=Paper= {{Paper |id=Vol-1839/MIT2016-p16 |storemode=property |title= Model of neuro-fuzzy prediction of confirmation timeout in a mobile ad hoc network |pdfUrl=https://ceur-ws.org/Vol-1839/MIT2016-p16.pdf |volume=Vol-1839 |authors=Igor Konstantinov,Kostiantyn Polshchykov,Sergej Lazarev,Olha Polshchykova }} == Model of neuro-fuzzy prediction of confirmation timeout in a mobile ad hoc network== https://ceur-ws.org/Vol-1839/MIT2016-p16.pdf

Mathematical and Information Technologies, MIT-2016 — Information technologies

Model of Neuro-Fuzzy Prediction of
Confirmation Timeout in a Mobile Ad Hoc
Network

Igor Konstantinov, Kostiantyn Polshchykov, Sergej Lazarev, and
Olha Polshchykova

Belgorod State University,
Pobeda Street 85, 308015 Belgorod, Russia
{konstantinov,polshchikov,lazarev,polshchikova}@bsu.edu.ru
http://www.bsu.edu.ru

Abstract. Confirmation timeout (Round Trip Time, RTT) is an im-
portant value in data networks. Correct prediction of this characteristic
allows us to estimate the network load in order to adequately select
packet sending and retransmission parameters. Approximate heuristic
models are used in the Transmission Control Protocol (TCP) for Round
Trip Time evaluation. The values of the coefficients in these models were
obtained experimentally for fixed topology networks. Therefore, the use
of these models in a dynamic topology network (mobile ad-hoc network)
is inefficient. This article represents an RTT prediction model based on
application of fuzzy neural network theory. This model relies upon zero-
order Sugeno-Type Fuzzy Inference algorithm. The input values of fuzzy
neural network are RTT values measured in the current and two previous
cycles. The output value is RTT value expected in the next cycle. The
proposed model is set up and examined by means of simulation exper-
iments. In these experiments the functioning of mobile ad-hoc network
which is used for communication software while counteracting emergen-
cies was simulated.

Keywords: neuro-fuzzy prediction, round trip time, mobile ad hoc net-
works, dangerous construction sites.

1 Introduction

Mobile ad hoc networks (MANET) are a promising direction in the development
of telecommunication technologies [1]. With its decentralized structure, ad hoc
networks provide the ability to transmit information when nodes are moving
randomly and under the impact of destructive factors [2, 3]. Due to rapid de-
ployment, autonomous power of each node, high survivability and the ability
to deliver messages with dynamically changing topology, ad hoc network can
be used for communication on dangerous construction sites [4]. Construction of
dangerous objects is carried out under the threat of destructive and damaging

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Mathematical and Information Technologies, MIT-2016 — Information technologies

natural and man-made factors that can cause explosions, fire, collapse, flooding,
radiation, poisoning and other emergencies.
The process of information exchange in a mobile ad hoc network is based
on the implementation of the packet data transfer. One of the important char-
acteristics in this case is RTT. Correct prediction of this value allows us to
estimate the network load to adequately select the parameters of packet sending
and retransmissions. Approximate heuristic models are used in the TCP for its
evaluation [5, 6]. The values of the coefficients in these models were obtained
experimentally for networks with a fixed topology, that is why their use in the
ad hoc networks does not give the desired effect. As a result, time of informa-
tion delivery increases significantly, which is unacceptable in the construction
of dangerous buildings, as the life and health of builders, as well as the ex-
tent of damage to constructed facilities, depend on the operational efficiency of
messages receiving in emergencies. Therefore, the development of an adequate
RTT forecasting model in the mobile ad hoc network is a topical applied science
problem, the solution of which is represented in the following researches.

2 Development of Neuro-Fuzzy Model

The neuro-fuzzy model is suggested to predict RTT in an ad hoc network. The
following values are used in this model: 𝑀 is RTT value measured in the current
cycle; 𝑀 𝑝𝑟1 is RTT value measured in the previous cycle; 𝑀 𝑝𝑟2 is RTT value
measured in the cycle preceding the previous one. The model allows us to cal-
culate the estimated value 𝑀 ̃︁ of the confirmation timeout for each of the next
cycles.
Construction of the model is carried out on the criterion of minimal com-
plexity. The following parameters correspond to this criterion: fuzzy inference
algorithm is the zero-order Sugeno [7], the number of membership functions for
each input value is 2, the shape of membership functions for each input value
is triangular, neuronal learning algorithm is error propagation [8]. The model is
using the following fuzzy rulebase:

̃︁ = 𝐽1 );
𝐼𝑓 (𝑀 = 𝑋1 )𝑎𝑛𝑑(𝑀 𝑝𝑟1 = 𝑌1 )𝑎𝑛𝑑(𝑀 𝑝𝑟2 = 𝑍1 ), 𝑡ℎ𝑒𝑛(𝑀 (1)

̃︁ = 𝐽2 );
𝐼𝑓 (𝑀 = 𝑋1 )𝑎𝑛𝑑(𝑀 𝑝𝑟1 = 𝑌1 )𝑎𝑛𝑑(𝑀 𝑝𝑟2 = 𝑍2 ), 𝑡ℎ𝑒𝑛(𝑀 (2)

...

̃︁ = 𝐽8 );
𝐼𝑓 (𝑀 = 𝑋2 )𝑎𝑛𝑑(𝑀 𝑝𝑟1 = 𝑌2 )𝑎𝑛𝑑(𝑀 𝑝𝑟2 = 𝑍2 ), 𝑡ℎ𝑒𝑛(𝑀 (3)

where 𝑋1 , 𝑋2 , 𝑌1 , 𝑌2 , 𝑍1 , 𝑍2 are terms number 1 and number 2 of the input
values 𝑀 , 𝑀 𝑝𝑟1 , 𝑀 𝑝𝑟2 ; 𝐽1 ... 𝐽8 are individual conclusions of the fuzzy rules.
Type and parameters of the membership functions for each input value are
shown in Fig. 1, Fig. 2 and Fig. 3.

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µ1(M) µ2(M)
1

X1 X2

ax1 ax2 bx1 bx2 M

Fig. 1. Type and parameters of the membership functions for the value 𝑀

µ1(M pr1) µ2(M pr1)
1

Y1 Y2

ay1 ay2 by1 by2 M pr1

Fig. 2. Type and parameters of the membership functions for the value 𝑀 𝑝𝑟1

µ1(M pr2) µ2(M pr2)
1

Z1 Z2

az1 az2 bz1 bz2 M pr2

Fig. 3. Type and parameters of the membership functions for the value 𝑀 𝑝𝑟2

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The model of forecasting Round Trip Time includes four structural neural
layers. Fuzzification procedure is performed by means of the first layer of neurons:
⎧
⎨ 1, 𝑀 < 𝑎𝑥1 ;
𝑏𝑥1 −𝑀
𝜇1 (𝑀 ) = 𝑏𝑥1 −𝑎𝑥1 , 𝑎𝑥1 ≤ 𝑀 < 𝑏𝑥1 ; (4)
⎩
0, 𝑀 ≥ 𝑏𝑥1 ;
⎧
⎨ 0, 𝑀 < 𝑎𝑥2 ;
𝑀 −𝑎𝑥2
𝜇2 (𝑀 ) = 𝑏𝑥2 −𝑎𝑥2 𝑥2 ≤ 𝑀 < 𝑏𝑥2 ;
, 𝑎 (5)
⎩
1, 𝑀 ≥ 𝑏𝑥2 ;
⎧
⎪
⎨ 1, 𝑀 𝑝𝑟1 < 𝑎𝑦1 ;
𝑝𝑟1
−𝑀
𝜇1 (𝑀 𝑝𝑟1 ) = 𝑏𝑦1
𝑏 −𝑎 , 𝑎𝑦1 ≤ 𝑀 𝑝𝑟1 < 𝑏𝑦1 ; (6)
⎪
⎩ 0, 𝑦1 𝑦1 𝑀 𝑝𝑟1 ≥ 𝑏 ;
𝑦1
⎧
𝑝𝑟1
⎪
⎨ 0, 𝑝𝑟1 𝑀 < 𝑎𝑦2 ;
−𝑎𝑦2
𝜇2 (𝑀 𝑝𝑟1 ) = 𝑀𝑏𝑦2 −𝑎 , 𝑎𝑦2 ≤ 𝑀 𝑝𝑟1 < 𝑏𝑦2 ; (7)
⎪
⎩ 1, 𝑦2
𝑝𝑟1
𝑀 ≥ 𝑏𝑦2 ;
⎧ 𝑝𝑟2
⎨ 1, 𝑀 < 𝑎𝑧1 ;
𝑝𝑟2 𝑏𝑧1 −𝑀 𝑝𝑟2
𝜇1 (𝑀 ) = , 𝑎𝑧1 ≤ 𝑀 𝑝𝑟2 < 𝑏𝑧1 ; (8)
⎩ 𝑏𝑧1 −𝑎𝑧1
0, 𝑀 𝑝𝑟2 ≥ 𝑏𝑧1 ;
⎧
⎨ 0, 𝑝𝑟2 𝑀 𝑝𝑟2 < 𝑎𝑧2 ;
𝑝𝑟2 𝑀 −𝑎𝑧2
𝜇2 (𝑀 ) = , 𝑎𝑧2 ≤ 𝑀 𝑝𝑟2 < 𝑏𝑧2 ; (9)
⎩ 𝑏𝑧2 −𝑎𝑧2 𝑝𝑟2
1, 𝑀 ≥ 𝑏𝑧2 .
Aggregation procedure is performed by the second layer of neurons:
𝐺1 = 𝜇1 (𝑀 ) ∧ 𝜇1 (𝑀 𝑝𝑟1 ) ∧ 𝜇1 (𝑀 𝑝𝑟1 ); (10)
𝑝𝑟1 𝑝𝑟1
𝐺2 = 𝜇1 (𝑀 ) ∧ 𝜇1 (𝑀 ) ∧ 𝜇2 (𝑀 ); (11)
...
𝐺8 = 𝜇2 (𝑀 ) ∧ 𝜇2 (𝑀 𝑝𝑟1 ) ∧ 𝜇2 (𝑀 𝑝𝑟1 ). (12)
Activation is a part of the ∑︀8defuzzification procedure. Calculation of the
amount of aggregated results 𝑟=1 𝐺𝑟 and the weighted sum of the aggregate
∑︀8
results 𝑟=1 𝐽𝑟 𝐺𝑟 are performed by means of the third layer of neurons.
The final part of defuzzification procedure is performed by means of the
fourth layer: ∑︀8
̃︁ 𝐽𝑟 𝐺𝑟
𝑀 = ∑︀𝑟=1 8 . (13)
𝑟=1 𝐺𝑟
In order to obtain the coefficient values needed to calculate membership
function, it is required to set the weights of neurons of the first layer. Training
of the neurons of the third layer is needed for evaluating the values of individual
fuzzy rules conclusions [9–15]. The receiving of training data for model setup
and evaluation of neuro-fuzzy forecasting RTT are carried out on the basis of
modeling of various scenarios of ad-hoc network application for communication
on dangerous construction sites.

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3 Modeling Information Streams Transmission

Let us consider an example in which mobile ad hoc network is used for commu-
nication in the construction of underground facilities. Fig. 4 and Fig. 5 show the
area of the construction works (limited by bold dotted line).

2
3
+

4 5

7 8 9

Fig. 4. The routes of transmission of information flows in a fixed network topology

This building belongs to the dangerous construction projects, because works
on its construction are carried out in the conditions of a possible collapse of
rocks. Works are carried out by a personnel shift which consists of:
1) head of the shift who uses ad hoc node 1;
2) eight workers equipped with ad hoc nodes with numbers 2-9.
Ad hoc units are denoted by small numbered circles, and coverage areas of
these units are limited by the corresponding circles of larger radius. The following
functions are performed by means of ad hoc nodes:
1) video streams to monitor the status of the facility, conditions and the
course of the work;
2) exchange of voice messages to control the construction process and the
coordination of countering emergencies;
3) transfer of data on the functional status and current location coordinates of
the builders, as well as data of monitoring external conditions on the construction
site.
In the given example the transmission of information streams is carried out
in an ad hoc network for a period of time of observation which lasts 50 seconds.
The characteristics of the streams are represented in Table 1 and Table 2.
Fig. 4 shows the situation where the network topology remains unchanged
during the considered time interval. The routes of information streams trans-

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3
2

4
5

7 8

Fig. 5. The routes of transmission of information flows in a dynamic network topology

Table 1. Characteristics of the transmitted information streams

Stream Type of Sending Receiving Transmission
number of transferred node number node number start time, s
1 video 4 1 0
2 data 5 1 8
3 acknowledgements 1 5 8
4 data 9 1 12
5 acknowledgements 1 9 12
6 voice 7 1 16
7 voice 1 7 16
8 video 8 1 22

Table 2. Estimated parameters

Parameter Value
Throughput of the radio channel 1000 Kbit/s
Throughput required to transmit video 256 Kbit/s
Throughput required to transmit voice 128 Kbit/s
Size of messages transmitted by data flow 1 MB

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mission correspond to the broken lines which connect the nodes-senders and
nodes-recipients.
Fig. 5 shows a scenario where an ad hoc network topology changes due to
the collapse of rock, which began at time 𝑡𝑒 =4 s. Collapse zone is highlighted
in gray. As a result of emergency workers who used ad hoc nodes 6 and 9 were
in the collapse zone and node 6 malfunctioned (corresponding circle in Fig. 5 is
crossed).
In response to the collapse, workers with ad hoc nodes 3-5, 8 and 9 have
moved. The locations of these nodes at the initial time in Fig. 5 are marked
by the dashed circles. In the modified network structure in Fig. 5 routes that
transmit information streams (numbered 2, 3, 5–8) differ from the corresponding
streams marked in Fig. 4.
Dynamism of network topology had an impact on the radio channels workload
and throughput available for transmission of data flows. For example, a radio
channel connecting the node 2 to node 1, except for the main streams of 1, 4
and 6, additional streams 2 and 8 started to transmit.
The responsiveness of the node 1 receiving the data file transmitted from the
node 9 is of great importance in an emergency. This file contains information
about the current parameters of health status and location of the worker who
has been exposed to the collapse. On the basis of the data head of the shift
can quickly and effectively coordinate the actions of other workers to rescue the
injured builder.
For the file to be delivered, streams 4 and 5 need to be transferred. The
combination of these interrelated streams is called a controlled flow (CF) [16].
The closed circuit formed by the channels through which CF is transferred is
called CF-circuit (Fig. 6).

Node 5 Node 2
Channel 5

C
l6

ha
ne

nn
n

el
ha

4
C

Node 9 Node 1
(Sender) (Recipient)
C
ha
3

nn
el
nn

el
1
ha
C

Channel 2
Node 5 Node 2

Fig. 6. CF-circuit

Duration of data file delivery from node 9 to node 1 is directly dependent on
the value 𝐸(𝑡), the current CF-circuit throughput available for CF transmission.

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To calculate this value, one should use the expression:

𝐸(𝑡) = 𝑚𝑖𝑛{𝐸𝑘 (𝑡)}, (14)

where 𝐸𝑘 (𝑡) is the current value of the channel throughput 𝑘 of the CF-circuit
[17].
The value 𝐸𝑘 (𝑡) can be figured out from the formula:
{︃
0, 𝑈𝑘 (𝑡) ≥ 𝑐;
𝐸𝑘 (𝑡) = 𝑐−𝑈𝑘 (𝑡) (15)
𝐷𝑘 (𝑡) , 𝑈𝑘 (𝑡) < 𝑐;

where 𝑐 is the throughput of the radio channel; 𝑈𝑘 (𝑡) is the current value of
the channel throughput 𝑘 required to transmit real-time streams; 𝐷𝑘 (𝑡) is the
number of data streams, having to be transmitted over the channel by the time
𝑡, 𝐷𝑘 (𝑡) ≥ 1.
The value 𝑈𝑘 (𝑡) can be determined using the following expression:
𝐿
∑︁
𝑈𝑘 (𝑡) = 𝑢𝑘𝑙 (𝑡), (16)
𝑙=1

where 𝑢𝑘𝑙 (𝑡) is the current value of the channel 𝑘 throughput required for real-
time stream transmission 𝑙; 𝐿 is the number of real-time streams, which need to
be transmitted on the CF-circuit channels.
The value of 𝑢𝑘𝑙 (𝑡) can be found from the formula:
{︂
𝜆𝑙 𝑎𝑘𝑙 , 𝑥𝑠𝑡𝑎𝑟𝑡
𝑙 ≤ 𝑡 < 𝑥𝑠𝑡𝑜𝑝
𝑙 ;
𝑢𝑘𝑙 (𝑡) = 𝑠𝑡𝑜𝑝 (17)
0, 𝑡 < 𝑥𝑠𝑡𝑎𝑟𝑡
𝑙 or 𝑡 ≥ 𝑥 𝑙 ,

where 𝜆𝑙 is the value of the bandwidth of the channel 𝑘 required to transmit
real-time stream 𝑙 [18]; 𝑎𝑘𝑙 is the value showing whether the transmission channel
is required on real-time stream 𝑙 channel 𝑘; 𝑥𝑠𝑡𝑎𝑟𝑡
𝑙 and 𝑥𝑠𝑡𝑜𝑝
𝑙 are instants of the
beginning and the end of transmission of real-time stream 𝑙.
The minimum possible duration of the CF transmission can be determined
using the following formula:
𝑠𝑡𝑜𝑝 𝑠𝑡𝑎𝑟𝑡
𝜏𝐶𝐹 = 𝜏𝐶𝐹 − 𝜏𝐶𝐹 , (18)
𝑠𝑡𝑎𝑟𝑡 𝑠𝑡𝑜𝑝
where 𝜏𝐶𝐹 is starting time of CF transmission; 𝜏𝐶𝐹 is closure time of CF-
stream transmission without packet loss and an ideal correspondence between
the intensity of sending data of the stream and the bandwidth of CF-circuit
available for the transmission.
𝑠𝑡𝑜𝑝
The value 𝜏𝐶𝐹 is calculated on the basis of the obtained values 𝐸( 𝑡). To do
this, use the formula:
∫︁ 𝜏𝐶𝐹
𝑠𝑡𝑜𝑝

𝑉 = 𝐸(𝑡) 𝑑𝑡, (19)
𝑠𝑡𝑎𝑟𝑡
𝜏𝐶𝐹

where 𝑉 is the size of the message transmitted by data flow.

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Table 3. 𝜆𝑙 , 𝑥𝑠𝑡𝑎𝑟𝑡
𝑙 and 𝑥𝑠𝑡𝑜𝑝
𝑙 values

𝑙 𝜆𝑙 , bit/s 𝑥𝑠𝑡𝑎𝑟𝑡
𝑙 ,s 𝑥𝑠𝑡𝑜𝑝
𝑙 ,s
1 256 0 >50
2 128 16 >50
3 128 16 >50
4 256 22 >50

Table 4. 𝑎𝑘𝑙 values

𝑘 𝑙=1 𝑙=2 𝑙=3 𝑙=4
1 0 0 0 0
2 0 0 0 1
3 1 1 0 1
4 0 0 1 0
5 0 0 0 0
6 0 0 0 0

E(t),
Kb/s
400
300
200
τCF
100

12 14 16 18 20 22 24 26 28 30 32 34 36 38 t, s

Fig. 7. The current values 𝐸(𝑡) in a network with a dynamic topology

E(t),
Kb/s
800
600
400
τCF
200

12 14 16 18 20 22 24 t, s

Fig. 8. The current values 𝐸(𝑡) in fixed topology network

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To calculate the function 𝐸(𝑡) in the case shown in Fig. 4 and Fig. 5, we used
data contained in Table 3 and Table 4.
Using these inputs, the function 𝐸(𝑡) is calculated and its form is shown in
Fig. 7. The fixed network topology function 𝐸(𝑡) has the form shown in Fig. 8.
Analysis of Fig. 7 and Fig. 8 shows that the change in the network topol-
ogy during information exchange leads to a significant deceleration of data file
transmission duration. In a network with a dynamic topology the value 𝜏𝐶𝐹 is
set to 39.7 s, and in case of a fixed network structure it is 𝜏𝐶𝐹 =24.2 s.

4 Setting Parameters of the Model and the Evaluation of
the Effectiveness of Its Application

In real operating conditions an ad hoc network overload and packet loss fre-
quently occur, so the actual value of the data file transfer duration can sig-
nificantly exceed the calculated value 𝜏𝐶𝐹 . To evaluate these characteristics a
number of simulation experiments were made, in which various scenarios of ap-
plying an ad hoc network for providing connectivity on dangerous construction
sites were simulated. For this purpose, a simulation model of information streams
transmissions in a network with dynamic topology was used. It was developed
in MatLab Simulink software environment. The simulation results provided ev-
idence for setting developed neuro-fuzzy model forecasting round trip time. On
the basis of these data the training matrix of the following form is made:
⎛ ⎞
𝑀1 𝑀2 𝑀3 𝑀4
⎜ 𝑀2 𝑀3 𝑀4 𝑀5 ⎟
⎜ ⎟
⎜ . . . . ⎟
⎜ ⎟ (20)
⎜ 𝑀𝑖 𝑀(𝑖+1) 𝑀(𝑖+2) 𝑀(𝑖+3) ⎟
⎜ ⎟
⎝ . . . . ⎠
𝑀(𝐼−3) 𝑀(𝐼−2) 𝑀(𝐼−1) 𝑀𝐼

where 𝑀𝑖 is a round trip time of confirmation in the loop 𝑖; 𝐼 is the number of
cycles in each simulation experiment, 𝐼=750.
Setting neuro-fuzzy model was carried out using software tools Fuzzy Logic
Toolbox. Table 5 shows the results of training the neurons of the first layer, while
Table 6 contains the results of training the neurons of the third layer.
To assess the efficiency of the developed and customized models, a number
of simulations for the transfer of information streams in an ad hoc network were
conducted. The selection of retransmission was simulated on the basis of the sug-
gested neuro-fuzzy forecasting RTT and the classical model of evaluation of this
quantity used in TCP. The results showed that the use of neuro-fuzzy forecast-
ing RTT in a large network load reduces deviations of timeout retransmission
on 5,7-19,2 percents. This contributes to minimizing retransmissions count and
average data stream transmission time by 4.2-9.6 percents.

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Table 5. Learning outcomes of the first layer of neurons

Parameter Value
𝑎𝑥1 3.64
𝑎𝑥2 25.18
𝑏𝑥1 3.62
𝑏𝑥2 27.90
𝑎𝑦1 3.69
𝑎𝑦2 28.10
𝑏𝑦1 3.55
𝑏𝑦2 27.79
𝑎𝑧1 3.61
𝑎𝑧2 28.01
𝑏𝑧1 3.62
𝑏𝑧2 27.81

Table 6. Learning outcomes of the third layer of neurons

Parameter Value
𝐻1 3.91
𝐻2 -6.02
𝐻3 7.26
𝐻4 8.74
𝐻5 31.51
𝐻6 20.74
𝐻7 27.92
𝐻8 26.49

5 Conclusion

Thus, the model of neuro-fuzzy prediction of confirmation timeout in the mobile
ad hoc network is synthesized. The model includes four neuron layers, performing
fuzzy inference procedure (fuzzification, aggregation, revitalization and defuzzi-
fication). To adjust the weights neurons we used training data, reflecting the
dynamics of the RTT in the ad hoc network used for communication on dan-
gerous construction sites. Simulations have shown that the use of the proposed
model for selecting timeout retransmission will significantly reduce the duration
of the transmission data flows in the mobile ad hoc network.

Acknowledgements. The research have been carried out with the financial
support of the Ministry of Education and Science of the Russian Federation (the
unique identifier of the project is RFMEFI57815X0138).

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