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

Transcription

1 Mode of Neuro-Fuzzy Prediction of Confirmation Timeout in a Mobie Ad Hoc Network Igor Konstantinov, Kostiantyn Poshchykov, Sergej Lazarev, and Oha Poshchykova Begorod State University, Pobeda Street 85, Begorod, Russia {konstantinov,poshchikov,azarev,poshchikova}@bsu.edu.ru Abstract. Confirmation timeout (Round Trip Time, RTT) is an important vaue in data networks. Correct prediction of this characteristic aows us to estimate the network oad in order to adequatey seect packet sending and retransmission parameters. Approximate heuristic modes are used in the Transmission Contro Protoco (TCP) for Round Trip Time evauation. The vaues of the coefficients in these modes were obtained experimentay for fixed topoogy networks. Therefore, the use of these modes in a dynamic topoogy network (mobie ad-hoc network) is inefficient. This artice represents an RTT prediction mode based on appication of fuzzy neura network theory. This mode reies upon zeroorder Sugeno-Type Fuzzy Inference agorithm. The input vaues of fuzzy neura network are RTT vaues measured in the current and two previous cyces. The output vaue is RTT vaue expected in the next cyce. The proposed mode is set up and examined by means of simuation experiments. In these experiments the functioning of mobie ad-hoc network which is used for communication software whie counteracting emergencies was simuated. Keywords: neuro-fuzzy prediction, round trip time, mobie ad hoc networks, dangerous construction sites. 1 Introduction Mobie ad hoc networks (MANET) are a promising direction in the deveopment of teecommunication technoogies [1]. With its decentraized structure, ad hoc networks provide the abiity to transmit information when nodes are moving randomy and under the impact of destructive factors [2, 3]. Due to rapid depoyment, autonomous power of each node, high survivabiity and the abiity to deiver messages with dynamicay changing topoogy, 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

2 natura and man-made factors that can cause exposions, fire, coapse, fooding, radiation, poisoning and other emergencies. The process of information exchange in a mobie ad hoc network is based on the impementation of the packet data transfer. One of the important characteristics in this case is RTT. Correct prediction of this vaue aows us to estimate the network oad to adequatey seect the parameters of packet sending and retransmissions. Approximate heuristic modes are used in the TCP for its evauation [5, 6]. The vaues of the coefficients in these modes were obtained experimentay for networks with a fixed topoogy, that is why their use in the ad hoc networks does not give the desired effect. As a resut, time of information deivery increases significanty, which is unacceptabe in the construction of dangerous buidings, as the ife and heath of buiders, as we as the extent of damage to constructed faciities, depend on the operationa efficiency of messages receiving in emergencies. Therefore, the deveopment of an adequate RTT forecasting mode in the mobie ad hoc network is a topica appied science probem, the soution of which is represented in the foowing researches. 2 Deveopment of Neuro-Fuzzy Mode The neuro-fuzzy mode is suggested to predict RTT in an ad hoc network. The foowing vaues are used in this mode: M is RTT vaue measured in the current cyce; M pr1 is RTT vaue measured in the previous cyce; M pr2 is RTT vaue measured in the cyce preceding the previous one. The mode aows us to cacuate the estimated vaue M of the confirmation timeout for each of the next cyces. Construction of the mode is carried out on the criterion of minima compexity. The foowing parameters correspond to this criterion: fuzzy inference agorithm is the zero-order Sugeno [7], the number of membership functions for each input vaue is 2, the shape of membership functions for each input vaue is trianguar, neurona earning agorithm is error propagation [8]. The mode is using the foowing fuzzy ruebase: If(M = X 1 )and(m pr1 = Y 1 )and(m pr2 = Z 1 ), then( M = J 1 ); (1) If(M = X 1 )and(m pr1 = Y 1 )and(m pr2 = Z 2 ), then( M = J 2 ); (2)... If(M = X 2 )and(m pr1 = Y 2 )and(m pr2 = Z 2 ), then( M = J 8 ); (3) where X 1, X 2, Y 1, Y 2, Z 1, Z 2 are terms number 1 and number 2 of the input vaues M, M pr1, M pr2 ; J 1... J 8 are individua concusions of the fuzzy rues. Type and parameters of the membership functions for each input vaue are shown in Fig. 1, Fig. 2 and Fig

3 1 µ 1 (M) µ 2 (M) X 1 X 2 a x1 a x2 b x1 b x2 M Fig. 1. Type and parameters of the membership functions for the vaue M 1 µ 1 (M pr1 ) µ 2 (M pr1 ) Y 1 Y 2 a y1 a y2 b y1 b y2 M pr1 Fig. 2. Type and parameters of the membership functions for the vaue M pr1 1 µ 1 (M pr2 ) µ 2 (M pr2 ) Z 1 Z 2 a z1 a z2 b z1 b z2 M pr2 Fig. 3. Type and parameters of the membership functions for the vaue M pr2 176

4 The mode of forecasting Round Trip Time incudes four structura neura ayers. Fuzzification procedure is performed by means of the first ayer of neurons: 1, M < a x1 ; b μ 1 (M) = x1 M b x1 a x1, a x1 M < b x1 ; (4) 0, M b x1 ; 0, M < a x2 ; M a μ 2 (M) = x2 b x2 a x2, a x2 M < b x2 ; (5) 1, M b x2 ; 1, M pr1 < a y1 ; μ 1 (M pr1 b ) = y1 M pr1 b y1 a y1, a y1 M pr1 < b y1 ; (6) 0, M pr1 b y1 ; 0, M pr1 < a y2 ; μ 2 (M pr1 M ) = pr1 a y2 b y2 a y2, a y2 M pr1 < b y2 ; (7) 1, M pr1 b y2 ; 1, M pr2 < a z1 ; μ 1 (M pr2 b ) = z1 M pr2 b z1 a z1, a z1 M pr2 < b z1 ; (8) 0, M pr2 b z1 ; 0, M pr2 < a z2 ; μ 2 (M pr2 M ) = pr2 a z2 b z2 a z2, a z2 M pr2 < b z2 ; (9) 1, M pr2 b z2. Aggregation procedure is performed by the second ayer of neurons: G 1 = μ 1 (M) μ 1 (M pr1 ) μ 1 (M pr1 ); (10) G 2 = μ 1 (M) μ 1 (M pr1 ) μ 2 (M pr1 ); (11)... G 8 = μ 2 (M) μ 2 (M pr1 ) μ 2 (M pr1 ). (12) Activation is a part of the defuzzification procedure. Cacuation of the amount of aggregated resuts 8 r=1 G r and the weighted sum of the aggregate resuts 8 r=1 J rg r are performed by means of the third ayer of neurons. The fina part of defuzzification procedure is performed by means of the fourth ayer: 8 r=1 M = J rg r 8 r=1 G. (13) r In order to obtain the coefficient vaues needed to cacuate membership function, it is required to set the weights of neurons of the first ayer. Training of the neurons of the third ayer is needed for evauating the vaues of individua fuzzy rues concusions [9 15]. The receiving of training data for mode setup and evauation of neuro-fuzzy forecasting RTT are carried out on the basis of modeing of various scenarios of ad-hoc network appication for communication on dangerous construction sites. 177

5 3 Modeing Information Streams Transmission Let us consider an exampe in which mobie ad hoc network is used for communication in the construction of underground faciities. Fig. 4 and Fig. 5 show the area of the construction works (imited by bod dotted ine) Fig. 4. The routes of transmission of information fows in a fixed network topoogy This buiding beongs to the dangerous construction projects, because works on its construction are carried out in the conditions of a possibe coapse of rocks. Works are carried out by a personne 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 sma numbered circes, and coverage areas of these units are imited by the corresponding circes of arger radius. The foowing functions are performed by means of ad hoc nodes: 1) video streams to monitor the status of the faciity, conditions and the course of the work; 2) exchange of voice messages to contro the construction process and the coordination of countering emergencies; 3) transfer of data on the functiona status and current ocation coordinates of the buiders, as we as data of monitoring externa conditions on the construction site. In the given exampe the transmission of information streams is carried out in an ad hoc network for a period of time of observation which asts 50 seconds. The characteristics of the streams are represented in Tabe 1 and Tabe 2. Fig. 4 shows the situation where the network topoogy remains unchanged during the considered time interva. The routes of information streams trans- 178

6 Fig. 5. The routes of transmission of information fows in a dynamic network topoogy Tabe 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 data acknowedgements data acknowedgements voice voice video Tabe 2. Estimated parameters Parameter Throughput of the radio channe Throughput required to transmit video Throughput required to transmit voice Size of messages transmitted by data fow Vaue 1000 Kbit/s 256 Kbit/s 128 Kbit/s 1 MB 179

7 mission correspond to the broken ines which connect the nodes-senders and nodes-recipients. Fig. 5 shows a scenario where an ad hoc network topoogy changes due to the coapse of rock, which began at time t e =4 s. Coapse zone is highighted in gray. As a resut of emergency workers who used ad hoc nodes 6 and 9 were in the coapse zone and node 6 mafunctioned (corresponding circe in Fig. 5 is crossed). In response to the coapse, workers with ad hoc nodes 3-5, 8 and 9 have moved. The ocations of these nodes at the initia time in Fig. 5 are marked by the dashed circes. 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 topoogy had an impact on the radio channes workoad and throughput avaiabe for transmission of data fows. For exampe, a radio channe connecting the node 2 to node 1, except for the main streams of 1, 4 and 6, additiona streams 2 and 8 started to transmit. The responsiveness of the node 1 receiving the data fie transmitted from the node 9 is of great importance in an emergency. This fie contains information about the current parameters of heath status and ocation of the worker who has been exposed to the coapse. On the basis of the data head of the shift can quicky and effectivey coordinate the actions of other workers to rescue the injured buider. For the fie to be deivered, streams 4 and 5 need to be transferred. The combination of these interreated streams is caed a controed fow (CF) [16]. The cosed circuit formed by the channes through which CF is transferred is caed CF-circuit (Fig. 6). Node 5 Node 2 Channe 5 Node 9 (Sender) Channe 6 Channe 1 Channe 2 Node 5 Node 2 Channe 4 Channe 3 Node 1 (Recipient) Fig. 6. CF-circuit Duration of data fie deivery from node 9 to node 1 is directy dependent on the vaue E(t), the current CF-circuit throughput avaiabe for CF transmission. 180

8 To cacuate this vaue, one shoud use the expression: E(t) = min{e k (t)}, (14) where E k (t) is the current vaue of the channe throughput k of the CF-circuit [17]. The vaue E k (t) can be figured out from the formua: { 0, Uk (t) c; E k (t) = c U k (t) D k (t), U (15) k(t) < c; where c is the throughput of the radio channe; U k (t) is the current vaue of the channe throughput k required to transmit rea-time streams; D k (t) is the number of data streams, having to be transmitted over the channe by the time t, D k (t) 1. The vaue U k (t) can be determined using the foowing expression: U k (t) = L u k (t), (16) =1 where u k (t) is the current vaue of the channe k throughput required for reatime stream transmission ; L is the number of rea-time streams, which need to be transmitted on the CF-circuit channes. The vaue of u k (t) can be found from the formua: { λ a u k (t) = k, x start t < x stop ; 0, t < x start or t x stop (17), where λ is the vaue of the bandwidth of the channe k required to transmit rea-time stream [18]; a k is the vaue showing whether the transmission channe is required on rea-time stream channe k; x start and x stop are instants of the beginning and the end of transmission of rea-time stream. The minimum possibe duration of the CF transmission can be determined using the foowing formua: τ CF = τ stop CF start τcf, (18) where τcf start is starting time of CF transmission; τ stop CF is cosure time of CFstream transmission without packet oss and an idea correspondence between the intensity of sending data of the stream and the bandwidth of CF-circuit avaiabe for the transmission. The vaue τ stop is cacuated on the basis of the obtained vaues E (t). To do CF this, use the formua: V = τ stop CF τ start CF where V is the size of the message transmitted by data fow. E(t) dt, (19) 181

9 Tabe 3. λ, x start and x stop vaues λ, bit/s x start, s x stop, s > > > >50 Tabe 4. a k vaues k =1 =2 =3 = E(t), Kb/s τ CF t, s Fig. 7. The current vaues E(t) in a network with a dynamic topoogy E(t), Kb/s τ CF t, s Fig. 8. The current vaues E(t) in fixed topoogy network 182

10 To cacuate the function E(t) in the case shown in Fig. 4 and Fig. 5, we used data contained in Tabe 3 and Tabe 4. Using these inputs, the function E(t) is cacuated and its form is shown in Fig. 7. The fixed network topoogy function E(t) has the form shown in Fig. 8. Anaysis of Fig. 7 and Fig. 8 shows that the change in the network topoogy during information exchange eads to a significant deceeration of data fie transmission duration. In a network with a dynamic topoogy the vaue τ CF is set to 39.7 s, and in case of a fixed network structure it is τ CF =24.2 s. 4 Setting Parameters of the Mode and the Evauation of the Effectiveness of Its Appication In rea operating conditions an ad hoc network overoad and packet oss frequenty occur, so the actua vaue of the data fie transfer duration can significanty exceed the cacuated vaue τ CF. To evauate these characteristics a number of simuation experiments were made, in which various scenarios of appying an ad hoc network for providing connectivity on dangerous construction sites were simuated. For this purpose, a simuation mode of information streams transmissions in a network with dynamic topoogy was used. It was deveoped in MatLab Simuink software environment. The simuation resuts provided evidence for setting deveoped neuro-fuzzy mode forecasting round trip time. On the basis of these data the training matrix of the foowing form is made: M 1 M 2 M 3 M 4 M 2 M 3 M 4 M M i M (i+1) M (i+2) M (i+3).... M (I 3) M (I 2) M (I 1) M I (20) where M i is a round trip time of confirmation in the oop i; I is the number of cyces in each simuation experiment, I=750. Setting neuro-fuzzy mode was carried out using software toos Fuzzy Logic Toobox. Tabe 5 shows the resuts of training the neurons of the first ayer, whie Tabe 6 contains the resuts of training the neurons of the third ayer. To assess the efficiency of the deveoped and customized modes, a number of simuations for the transfer of information streams in an ad hoc network were conducted. The seection of retransmission was simuated on the basis of the suggested neuro-fuzzy forecasting RTT and the cassica mode of evauation of this quantity used in TCP. The resuts showed that the use of neuro-fuzzy forecasting RTT in a arge network oad reduces deviations of timeout retransmission on 5,7-19,2 percents. This contributes to minimizing retransmissions count and average data stream transmission time by percents. 183

11 Tabe 5. Learning outcomes of the first ayer of neurons Parameter Vaue a x a x b x b x a y a y b y b y a z a z b z b z Tabe 6. Learning outcomes of the third ayer of neurons Parameter Vaue H H H H H H H H Concusion Thus, the mode of neuro-fuzzy prediction of confirmation timeout in the mobie ad hoc network is synthesized. The mode incudes four neuron ayers, performing fuzzy inference procedure (fuzzification, aggregation, revitaization and defuzzification). To adjust the weights neurons we used training data, refecting the dynamics of the RTT in the ad hoc network used for communication on dangerous construction sites. Simuations have shown that the use of the proposed mode for seecting timeout retransmission wi significanty reduce the duration of the transmission data fows in the mobie ad hoc network. Acknowedgements. The research have been carried out with the financia support of the Ministry of Education and Science of the Russian Federation (the unique identifier of the project is RFMEFI57815X0138). 184

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