtd> <msub> <mi>x</mi> <mn>1</mn> </msub> <mi>&sigma;</mi> <mo>&lt;</mo> <mn>0</mn> <mo>,</mo> </mtd> </mtr> </mtable> </mfenced> </mrow> </math> |x₁|＜M，

p(t)＝θ， <math> <mrow> <mi>&theta;</mi> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mi>M</mi> <mo>,</mo> </mtd> <mtd> <mi>&sigma;</mi> <mo>></mo> <mn>0</mn> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>m</mi> <mo>,</mo> </mtd> <mtd> <mi>&sigma;</mi> <mo>&lt;</mo> <mn>0</mn> <mo>,</mo> </mtd> </mtr> </mtable> </mfenced> </mrow> </math> |x₁|＞M，

wherein:

p (t) is the packet drop probability, i.e. the amount of control of the controller,

q₀for the queue-length target value to be,

q₁and q is₂Instantaneous sample value of queue length, wherein q₁Is t₁Queue length of time of day, q₂Is t₂Queue length of time, t₂Is the current time, t₂＞t₁，

x₁Is t₂Time queue length and queue length target value q₀The difference between the difference of the two phases,

psi is a proportional control coefficient,

in the sliding mode variable structure controller, the switching line sigma is wx₁+x₂W is a sliding mode parameter,

theta is a constant value control set value,

m is the maximum value of the control quantity p (t), M is 1,

m is the minimum value of the control quantity p (t), m is 0,

in the above formula, when N (t) is 1-300, N (t) is the number of active sessions,

q₀0-300 packets, the default size of a packet is 500 bytes,

c (t) 1250-7500 packets/sec, C (t) link capacity,

r (t) is 0 to 0.4 seconds, R (t) is a round-trip delay,

then: α ═ 0.96, β ═ -0.96, ω ═ 2;

initializing step (2), setting:

t is the sample period of the queue length,

last time is used to record the system time to determine whether the next sampling period is reached, initialized to the current time,

x₂record t₁Time t₂The value of the change in queue length at a time,

z records the value of the switching function, z 2 × x₁+x₂；

Step (3) waiting for a new packet to arrive: if a new packet arrives, judging whether the current time arrives at last _ time + T seconds, if so, executing the step (4), and if not, executing the step (6);

step (4) let x₁＝q₂-q₀，q₂For the current queue length, x₂＝q₂-q₁；

Step (5) assigning last _ time as the current time;

step (6) of judging | x₁If | M is true, if | x₁If the value is greater than M, executing the step (7), otherwise, executing the step (8);

step (7) executing constant value control:

judging whether z is greater than 0.0, if z is greater than 0.0, making p equal to 1.0, otherwise, making p equal to 0.0;

turning to step (9);

step (8) performs proportional control:

judgment of x₁Whether xxz > 0.0 is true, if x₁X z > 0.0, let p be 0.96 x₁Otherwise, let p be-0.96 × x₁；

Step (9) discarding the packet with probability p;

and (5) turning to the step (3) in the step (10), and repeatedly executing the step (3) to the step (9) until the end.

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