Mathematical and Information Technologies, MIT-2016 β€” 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 174 Mathematical and Information Technologies, MIT-2016 β€” 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 π‘π‘Ÿ1 is RTT value measured in the previous cycle; 𝑀 π‘π‘Ÿ2 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 )π‘Žπ‘›π‘‘(𝑀 π‘π‘Ÿ1 = π‘Œ1 )π‘Žπ‘›π‘‘(𝑀 π‘π‘Ÿ2 = 𝑍1 ), π‘‘β„Žπ‘’π‘›(𝑀 (1) ̃︁ = 𝐽2 ); 𝐼𝑓 (𝑀 = 𝑋1 )π‘Žπ‘›π‘‘(𝑀 π‘π‘Ÿ1 = π‘Œ1 )π‘Žπ‘›π‘‘(𝑀 π‘π‘Ÿ2 = 𝑍2 ), π‘‘β„Žπ‘’π‘›(𝑀 (2) ... ̃︁ = 𝐽8 ); 𝐼𝑓 (𝑀 = 𝑋2 )π‘Žπ‘›π‘‘(𝑀 π‘π‘Ÿ1 = π‘Œ2 )π‘Žπ‘›π‘‘(𝑀 π‘π‘Ÿ2 = 𝑍2 ), π‘‘β„Žπ‘’π‘›(𝑀 (3) where 𝑋1 , 𝑋2 , π‘Œ1 , π‘Œ2 , 𝑍1 , 𝑍2 are terms number 1 and number 2 of the input values 𝑀 , 𝑀 π‘π‘Ÿ1 , 𝑀 π‘π‘Ÿ2 ; 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. 175 Mathematical and Information Technologies, MIT-2016 β€” Information technologies Β΅1(M) Β΅2(M) 1 X1 X2 ax1 ax2 bx1 bx2 M Fig. 1. Type and parameters of the membership functions for the value 𝑀 Β΅1(M pr1) Β΅2(M pr1) 1 Y1 Y2 ay1 ay2 by1 by2 M pr1 Fig. 2. Type and parameters of the membership functions for the value 𝑀 π‘π‘Ÿ1 Β΅1(M pr2) Β΅2(M pr2) 1 Z1 Z2 az1 az2 bz1 bz2 M pr2 Fig. 3. Type and parameters of the membership functions for the value 𝑀 π‘π‘Ÿ2 176 Mathematical and Information Technologies, MIT-2016 β€” Information technologies 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 < π‘Žπ‘₯1 ; 𝑏π‘₯1 βˆ’π‘€ πœ‡1 (𝑀 ) = 𝑏π‘₯1 βˆ’π‘Žπ‘₯1 , π‘Žπ‘₯1 ≀ 𝑀 < 𝑏π‘₯1 ; (4) ⎩ 0, 𝑀 β‰₯ 𝑏π‘₯1 ; ⎧ ⎨ 0, 𝑀 < π‘Žπ‘₯2 ; 𝑀 βˆ’π‘Žπ‘₯2 πœ‡2 (𝑀 ) = 𝑏π‘₯2 βˆ’π‘Žπ‘₯2 π‘₯2 ≀ 𝑀 < 𝑏π‘₯2 ; , π‘Ž (5) ⎩ 1, 𝑀 β‰₯ 𝑏π‘₯2 ; ⎧ βŽͺ ⎨ 1, 𝑀 π‘π‘Ÿ1 < π‘Žπ‘¦1 ; π‘π‘Ÿ1 βˆ’π‘€ πœ‡1 (𝑀 π‘π‘Ÿ1 ) = 𝑏𝑦1 𝑏 βˆ’π‘Ž , π‘Žπ‘¦1 ≀ 𝑀 π‘π‘Ÿ1 < 𝑏𝑦1 ; (6) βŽͺ ⎩ 0, 𝑦1 𝑦1 𝑀 π‘π‘Ÿ1 β‰₯ 𝑏 ; 𝑦1 ⎧ π‘π‘Ÿ1 βŽͺ ⎨ 0, π‘π‘Ÿ1 𝑀 < π‘Žπ‘¦2 ; βˆ’π‘Žπ‘¦2 πœ‡2 (𝑀 π‘π‘Ÿ1 ) = 𝑀𝑏𝑦2 βˆ’π‘Ž , π‘Žπ‘¦2 ≀ 𝑀 π‘π‘Ÿ1 < 𝑏𝑦2 ; (7) βŽͺ ⎩ 1, 𝑦2 π‘π‘Ÿ1 𝑀 β‰₯ 𝑏𝑦2 ; ⎧ π‘π‘Ÿ2 ⎨ 1, 𝑀 < π‘Žπ‘§1 ; π‘π‘Ÿ2 𝑏𝑧1 βˆ’π‘€ π‘π‘Ÿ2 πœ‡1 (𝑀 ) = , π‘Žπ‘§1 ≀ 𝑀 π‘π‘Ÿ2 < 𝑏𝑧1 ; (8) ⎩ 𝑏𝑧1 βˆ’π‘Žπ‘§1 0, 𝑀 π‘π‘Ÿ2 β‰₯ 𝑏𝑧1 ; ⎧ ⎨ 0, π‘π‘Ÿ2 𝑀 π‘π‘Ÿ2 < π‘Žπ‘§2 ; π‘π‘Ÿ2 𝑀 βˆ’π‘Žπ‘§2 πœ‡2 (𝑀 ) = , π‘Žπ‘§2 ≀ 𝑀 π‘π‘Ÿ2 < 𝑏𝑧2 ; (9) ⎩ 𝑏𝑧2 βˆ’π‘Žπ‘§2 π‘π‘Ÿ2 1, 𝑀 β‰₯ 𝑏𝑧2 . Aggregation procedure is performed by the second layer of neurons: 𝐺1 = πœ‡1 (𝑀 ) ∧ πœ‡1 (𝑀 π‘π‘Ÿ1 ) ∧ πœ‡1 (𝑀 π‘π‘Ÿ1 ); (10) π‘π‘Ÿ1 π‘π‘Ÿ1 𝐺2 = πœ‡1 (𝑀 ) ∧ πœ‡1 (𝑀 ) ∧ πœ‡2 (𝑀 ); (11) ... 𝐺8 = πœ‡2 (𝑀 ) ∧ πœ‡2 (𝑀 π‘π‘Ÿ1 ) ∧ πœ‡2 (𝑀 π‘π‘Ÿ1 ). (12) Activation is a part of the βˆ‘οΈ€8defuzzification procedure. Calculation of the amount of aggregated results π‘Ÿ=1 πΊπ‘Ÿ and the weighted sum of the aggregate βˆ‘οΈ€8 results π‘Ÿ=1 π½π‘Ÿ πΊπ‘Ÿ are performed by means of the third layer of neurons. The final part of defuzzification procedure is performed by means of the fourth layer: βˆ‘οΈ€8 ̃︁ π½π‘Ÿ πΊπ‘Ÿ 𝑀 = βˆ‘οΈ€π‘Ÿ=1 8 . (13) π‘Ÿ=1 πΊπ‘Ÿ 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. 177 Mathematical and Information Technologies, MIT-2016 β€” Information technologies 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). 1 2 3 + 4 5 6 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- 178 Mathematical and Information Technologies, MIT-2016 β€” Information technologies 1 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 179 Mathematical and Information Technologies, MIT-2016 β€” Information technologies 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 𝑑𝑒 =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(𝑑), the current CF-circuit throughput available for CF transmission. 180 Mathematical and Information Technologies, MIT-2016 β€” Information technologies To calculate this value, one should use the expression: 𝐸(𝑑) = π‘šπ‘–π‘›{πΈπ‘˜ (𝑑)}, (14) where πΈπ‘˜ (𝑑) is the current value of the channel throughput π‘˜ of the CF-circuit [17]. The value πΈπ‘˜ (𝑑) can be figured out from the formula: {οΈƒ 0, π‘ˆπ‘˜ (𝑑) β‰₯ 𝑐; πΈπ‘˜ (𝑑) = π‘βˆ’π‘ˆπ‘˜ (𝑑) (15) π·π‘˜ (𝑑) , π‘ˆπ‘˜ (𝑑) < 𝑐; where 𝑐 is the throughput of the radio channel; π‘ˆπ‘˜ (𝑑) is the current value of the channel throughput π‘˜ required to transmit real-time streams; π·π‘˜ (𝑑) is the number of data streams, having to be transmitted over the channel by the time 𝑑, π·π‘˜ (𝑑) β‰₯ 1. The value π‘ˆπ‘˜ (𝑑) can be determined using the following expression: 𝐿 βˆ‘οΈ π‘ˆπ‘˜ (𝑑) = π‘’π‘˜π‘™ (𝑑), (16) 𝑙=1 where π‘’π‘˜π‘™ (𝑑) is the current value of the channel π‘˜ 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 π‘’π‘˜π‘™ (𝑑) can be found from the formula: {οΈ‚ πœ†π‘™ π‘Žπ‘˜π‘™ , π‘₯π‘ π‘‘π‘Žπ‘Ÿπ‘‘ 𝑙 ≀ 𝑑 < π‘₯π‘ π‘‘π‘œπ‘ 𝑙 ; π‘’π‘˜π‘™ (𝑑) = π‘ π‘‘π‘œπ‘ (17) 0, 𝑑 < π‘₯π‘ π‘‘π‘Žπ‘Ÿπ‘‘ 𝑙 or 𝑑 β‰₯ π‘₯ 𝑙 , where πœ†π‘™ is the value of the bandwidth of the channel π‘˜ required to transmit real-time stream 𝑙 [18]; π‘Žπ‘˜π‘™ is the value showing whether the transmission channel is required on real-time stream 𝑙 channel π‘˜; π‘₯π‘ π‘‘π‘Žπ‘Ÿπ‘‘ 𝑙 and π‘₯π‘ π‘‘π‘œπ‘ 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: π‘ π‘‘π‘œπ‘ π‘ π‘‘π‘Žπ‘Ÿπ‘‘ 𝜏𝐢𝐹 = 𝜏𝐢𝐹 βˆ’ 𝜏𝐢𝐹 , (18) π‘ π‘‘π‘Žπ‘Ÿπ‘‘ π‘ π‘‘π‘œπ‘ where 𝜏𝐢𝐹 is starting time of CF transmission; 𝜏𝐢𝐹 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. π‘ π‘‘π‘œπ‘ The value 𝜏𝐢𝐹 is calculated on the basis of the obtained values 𝐸( 𝑑). To do this, use the formula: ∫︁ 𝜏𝐢𝐹 π‘ π‘‘π‘œπ‘ 𝑉 = 𝐸(𝑑) 𝑑𝑑, (19) π‘ π‘‘π‘Žπ‘Ÿπ‘‘ 𝜏𝐢𝐹 where 𝑉 is the size of the message transmitted by data flow. 181 Mathematical and Information Technologies, MIT-2016 β€” Information technologies Table 3. πœ†π‘™ , π‘₯π‘ π‘‘π‘Žπ‘Ÿπ‘‘ 𝑙 and π‘₯π‘ π‘‘π‘œπ‘ 𝑙 values 𝑙 πœ†π‘™ , bit/s π‘₯π‘ π‘‘π‘Žπ‘Ÿπ‘‘ 𝑙 ,s π‘₯π‘ π‘‘π‘œπ‘ 𝑙 ,s 1 256 0 >50 2 128 16 >50 3 128 16 >50 4 256 22 >50 Table 4. π‘Žπ‘˜π‘™ values π‘˜ 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 Ο„CF 100 12 14 16 18 20 22 24 26 28 30 32 34 36 38 t, s Fig. 7. The current values 𝐸(𝑑) in a network with a dynamic topology E(t), Kb/s 800 600 400 Ο„CF 200 12 14 16 18 20 22 24 t, s Fig. 8. The current values 𝐸(𝑑) in fixed topology network 182 Mathematical and Information Technologies, MIT-2016 β€” Information technologies To calculate the function 𝐸(𝑑) 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(𝑑) is calculated and its form is shown in Fig. 7. The fixed network topology function 𝐸(𝑑) 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 𝜏𝐢𝐹 is set to 39.7 s, and in case of a fixed network structure it is 𝜏𝐢𝐹 =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 𝜏𝐢𝐹 . 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: βŽ› ⎞ 𝑀1 𝑀2 𝑀3 𝑀4 ⎜ 𝑀2 𝑀3 𝑀4 𝑀5 ⎟ ⎜ ⎟ ⎜ . . . . ⎟ ⎜ ⎟ (20) ⎜ 𝑀𝑖 𝑀(𝑖+1) 𝑀(𝑖+2) 𝑀(𝑖+3) ⎟ ⎜ ⎟ ⎝ . . . . ⎠ 𝑀(πΌβˆ’3) 𝑀(πΌβˆ’2) 𝑀(πΌβˆ’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. 183 Mathematical and Information Technologies, MIT-2016 β€” Information technologies Table 5. Learning outcomes of the first layer of neurons Parameter Value π‘Žπ‘₯1 3.64 π‘Žπ‘₯2 25.18 𝑏π‘₯1 3.62 𝑏π‘₯2 27.90 π‘Žπ‘¦1 3.69 π‘Žπ‘¦2 28.10 𝑏𝑦1 3.55 𝑏𝑦2 27.79 π‘Žπ‘§1 3.61 π‘Žπ‘§2 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). 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