 Open Access
 Authors : Marvis I. Aririguzo , C. B. Mbachu
 Paper ID : IJERTV10IS050018
 Volume & Issue : Volume 10, Issue 05 (May 2021)
 Published (First Online): 21052021
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Transport Control Protocol Based Computer Wireless Network Performance Enhancement
Marvis I. Aririguzo Federal Polytechnic Nekede, Owerri, Nigeria
C.B. Mbachu
Chukwuemeka Odumegwu Ojukwu University Uli, Nigeria
Abstract This work aims at developing a robust compensator for TCP queue based wireless network using H2 optimization technique. The objectives of this work are to improve the performance of the TCP by reducing the tracking error, settling time and to improve the stability of the system by increasing the gain margin to be greater than or equal to 20dB and increasing the phase margin to be greater than or equal to 60deg. The TCP is a vital organ in every wireless network and due to the increasing reliance on the wireless network by most human activities, it has suffered from disturbances most especially traffic congestion. The H2 optimization technique was applied to improve the performance and stability of the system while considering the disturbance and system output error. The H2 compensated TCP (H2TCP) queue achieved a reduced settling time of 0.000419sec and a 0dB reference tracking error which showed good network throughput. The H2TCP queue system recorded a gain margin of 20.3dB and 78.9deg phase margin. It was concluded that the H2TCP network achieved improved performance and robust stability and hence can maintain optimal performance and stability even in the presence of high disturbances.
KeywordsTCP; H2 Synthesis; Wireless Network; Tracking Error; Stability Margins

INTRODUCTION
The rapid increase in the amount of network traffic causes difficulty of data transfers in computer networks and this difficulty is described as congestion. This congestion in computer networks is a problem which must be solved in order to achieve optimal function of the network. The information exchange in the computer networks are better controlled by the Transmission Control Protocol (TCP) which is one of the common transport protocols whereby a sender has authority to set its transmission rate using a window flow control mechanism. However, the TCP network traffic control method has drawbacks such as low efficiencies of communications because this method uses the mechanism to avoid congestion after congestion once appears in computer networks [1]. Congestion has been a common challenge of the high traffic communication network due to the tremendous amount of information exchange.
TCP has no information of network mechanisms contributing to packet loss such as the congested router. Thus, routers must assume a role in network management by sensing congestion and preemptively signaling TCP rather than have it react to nonreceived packets [2]. The simplest form of the active queue management (AQM), termed drop tail, drops arriving packets when the routers buffer is full. Drawbacks of this scheme include flowsynchronization, in
[3] and performance degradation due to the excessive time outs and restarts arising when the trailing end of a sequence of data packets is dropped. Motivated by droptails inefficiencies, the random early detection (RED) scheme was introduced in [3]. Rather than waiting for buffer overflow to occur, RED anticipates congestion by measuring the routers average queue length and throttling the senders rate accordingly. Since TCP is an endtoend protocol, RED achieves this signaling indirectly by randomly marking packets and routing them to the receiver. The receiver, in turn, completes the feedback by acknowledging the receipt of marked packets to the sender. Upon receipt of such acknowledgments, the sender adjusts its rate according to the TCP algorithm. The randomness in REDs packetmarking scheme was meant to eliminate flowsynchronization and introduce fairmarking while queueaveraging was introduced to attenuate the effects of bursty traffic on the feedback signal [2]. Incidentally, there is a crucial drawback in deploying RED stems from tuning difficulties where the performance of RED can approach that of a droptail router. Due to these deficiencies in the basic RED mechanism, researchers have continued to propose modifications to solve them as presented in [4, 5].Many other control measures have been implemented to improve the performance of the TCP/AQM wireless network system such as the Proportional Integral (PI) controller which was confirmed in [6] to outperform RED significantly. However, PI has the ability to improve the stability of the system by achieving an improved steady state error but it has some limitations such as poor performance in disturbance rejection. Advanced robust control techniques, such as H2 synthesis or H2 optimization technique, were formulated to include the plant model. H2 optimization technique finds a controller which minimizes the H2 norm of the closedloop transfer function and internally stabilizes the system [7].
In this work, a robust compensator was developed for the TCP/AQM system performance and stability improvement and robustness using H2 synthesis. To achieve the performance and stability improvement and robustness, the reference tracking error must be reduced possibly to 0dB, settling time must be reduced to less than one second, the gain and phase margins (i.e., stability margins) must be greater than or equal to 20dB and 60deg [8] respectively.

LITERATURE REVIEW

Transport Control Protocol
TCP is a network communication protocol designed to send data packets over the Internet through the International Standard Organization (OSI) layer. It is a transport layer
protocol in the OSI layer and it is used to create a connection between remote computers by transporting and ensuring the delivery of messages over supporting networks and the Internet. The message sender continuously probes the networks available bandwidth and increases its window size to garner maximum share of network resource after every successful transmission. For every successful endtoend packet transmission, TCP increases the senders window size. On the other hand, TCP reduces or cuts the window size in half whenever a senders packet does not reach the receiver and this causes packet loss. Such packet losses can affect network performance and reliability by decreasing the senders effective transmission rate and increasing delay due to packet retransmission. Some of the drawbacks of this scheme include flowsynchronization [3] and performance degradation due to the excessive timeouts and restarts arising when the trailing end of a sequence of data packets is dropped [2].

Active Queue Management (AQM)
AQM is a controller mechanism to identify congestion before the router buffers become full [9]. Thus, it detects congestion at the early stage. It was designed to maintain dropping/marking probabilities, the routers probabilistically drop or mark packets before the queue is full. An Active Queue Management system is used to control the length of a queue so that it does not run full, adding its maximum (usually bloated) delay under load. Such management also enables TCP to do its job of sharing links properly, without which it cannot function as intended. AQM behavior is influenced by variations in main network parameters such as link capacity and number of TCP sessions. Generally, these parameters do not have static values, but in some conditions, it is possible to assume their variations negligible. Most of AQM methods are designed for networks with limited parameter variations.

H2 Synthesis
H2 control theories have been active areas of research for the years and have been successfully introduced to many engineeing applications [7]. It is a method of robust controller design which makes use of weights to form an augmented form of the plant to be controlled and produces a controller through loopshaping. H2 optimization finds a controller which minimizes the H2 norm of the closedloop transfer function and internally stabilizes the system [7]. The H2 norm of a signal is the mean energy with respect to the frequency. If there are uncertainties in the system model, some quantity combining the H2 synthesis can be a desirable measure of a systems robust performance. Thus the H2 performance criterion provides an interesting measure for the controller evaluation. The theory of H2 synthesis was discussed in [10, 11] and the theoretic motivation for the H2 control problem was discussed in [12]. The same method is used for convex parameterization of fixedorder Hinfinity controllers in [13]. The robustness capabilities and application of H2 and its iteration limits are discussed in [14].

FluidFlow Model of TCP Behaviour
The TCP/AQM has been modeled in [15, 16, 17] using the fluid flow modeling method. This mathematical model is described by a secondorder system with time delay. The
dynamic model of TCP flows is developed by using a fluid flow model without considering slow start and timeout mechanisms [18]. Based on this system, a type of AQM is constructed, which takes into account delays into the network. This model is described by the following nonlinear differential equations. This model is described by the following nonlinear differential equations [17]:
(1)
where and denote the timederivatives of W(t) and q(t) , respectively. W(t) denotes the TCP window size, q(t) denotes the queue length in the router.
p(t ) denotes the probability packet marking/dropping . R(t) denotes the roundtrip time, C(t) denotes the link capacity. Tp denotes the propagation delay. N(t) denotes the load factor (Number of TCP sessions). The first differential equation in equation (1) describes the TCP window control dynamic and the second equation models the bottleneck queue length. The queue length and window size are positive, bounded quantities, i.e., , W window size, respectively. Also, the marketing probability p takes value only in [0,1]. In this model, the congestion window W(t) increases linearly if no packet loss is detected; otherwise it halves. Although an AQM router is a nonlinear system, in order to analyze certain types of properties and design controllers, a linear model is needed. To linearize (1), first it was assumed that the number of TCP sessions and link capacity are constant, i.e., N(t)N ,C(t) C.
Taking (W, q) as the state and p as input, the operating point (W0,q0, p0) is then defined by and so that , , , , .
Linearizing (1) about the operating point to obtain:
(2)
Where , , represent the perturbed variables around the operating point.
For typical network conditions [18],
(3)
Considering the following dynamics and performing Laplace transform on (3), gives:
(4)
mathematical model. This difference is therefore controlled using a controller which has especially some robustness characteristics. Considering the fluid flow model of the TCP/AQM mathematical equation in (4) The TCP queue system can simplified as follows:
(5)
Where: ,
As the network parameter {N, C, R0} are positive, where R0> 0 is the time delay, and C(s) is the first order controller having the form.
where is the TCPs dynamic, is the queues dynamic
Substituting B and Q in equation (5), gives:
(6)

Related Works
Robustness has been an important issue in control systems design [19]. Robust control is a vital area in control design that is gaining more popularity and interest every day. Recently, it has been considered in the most automatic control because of its control goals. A successfully designed control system should be always able to maintain stability and performance level in spite of uncertainties in system dynamics and/or in the working environment to a certain degree [19]. Design requirements such as gain margin and phase margin in using classical frequencydomain techniques are solely for the purpose of robustness [19]. In [20] a robust Controller/Observer for TCP/AQM network was designed: First application to intrusion detection systems for drone fleet. Their work aims at realizing a robust congestion control system for TCP/AQM network of the drone fleet. This an important aspect of the robust control application because the drone requires a reliable and stable congestion control despite significant disturbances it may experience due to its required speed of control signal communications. The analyses for the controller design were mostly carried out in time domain which does not determine the appropriate robustness characteristics such as the gain and phase margins for a controlled system. The trajectory tracking error was not determined; this shows the proper performance of the system output for performance robustness was carried in [2]. Some recent works have shown the benefit of using proportional feedback in TCP/AQM networks. By using proportional feedback, the marking probability is proportional to the instantaneous queue length. They worked on addressing the nonlinearities directly and establishing some stability results when the marking is proportional. In the case of delay free marking, they showed the systems equilibrium point to be asymptotically stable for all proportional gains.


METHODOLOGY
The performance enhancement or optimization of every physical system requires capturing the behaviors of the system in a mathematical equation which makes it possible to easily analyze and enhance the system more adequately. However, the mathematical equation or model of a physical system does not show completely the system. Hence there is always a difference between the real physical system and its
A. Robust Compensator Development Using H2 Synthesis
Considering the closedloop AQM system with K(s) as the transfer function of the compensator, and G(s) as the transfer function of the plant dynamic as shown in figure 1, the output of the system is measured, fedback and compared with the reference input or the desired output to produce an error signal which is to be controlled or compensated by the compensator. This model presents the dynamics of the queue and the congestion window as a time delay system. Taking into account this characteristic, it is expected to reflect the TCP queue behavior in control congestion.
Figure 1: Block diagram of the TCP queue system plant The mathematical model of the controlled TCP plant in
figure 1 is expressed as follows:
(7)
Figure 2: TCP Queue plant Closedloop control with the weights
Applying the weighting functions Ws, Wks and Wt to the TCP plant G(s) as shown in figure 2 and applying the H2 synthesis syntax to generate the controller K for the system optimization. The augmented function P, is generated as follows:
(8)
Then the compensator is developed in state space format as follows:
(9)
To generate the controlled system function CL the expression becomes:
220
200
180
Magnitude (dB)
Magnitude (dB)
160
140
120
100
80
60
TCP/AQM Unit Response vs frequency
System: G
Gain Margin (dB): 68.3 At frequency (rad/s): 402 Closed loop stable? No
System: G
Gain Margin (dB): 68.3 At frequency (rad/s): 402 Closed loop stable? No
40
40
System: G
Peak gain (dB): 214
At frequency (rad/s): 4e11
System: G
Gain Margin dB): 147
At frequency (rad/s): 3.44 Closed loop stable? No
Sys Gai At f Clo
tem: G
n Margin (dB): 71.9 requency (rad/s): 327 sed loop stable? No
System: G
Peak gain (dB): 214
At frequency (rad/s): 4e11
System: G
Gain Margin (dB): 147
At frequency (rad/s): 3.44 Closed loop stable? No
Sys Gai At f Clo
tem: G
n Margin (dB): 71.9 requency (rad/s): 327 sed loop stable? No
(10) 4 2
10 10
0 2
10 10
The developed robust compensator K was applied in equation
(7) to analyze the behavior of the H2 compensated TCP queue system.
The following network parameters were used for the simulation and adopted from (Testouri et al., 2012): N=60, C=3750 packets/s and R0= 0.25s.

RESULTS AND DISCUSSION
Figures 3 and 4 show the TCP Queue responses in time and frequency domains.
Frequency (rad/s)
Figure 4: TCP queue response in frequency
The TCP queue recorded 214 seconds of peak magnitude which is an improvement. However, it recorded a negative gain margin of 71.9d which shows that the system is unstable.
A. H2 Compensated TCP Queue Analysis Results
The weights that achieved the desired loop shape of the optimization are presented as follows:
10
x 10
System: G
Settling time (seconds): 1.96e+03
System: G
Peak amplitude: >= 5.27e+10 Overshoot (%): 0
At time (seconds): > 4.5e+03
System: G
Settling time (seconds): 1.96e+03
System: G
Peak amplitude: >= 5.27e+10 Overshoot (%): 0
At time (seconds): > 4.5e+03
6
TCP/AQM Unit Response vs time
(11)
5 (12)
Figure 5 shows the H2 compensated TCP Queue response in
Amplitude
Amplitude
4 time domain while figure 6 shows the H2 compensated TCP Queue response in frequency domain. Figure 7 shows the H2 compensated TCP Queue sensitivity plot. Figure 8 shows the
3 H2 compensated TCP Queue open loop gain graph while figure 9 shows the H2 compensated TCP Queue open loop
2 phase graph.
1
1
0.9
System: CS I/O: y to Out(1)
System: CS I/O: y to Out(1)
0
0 500 1000 1500 2000 2500 3000 3500 4000 4500
Time (seconds)
Figure 3: TCP Queue response in time
The TCP queue recorded a settling time of 1.96e+03 seconds which is very high and it shows a very low speed characteristic.
0.8
TCP Queue Amplitude
TCP Queue Amplitude
0.7
0.6
0.5
0.4
Settling time (seconds): 0.000419 Peak amplitude: >= 0.995
Overshoot (%): 0
At time (seconds): > 0.0006
0.3
0.2
0.1
0
0 1 2 3 4 5 6
Time (seconds)
4
x 10
Figure 5: H2 Compensated TCP queue complementary sensitivity in time domain
Settling time in figure 5 was reduced to 0.000419 seconds which can support fast information transfer.
0
10
20
TCP Queue Magnitude (dB)
TCP Queue Magnitude (dB)
System: CS
60
40
20
TCP Queue Magnitude (dB)
TCP Queue Magnitude (dB)
0
20
40
System: OLG I/O: In(1) to y
Peak gain (dB): 57.9
At frequency (rad/s): 4e11
System: OLG
Gain Margin (dB): 20.3
System: OLG I/O: In(1) to y
Frequency (rad/s): 1.11e+04 Magnitude (dB): 3.04
30
40
50
Gain Margin (dB): 19.4
At frequency (rad/s): 5.69e+04 Closed loop stable? Yes
60
80
At frequency (rad/s): 5.69e+04 Closed loop stable? Yes
60
100
70
80
120
140
1 0
1 2 3 4 5 6 7
10 10 10 10 10 10 10 10 10
90
100
0 1
10 10
2 3 4 5
10 10 10 10
Frequency (rad/s)
Frequency (rad/s)
Figure 8: H2 Compensated TCP Queue open loop gain graph
6
10
In figure 8, the loop gain recorded peak magnitude of 57.9dB
Figure 6: H2 Compensated TCP Queue complementary sensitivity in frequency domain
The H2 compensated TCP queue recorded a reference tracking error of 0dB and it tracked the 0dB for long frequency range. This shows enhanced performance of the H2 compensated TCP queue system.
10
and gain margin of 20.3dB. This means that the system achieved good stability.
System: OLG
Phase Margin (deg): 78.9 Delay Margin (sec): 0.000176 At frequency (rad/s): 7.81e+03 Closed loop stable? Yes
System: OLG
Phase Margin (deg): 78.9 Delay Margin (sec): 0.000176 At frequency (rad/s): 7.81e+03 Closed loop stable? Yes
0
45
0
TCP Queue Magnitude (dB)
TCP Queue Magnitude (dB)
10
20
30
System: SD I/O: y to Out(1)
Peak gain (dB): 1.54
At frequency (rad/s): 3.25e+04
90
TCP Queue Phase (deg)
TCP Queue Phase (deg)
135
180
225
40
270
1 0 1 2
3 4 5 6 7
10 10
10 10
10 10 10 10 10
Frequency (rad/s)
50
60
1 0 1 2 3 4 5
10 10 10 10 10 10 10
Frequency (rad/s)
Figure 7: H2 Compensated TCP Queue sensitivity plot
The sensitivity graph recorded peak gain of 0.024dB which means the system recorded less sensitivity to disturbance.
Figure 9: H2 Compensated TCP Queue open loop phase graph
In figure 9 the system recorded phase margin of 78.9deg. This shows that the improved system is robustly stable. The H2 compensated TCP achieved reduced settling time of 0.000419 seconds and overshoot of 0%, which show that system improved in performance. The system achieved gain margin of 20.3dB and phase margin of 78.9deg. This means that the H2 compensated TCP queue system achieved robust performance and stable. The generated compensated K transfer function is expressed as follows:
(13)

CONCLUSION
The aim of this work which is to enhance the performance and stability of the TCP queue network system using H2 synthesis technique was successfully achieved. In order to improve the performance and stability of the TCP queue
network system so that it can maintain optimal performance and good stability even in the presence of significant disturbance, a robust compensator was designed using H2 synthesis technique.
The TCP model was analyzed and it was observed that the system was unstable and very slow with high settling time. The H2 optimized TCP (H2TCP) was able to achieve improved performance with reduced settling time of 0.000419 seconds which means that the system becomes faster in addressing congestion issues and other disturbances. The H2TCP queue system also achieved 0dB tracking error and robust stability margins of 20.3dB gain margin and 78.9degrees phase margin.
It was concluded that the H2 synthesis optimization achieved TCP queue improved performance and stability robustness characteristics [21] with good network throughput.
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