Studyng the Relatonshp between Network Measurement Parameters and Avalable Bandwdth for Accurate Estmaton Hazem M. El-Bakry Faculty of Computer Scence & Informaton Systems, Mansoura Unversty, EGYPT E-mal: helbakry20@yahoo.com Nkos Mastoraks Techncal Unversty of Sofa, BULGARIA Abstract: Accurate avalable bandwdth measurement s very useful for network performance modelng, system admnstrators who want to transfer large amounts of data from one data repostory to another, n case of grd, job schedulers, use the pror knowledge about the avalable bandwdth whle schedulng the job and performng any data ntensve actvty over the grd. Unfortunately, avalable bandwdth s also very dffcult parameter to measure whch s further dependent on many factors especally over very heterogeneous envronment such as the nternet. A lot of research s carred out these days over the technques to measure the avalable bandwdth but none of them provde us wth 100% accurate results. In ths paper we would dscuss relatonshps of dfferent parameters wth avalable bandwdth.e. jtter, packet loss, throughput and blockng probablty. These factors play a very mportant role n the accurate measurement of avalable bandwdth but at the same tme they are very rarely gven consden whle measurement of avalable bandwdth. Ths paper hghlghts the mportance of these parameters whle measurng avalable bandwdth. In addton, a new approach for fast detectng certan nformaton n a channel s presented. The entre data are collected together n a long vector and then tested as a one pattern. Proposed fast tme delay neural networks (FTDNNs) use cross correlaton n the frequency doman between the tested data and the weghts of neural networks. It s proved mathematcally and practcally that the number of computaton steps requred for the presented tme delay neural networks s less than that needed by conventonal tme delay neural networks (CTDNNs). Smulaton results usng MATLAB confrm the theoretcal computatons. Keywords: Avalable Bandwdth, Jtter, Packet Loss, Throughput and Blockng Probablty, Fast Informaton Detecton, Cross Correlaton, Frequency Doman I. Introducton Inferrng the unused capacty or avalable bandwdth s of great mportance for varous network applcatons. Avalable Bandwdth measurement s of nterest for network protocols, system admnstrators who want to transfer large amounts of data from one data repostory to another, n case of grd, job schedulers use the pror knowledge about the avalable bandwdth whle schedulng the job and performng any data ntensve actvty over the network. But at the same tme avalable bandwdth s also very dffcult to be measured exactly. The reason beng that t s dependent on number of factors and shows very dscrete behavor over the network. Avalable bandwdth s also dependent a great deal on the heterogenety of the network. Avalable bandwdth s also a key factor n several network technologes. Several applcatons can beneft from knowng the avalable bandwdth of ther network paths. For example, peer to peer applcatons from ther dynamc user level networks based on avalable bandwdth between peers. The word bandwdth s often msnterpreted as avalable bandwdth but the matter of fact s that these two are dfferent enttes. Bandwdth s the maxmum amount of data that the lnk can provde over the network and on the other hand avalable bandwdth s the maxmum bandwdth mnus consumed bandwdth. In ths paper we wll defne specfc factors and parameters whch have drect relatonshp wth avalable bandwdth, hghlghtng the scope and relevance of each of the factor. All these aspects are mportant as they all effect the applcatons that use avalable bandwdth. A lot of research s carred out these days over the technques to measure the avalable bandwdth but none of them provde us wth accurate results. There are a number of technques that have been ISSN: 1790-2769 805 ISBN: 978-960-474-124-3
proposed for the measurement of avalable bandwdth over the network. There are two technques that are most wdely deployed n order measure the avalable bandwdth over the network. The frst of them s the statstcal cross traffc technque. Ths technque reles on measurement of varous network parameters and then applyng statstcal approaches to measure the avalable bandwdth. These technques are nhertably neffcent and consume a lot of network resources. The second technque s tme dsperson n packet tran. Ths technque reles on sendng the packet trans of probe packets to destnaton network and then measurng the dfference n the tmes the two packets reachng the destnaton. II. Methodology We have adopted a very smple but very comprehensve methodology n order to see the relatonshp of dfferent factors wth the avalable bandwdth. We gathered the data about dfferent parameters usng the tools.e. IPERF, PngER and Abng. We conducted dfferent tests usng the above mentoned tools at the same tme on nodes located at dfferent geographcal locatons of the world.e. from Pakstan to Korea etc. We then generated plots showng the relatonshp among dfferent parameters and the avalable bandwdth. A) Tools and technques: 1. Abng: Abng s an avalable bandwdth measurement tool that s based on the prncple of packet par dsperson or mostly referred to as dsperson n packet tran. Ths technque s dscussed n many papers [4,5,6]. The basc prncple s smple: one sends packet probes to the fnal destnaton and measures the nter-packet delay between the packets as they arrve at the destnaton. Abng s farly effcent at the hgh capacty networks rangng from 100Mbps to 1000Mbps. In ths way ths tool has a non ntrusve advantage over the other tools that operate over the slow speed networks. Abng sends several (typcally 20) closely spaced probes to one destnaton as a tran. The evaluaton of the observed packet par delays s based on detaled techncal analyss of the problems that are expected to meet n the routers and other network devces. 2. PngER: Tools to mplement the png related measurements and analyss are referred to as PngER. Png s used to measure the response tme, the packet loss percentages, the varablty of the response tme both short term and longer, and the lack of reach ablty,.e. no response for a successon of pngs. The archtecture of the PngER s based on 3 components 1) The remote Regons 2) The Montorng Ste 3) The archve and analyss stes as mentoned n[2]. PngER also enables us to measure jtter, packet loss and throughput [9]. 3. IPERF: IPERF s an avalable bandwdth measurement tool whch s used to measure the end to end achevable bandwdth, usng TCP streams, allowng varatons n parameters lke TCP wndow sze and number of parallel streams as dscussed n [3]. IPERF measures end to end avalable bandwdth between two hosts. We need to run IPERF for farly long amount of tme to get the accurate values. IPERF s also very resource consumng tool as t consumes a lot of bandwdth whle sendng the probng packets at small nterval, mostly after 30 sec. IPERF also provdes us wth the packet loss and jtter over the network lnk We used all of the above mentoned tools to gather dfferent parameters and then see the relatonshp of these parameters wth the avalable bandwdth and then we see the effect of these parameters over the avalable bandwdth. III. Relatonshp wth Avalable Bandwdth: A) Packet Loss: Avalable bandwdth has a very strong relatonshp wth packet loss. It has been observed that as the bandwdth ncreases the packet loss decreases. The hgher the avalable bandwdth the lower s the packet loss or n terms of packet loss we can say that the hgher the packet loss the lower s the avalable bandwdth. Ths means that these two parameters are nversely proportonal to each other. The same results are shown by the Fg. 1 shown below. From the above graph t s clear that as the packet loss over the network ncrease the avalable bandwdth starts to decrease steadly. The packet loss n the network nfers that the network s n the congested state or the partcular porton on the lnk s over crowded whch cases the packets to be dropped at queues and thus results n the eventual decrease of the avalable bandwdth. ISSN: 1790-2769 806 ISBN: 978-960-474-124-3
B) Jtter: Jtter s also one of the mportant parameters that show the performance of the network at a partcular nterval. Whle desgnng the tools for the avalable bandwdth the relatonshp between the jtter and the avalable bandwdth needs to be carefully consdered. These two do not have do not seem to have a very clear relatonshp but mprovng on the jtter can help mprove the measurement of the avalable bandwdth. Jtter s the defned as the varance n the delay. Consdered two packets P1 and P2 sent after one an other over the network. The delay of packet P1 from source to destnaton s sad to be S1 and the delay of the packet P2 s S2. The combned delay D1 would be the dfference n the delays for those partcular packets. Ths can be explaned by a smple equaton stated below: Combned Delay= S2-S1 (1) Smlarly the combned delay between the next subsequent packet par s D2 so the Jtter between the two delays would be: Jtter= D2-D1 (2) As shown from the equaton there s no drect relatonshp between the jtter and the avalable bandwdth. But the pont to of gvng jtter so much mportance s that mprovng on jtter means that the network s n the consstent state whch greatly mproves the measurement accuracy of other factors lke queung delays over the routers whch drectly effect the measurement of the avalable bandwdth n packet par dsperson technques. The effect of jtter over the measurement of avalable bandwdth can be shown by the graph shown below n Fg. 2. It s clear from the above graph that there s a lot of varaton n the jtter and at the same tme there are a lot of varatons n the avalable bandwdth. But these two clearly do not have a drect relatonshp among each other. But the jtter affects other parameters effectng avalable bandwdth. So f the jtter s stablzed then the avalable bandwdth wll stablze and we can get a more exact measurement of avalable bandwdth. C) Throughput: Throughput s the number of bts transferred per unt tme over the network. The %age throughput s the total number of bts sent dvded by the total no of bts receved per unt tme. The through put has a drect relatonshp wth the avalable bandwdth. As the throughput ncreases the avalable bandwdth also ncreases. Ths s relatvely easy to nfer that hgher throughput means less number of the packets lost whle transmsson over the network thus decreasng the %age of the packets lost. As mentoned above the packet loss has a drect relatonshp wth the avalable bandwdth. In the same context f the % age throughput over the network s good ths wll result n effcent and accurate measurement of avalable bandwdth. The statement that the ncrease n throughput results n the ncrease n the avalable bandwdth s proved by the Fg. 3. There s a steady ncrease n the avalable bandwdth wth the ncrease n the throughput. Ths conforms to the statement that we have stated above for the relatonshp of throughput wth the avalable bandwdth. So f we ncrease the through put of the network ths wll greatly remove the nose over the network and then there s a far chance that we can enhance accuracy n measurng the avalable bandwdth. D) Blockng Probablty: Blockng probablty s the probablty that the transmsson would be blocked due to less amount of bandwdth avalable then s requred to transfer the data over the network. The avalable bandwdth s drectly related wth the blockng probablty. The more the avalable bandwdth of the lnk the less s the blockng probablty. The blockng probablty provdes us wth a good measure of how effcent s the network n executng the jobs that are submtted over the network. IV. Fast Informaton Detecton n a Certan Channel by usng Hgh Speed Tme Delay Neural Networks Fndng certan nformaton n a gven channel s a searchng problem. What s requred s to detect certan nformaton n the transferred seral data. Frst neural networks are traned to classfy the requred nformaton from other examples and ths s done n tme doman. In nformaton detecton phase, each poston n the ncomng s tested for presence or absence of the requred nformaton. At each poston n the one dmensonal, each sub- s multpled by a wndow of weghts, whch has the same sze as the sub-. The outputs of neurons n the hdden layer are multpled by the weghts of the output layer. When the fnal output s hgh, ths means that the sub- under test contans the ISSN: 1790-2769 807 ISBN: 978-960-474-124-3
requred nformaton and vce versa. Thus, we may conclude that ths searchng problem s a cross correlaton between the ncomng seral data and the weghts of neurons n the hdden layer. The convoluton theorem n mathematcal analyss says that a convoluton of f wth h s dentcal to the result of the followng steps: let F and H be the results of the Fourer Transformaton of f and h n the frequency doman. Multply F and H* n the frequency doman pont by pont and then transform ths product nto the spatal doman va the nverse Fourer Transform. As a result, these cross correlatons can be represented by a product n the frequency doman. Thus, by usng cross correlaton n the frequency doman, speed up n an order of magntude can be acheved durng the detecton process [15-22]. Assume that the sze of the ntruson code s 1xn. In ntruson detecton phase, a sub I of sze 1xn (sldng wndow) s extracted from the tested, whch has a sze of 1xN. Such sub, whch may be an ntruson code, s fed to the neural network. Let W be the of weghts between the sub- and the hdden layer. Ths vector has a sze of 1xn and can be represented as 1xn. The output of hdden neurons h() can be calculated as follows [15-22]: n h = g + W (k)i(k) b (3) k = 1 where g s the actvaton functon and b() s the bas of each hdden neuron (). Equaton 1 represents the output of each hdden neuron for a partcular sub- I. It can be obtaned to the whole Z as follows: n/2 h (u) = g W (k) Z(u+ k) + b (4) k = n/2 Eq.4 represents a cross correlaton open. Gven any two functons f and d, ther cross correlaton can be obtaned by [12]: d(x) f(x) = f(x+ n)d(n) (5) n= Therefore, Eq. 4 may be wrtten as follows [10]: h = g( W Z+ b ) (6) where h s the output of the hdden neuron () and h (u) s the actvty of the hdden unt () when the sldng wndow s located at poston (u) and (u) [N-n+1]. Now, the above cross correlaton can be expressed n terms of one dmensonal Fast Fourer Transform as follows [10]: W Z= F 1 F Z ( ( ) F* ( W ) (7) Hence, by evaluatng ths cross correlaton, a speed up can be obtaned comparable to conventonal neural networks. Also, the fnal output of the neural network can be evaluated as follows: q O(u) = g = Wo() h (u) + bo (8) 1 where q s the number of neurons n the hdden layer. O(u) s the output of the neural network when the sldng wndow located at the poston (u) n the Z. W o s the weght between hdden and output layer. The complexty of cross correlaton n the frequency doman can be analyzed as follows: 1- For a tested of 1xN elements, the 1D- FFT requres a number equal to Nlog 2 N of complex computaton steps [11]. Also, the same number of complex computaton steps s requred for computng the 1D-FFT of the weght at each neuron n the hdden layer. 2- At each neuron n the hdden layer, the nverse 1D-FFT s computed. Therefore, q backward and (1+q) forward transforms have to be computed. Therefore, for a gven under test, the total number of opens requred to compute the 1D- FFT s (2q+1)Nlog 2 N. 3- The number of computaton steps requred by FTDNNs s complex and must be converted nto a real verson. It s known that, the one dmensonal Fast Fourer Transform requres (N/2)log 2 N complex multplcatons and Nlog 2 N complex addtons [11]. Every complex multplcaton s realzed by sx real floatng pont opens and every complex addton s mplemented by two real floatng pont opens. Therefore, the total number of computaton steps requred to obtan the 1D-FFT of a 1xN s: ρ=6((n/2)log 2 N) + 2(Nlog 2 N) (9) whch may be smplfed to: ρ=5nlog 2 N (10) 4- Both the and the weght matrces should be dot multpled n the frequency doman. Thus, a number of complex computaton steps equal to qn should be consdered. Ths means 6qN real opens wll be added to the number of computaton steps requred by FTDNNs. 5- In order to perform cross correlaton n the frequency doman, the weght must be extended to have the same sze as the. So, a number of zeros = (N-n) must be added to the weght. Ths requres a total real number of computaton steps = q(n-n) for all neurons. Moreover, after computng the FFT for the weght, the conjugate of ths must be obtaned. As a result, a real number of computaton ISSN: 1790-2769 808 ISBN: 978-960-474-124-3
steps = qn should be added n order to obtan the conjugate of the weght for all neurons. Also, a number of real computaton steps equal to N s requred to create butterfles complex numbers (e -jk(2πn/n) ), where 0<K<L. These (N/2) complex numbers are multpled by the elements of the or by prevous complex numbers durng the computaton of FFT. To create a complex number requres two real floatng pont opens. Thus, the total number of computaton steps requred for FTDNNs becomes: σ=(2q+1)(5nlog 2 N) +6qN+q(N-n)+qN+N (11) whch can be reformulated as: σ=(2q+1)(5nlog 2 N)+q(8N-n)+N (12) 6- Usng sldng wndow of sze 1xn for the same of 1xN pxels, q(2n-1)(n-n+1) computaton steps are requred when usng CTDNNs for certan nformaton detecton or processng (n) data. The theoretcal speed up factor η can be evaluated as follows: q(2n-1)(n- n+ 1) η = (13) (2q+ 1)(5Nlog2 N) + q(8n- n) + N Tme delay neural networks accept seral data wth fxed sze (n). Therefore, the number of neurons equals to (n). Instead of treatng (n) s, the proposed new approach s to collect all the ncomng data together n a long vector (for example 100xn). Then the data s tested by tme delay neural networks as a sngle pattern wth length L (L=100xn). Such a test s performed n the frequency doman as descrbed before. The combned nformaton n the ncomng data may have real or complex values n a form of one or two dmensonal array. Complex-valued neural networks have many applcatons n felds dealng wth complex numbers such as telecommuncatons, speech recognton and mage processng wth the Fourer Transform [13,14]. Complex-valued neural networks mean that the s, weghts, thresholds and the actvaton functon have complex values. In ths secton, formulas for the speed up wth dfferent types of s (real /complex) wll be presented. Also, the speed up n case of a one and two dmensonal ncomng wll be concluded. The open of FTDNNs depends on computng the Fast Fourer Transform for both the and weght matrces and obtanng the resultng two matrces. After performng dot multplcaton for the resultng two matrces n the frequency doman, the Inverse Fast Fourer Transform s determned for the fnal. Here, there s an excellent advantage wth FTDNNs that should be mentoned. The Fast Fourer Transform s already dealng wth complex numbers, so there s no change n the number of computaton steps requred for FTDNNs. Therefore, the speed up n case of complex-valued tme delay neural networks can be evaluated as follows: 1) In case of real s A) For a one dmensonal Multplcaton of (n) complex-valued weghts by (n) real s requres (2n) real opens. Ths produces (n) real numbers and (n) magnary numbers. The addton of these numbers requres (2n-2) real opens. The multplcaton and addton opens are repeated (Nn+1) for all possble sub matrces n the ncomng. In addton, all of these procedures are repeated at each neuron n the hdden layer. Therefore, the number of computaton steps requred by conventonal neural networks can be calculated as: θ=2q(2n-1)(n-n+1) (14) The speed up n ths case can be computed as follows: 2q(2n-1)(N- n+ 1) η = (15) (2q+ 1)(5Nlog N) + q(8n- n) N 2 + The theoretcal speed up for searchng short successve (n) code n a long vector (L) usng complex-valued tme delay neural networks s shown n Tables 1, 2, and 3. Also, the practcal speed up for manpulatng matrces of dfferent szes (L) and dfferent szed weght matrces (n) usng a 2.7 GHz processor and MATLAB s shown n Table 4. B) For a two dmensonal Multplcaton of (n 2 ) complex-valued weghts by (n 2 ) real s requres (2n 2 ) real opens. Ths produces (n 2 ) real numbers and (n 2 ) magnary numbers. The addton of these numbers requres (2n 2-2) real opens. The multplcaton and addton opens are repeated (N-n+1) 2 for all possble sub matrces n the ncomng. In addton, all of these procedures are repeated at each neuron n the hdden layer. Therefore, the number of computaton steps requred by conventonal neural networks can be calculated as: θ=2q(2n 2-1)(N-n+1) 2 (16) The speed up n ths case can be computed as follows: 2 2q(2n -1)(N- n+ 1) η = (17) 2 2 2 2 (2q+ 1)(5N log N ) + q(8n - n ) + N 2 The theoretcal speed up for detectng (nxn) real valued sub n a large real valued (NxN) usng complex-valued tme delay neural networks s shown n Tables 5, 6, 7. Also, the practcal speed up for manpulatng matrces of dfferent szes (NxN) and dfferent szed code 2 ISSN: 1790-2769 809 ISBN: 978-960-474-124-3
matrces (n) usng a 2.7 GHz processor and MATLAB s shown n Table 8. 2) In case of complex s A) For a one dmensonal Multplcaton of (n) complex-valued weghts by (n) complex s requres (6n) real opens. Ths produces (n) real numbers and (n) magnary numbers. The addton of these numbers requres (2n-2) real opens. Therefore, the number of computaton steps requred by conventonal neural networks can be calculated as: θ=2q(4n-1)(n-n+1) (18) The speed up n ths case can be computed as follows: 2q(4n-1)(N- n+ 1) η = (19) (2q+ 1)(5Nlog2 N) + q(8n- n) + N The theoretcal speed up for searchng short complex successve (n) code n a long complexvalued vector (L) usng complex-valued tme delay neural networks s shown n Tables 9, 10, and 11. Also, the practcal speed up for manpulatng matrces of dfferent szes (L) and dfferent szed weght matrces (n) usng a 2.7 GHz processor and MATLAB s shown n Table 12. B) For a two dmensonal Multplcaton of (n 2 ) complex-valued weghts by (n 2 ) real s requres (6n 2 ) real opens. Ths produces (n 2 ) real numbers and (n 2 ) magnary numbers. The addton of these numbers requres (2n 2-2) real opens. Therefore, the number of computaton steps requred by conventonal neural networks can be calculated as: θ=2q(4n 2-1)(N-n+1) 2 (20) The speed up n ths case can be computed as follows: 2 2q(4n -1)(N- n+ 1) η = (21) 2 2 2 2 (2q+ 1)(5N log N ) + q(8n - n ) + N 2 The theoretcal speed up for detectng (nxn) complex-valued sub n a large complexvalued (NxN) usng complex-valued neural networks s shown n Tables 13, 14, and 15. Also, the practcal speed up for manpulatng matrces of dfferent szes (NxN) and dfferent szed code matrces (n) usng a 2.7 GHz processor and MATLAB s shown n Table 16. An nterestng pont s that the memory capacty s reduced when usng FTDNN. Ths s because the number of varables s reduced compared wth CTDNN. 2 V. Concluson Accurate estmate of the avalable bandwdth s very use full for many applcatons workng on the network. Measurement of avalable bandwdth s even more crutal especally n case of large hgh speed networks lke the nternet2 and n heterogeneous envronments lke the GRID. All the above mentoned parameters have a very strong relatonshp wth avalable bandwdth. Effcent measurement of avalable bandwdth requres very close consdens on these parameters of the network whch are often gnored. Pror knowledge of these parameters can also help already exstng tools to a great extent n accurate estmaton of the avalable bandwdth. Furthermore, new FTDNNs for fast detectng certan nformaton n a gven channel have been presented. Theoretcal computatons have shown that FTDNNs requre fewer computaton steps than conventonal ones. Ths has been acheved by applyng cross correlaton n the frequency doman between the data and the weghts of tme delay neural networks. Smulaton results have confrmed ths proof by usng MATLAB. References: [1] ABwE: A practcal approach to avalable bandwdth, Jr Navratl and R.Les. Cottrel. Stranford Lnear Accelerator Center (SLAC). [2] http://www.slac.stanford.edu/comp/net/wanmon/tutoral.html#pnger [3] Measurng end-to-end bandwdth wth IPERF usng web100 Ajay Trmula, Les Cottrel, Tom Dungan [4] R.L. Cater and M.E. Crovella Measurng Bottelneck Lnk Speed n Packet-Setched Networks [5] V.Jacobson, Pathchar A tool to nfer characterstcs of nternet paths [6] V.Paxson, End to end Internet packet dynamcs IEEE /ACM Transton on Networkng. [7] PathChrp: Effcent Avalable Bandwdth Estmaton for Network Paths. Vnay J. Rebro, Rudolf H. Red, Rchard G. Baranuk, Jr Navtral, Les Cottrel. [8] Network Metrcs for GRID Applcatons and Servces Draft (NMWG Internal Draft). [9] The Pnger Project (http://wwwepm.slac.stanford.edu/pnger/) [10] H. M. El-Bakry, "New Faster Normalzed Neural Networks for Sub-Matrx Detecton usng Cross Correlaton n the Frequency Doman and Matrx Decomposton," Appled Soft Computng journal, vol. 8, ssue 2, March 2008, pp. 1131-1149. [11] J. W. Cooley, and J. W. Tukey, "An algorthm for the machne calculaton of complex Fourer seres," Math. Comput. 19, 297 301 (1965). ISSN: 1790-2769 810 ISBN: 978-960-474-124-3
[12] R. Klette, and Zamperon, "Handbook of mage processng operators, " John Wley & Sonsltd, 1996. [13] A. Hrose, Complex-Valued Neural Networks Theores and Applcatons, Seres on nnovatve Intellegence, vol.5. Nov. 2003. [14] S. Jankowsk, A. Lozowsk, M. Zurada, Complexvalued Multstate Neural Assocatve Memory, IEEE Trans. on Neural Networks, vol.7, 1996, pp.1491-1496. [15] Hazem M. El-Bakry, "Human Irs Detecton Usng Fast Cooperatve Modular Neural Nets and Image Decomposton," Machne Graphcs & Vson Journal (MG&V), vol. 11, no. 4, 2002, pp. 498-512. [16] Hazem M. El-Bakry, "Face detecton usng fast neural networks and mage decomposton," Neurocomputng Journal, vol. 48, 2002, pp. 1039-1046. [17] Hazem M. El-Bakry, and Qangfu Zhao, "Speedngup Normalzed Neural Networks For Face/Object Detecton," Machne Graphcs & Vson Journal (MG&V), vol. 14, No.1, 2005, pp. 29-59. [18] Hazem M. El-Bakry, "An Effcent Algorthm for Pattern Detecton usng Combned Classfers and Data Fuson," Accepted for publcaton n Informaton Fuson Journal. [19] Hazem M. El-Bakry, "A Novel Hgh Speed Neural Model for Fast Pattern Recognton," Accepted for publcaton n Soft Computng Journal. [20] Hazem M. El-Bakry, "Fast Vrus Detecton by usng Hgh Speed Tme Delay Neural Networks," Accepted for publcaton n journal of computer vrology. [21] Hazem M. El-Bakry, "New Fast Prncpal Component Analyss For Real-Tme Face Detecton," Accepted for publcaton n MG&V Journal. [22] Hazem M. El-Bakry, "A New Neural Desgn for Faster Pattern Detecton Usng Cross Correlaton and Matrx Decomposton," Accepted for publcaton n Neural World journal. 1200 Avalable Bandwdth 1000 800 600 400 200 0 0.45 0.93 1 1.4 2.7 4 5.5 7.1 7.7 8.4 11 12 13 14 15 16 18 19 20 21 22 23 25 30 Packet Loss Fg. 1: Relatonshp between Packet loss and Avalable Bandwdth 35 30 25 20 Jtter 15 10 5 0 686 728 773 791 818 822 826 835 840 847 865 874 889 896 906 909 920 929 941 960 965 974 978 998 1011 1027 1033 1036 1040 1051 Avalable Bandwdth Fg. 2: Relatonshp between avalable bandwdth and jtter ISSN: 1790-2769 811 ISBN: 978-960-474-124-3
1200 1000 800 600 400 200 0 65 72 77 79 80 81 83 85 86 88 89 92 92.9 94.7 Bandwdth 97.3 98.7 99 99.6 Throughput Fg. 3: Relatonshp between avalable bandwdth and throughput Table 1: The theoretcal speed up for tme delay neural networks (1D-real values, n=400). Length of 10000 4.6027e+008 4.2926e+007 10.7226 40000 1.8985e+009 1.9614e+008 9.6793 90000 4.2955e+009 4.7344e+008 9.0729 160000 7.6513e+009 8.8219e+008 8.6731 250000 1.1966e+010 1.4275e+009 8.3823 360000 1.7239e+010 2.1134e+009 8.1571 490000 2.3471e+010 2.9430e+009 7.9752 640000 3.0662e+010 3.9192e+009 7.8237 Table 2: The theoretcal speed up for tme delay neural networks (1D-real values, n=625). Length of 10000 7.0263e+008 4.2919e+007 16.3713 40000 2.9508e+009 1.9613e+008 15.0452 90000 6.6978e+009 4.7343e+008 14.1474 160000 1.1944e+010 8.8218e+008 13.5388 250000 1.8688e+010 1.4275e+009 13.0915 360000 2.6932e+010 2.1134e+009 12.7433 490000 3.6674e+010 2.9430e+009 12.4612 640000 4.7915e+010 3.9192e+009 12.2257 ISSN: 1790-2769 812 ISBN: 978-960-474-124-3
Table 3: The theoretcal speed up for tme delay neural networks (1D-real values, n=900). Length of 10000 9.823 e+008 4.2911e+007 22.8933 40000 4.2206e+009 1.9612e+008 21.5200 90000 9.6176e+009 4.7343e+008 20.3149 160000 1.7173e+010 8.8217e+008 19.4671 250000 2.6888e+010 1.4275e+009 18.8356 360000 3.8761e+010 2.1134e+009 18.3409 490000 5.2794e+010 2.9430e+009 17.9385 640000 6.8985e+010 3.9192e+009 17.6018 Table 4: Practcal speed up for tme delay neural networks (1D-real values ). Length of (n=400) (n=625) (n=900) 10000 17.88 25.94 35.21 40000 17.19 25.11 34.43 90000 16.65 24.56 33.59 160000 16.14 24.14 33.05 250000 15.89 23.76 32.60 360000 15.58 23.23 32.27 490000 15.28 22.87 31.99 640000 14.08 22.54 31.78 Table 5: The theoretcal speed up for tme delay neural networks (2D-real values, n=20). Sze of 100x100 3.1453e+008 4.2916e+007 7.3291 200x200 1.5706e+009 1.9610e+008 8.0091 300x300 3.7854e+009 4.7335e+008 7.9970 400x400 6.9590e+009 8.8203e+008 7.8898 500x500 1.1091e+010 1.4273e+009 7.7711 600x600 1.6183e+010 2.1130e+009 7.6585 700x700 2.2233e+010 2.9426e+009 7.5556 800x800 2.9242e+010 3.9186e+009 7.4623 Table 6: The theoretcal speed up for tme delay neural networks (2D-real values, n=25). Sze of 100x100 4.3285e+008 4.2909e+007 10.0877 200x200 2.3213e+009 1.9609e+008 11.8380 300x300 5.7086e+009 4.7334e+008 12.0602 400x400 1.0595e+010 8.8202e+008 12.0119 500x500 1.6980e+010 1.4273e+009 11.8966 600x600 2.4863e+010 2.1130e+009 11.7667 700x700 3.4246e+010 2.9425e+009 11.6381 800x800 4.5127e+010 3.9185e+009 11.5163 ISSN: 1790-2769 813 ISBN: 978-960-474-124-3
Table 7: The theoretcal speed up for tme delay neural networks (2D-real values, n=30). Sze of 100x100 5.4413e+008 4.2901e+007 12.6834 200x200 3.1563e+009 1.9608e+008 16.0966 300x300 7.9272e+009 4.7334e+008 16.7476 400x400 1.4857e+010 8.8201e+008 16.8444 500x500 2.3946e+010 1.4273e+009 16.7773 600x600 3.5193e+010 2.1130e+009 16.6552 700x700 4.8599e+010 2.9425e+009 16.5160 800x800 6.4164e+010 3.9185e+009 16.3745 Table 8: Practcal speed up for tme delay neural networks (2D-real values ). Sze of (n=20) (n=25) (n=30) 100x100 17.19 22.32 31.74 200x200 17.61 22.89 32.55 300x300 16.54 23.66 33.71 400x400 15.98 22.95 34.53 500x500 15.62 22.49 33.32 600x600 15.16 22.07 32.58 700x700 14.87 21.83 32.16 800x800 14.64 21.61 31.77 Table 9: The theoretcal speed up for tme delay neural networks (1D-complex values, n=400). Length of 100x100 9.2111e+008 4.2926e+007 21.4586 200x200 3.7993e+009 1.9614e+008 19.3706 300x300 8.5963e+009 4.7344e+008 18.1571 400x400 1.5312e+010 8.8219e+008 17.3570 500x500 2.3947e+010 1.4275e+009 16.7750 600x600 3.4500e+010 2.1134e+009 16.3245 700x700 4.6972e+010 2.9430e+009 15.9604 800x800 3.9192e+009 6.1363e+010 15.6571 Table 10: The theoretcal speed up for tme delay neural networks (1D-complex values, n=625). Length of 100x100 1.4058e+009 4.2919e+007 32.7558 200x200 5.9040e+009 1.9613e+008 30.1025 300x300 1.3401e+010 4.7343e+008 28.3061 400x400 2.3897e+010 8.8218e+008 27.0883 500x500 3.7391e+010 1.4275e+009 26.1934 600x600 5.3885e+010 2.1134e+009 25.4969 700x700 7.3377e+010 2.9430e+009 24.9324 800x800 9.5868e+010 3.9192e+009 24.4612 ISSN: 1790-2769 814 ISBN: 978-960-474-124-3
Table 11: The theoretcal speed up for tme delay neural networks (1D-complex values, n=900). Length of 100x100 1.9653e+009 4.2911e+007 45.7993 200x200 8.4435e+009 1.9612e+008 43.0519 300x300 1.9240e+010 4.7343e+008 40.6410 400x400 3.4356e+010 8.8217e+008 38.9450 500x500 5.3791e+010 1.4275e+009 37.6817 600x600 7.7544e+010 2.1134e+009 36.6920 700x700 1.0562e+011 2.9430e+009 35.8870 800x800 1.3801e+011 3.9192e+009 35.2134 Table 12: Practcal speed up for tme delay neural networks (1D-complex values ). Length of (n=400) (n=625) (n=900) 10000 37.90 53.58 70.71 40000 36.82 52.89 69.43 90000 36.34 52.47 68.69 160000 35.94 51.88 68.05 250000 35.69 51.36 67.56 360000 35.28 51.02 67.15 490000 34.97 50.78 66.86 640000 34.67 50.56 66.58 Table 13: The theoretcal speed up for tme delay neural networks (2D-complex values, n=20). Sze of 100x100 6.2946e+008 4.2916e+007 14.6674 200x200 3.1431e+009 1.9610e+008 16.0281 300x300 7.5755e+009 4.7335e+008 16.0040 400x400 1.3927e+010 8.8203e+008 15.7894 500x500 2.2197e+010 1.4273e+009 15.5519 600x600 3.2386e+010 2.1130e+009 15.3266 700x700 4.4493e+010 2.9426e+009 15.1206 800x800 5.8520e+010 3.9186e+009 14.9340 Table 14: The theoretcal speed up for tme delay neural networks (2D-complex values, n=25). Sze of 100x100 8.6605e+008 4.2909e+007 20.1836 200x200 4.6445e+009 1.9609e+008 23.6856 300x300 1.1422e+010 4.7334e+008 24.1301 400x400 2.1198e+010 8.8202e+008 24.0333 500x500 3.3973e+010 1.4273e+009 23.8028 600x600 4.9746e+010 2.1130e+009 23.5427 700x700 6.8519e+010 2.9425e+009 23.2856 800x800 9.0290e+010 3.9185e+009 23.0418 ISSN: 1790-2769 815 ISBN: 978-960-474-124-3
Table 15: The theoretcal speed up for tme delay neural networks (2D-complex values, n=30). Sze of 100x100 1.0886e+009 4.2901e+007 25.3738 200x200 6.3143e+009 1.9608e+008 32.2021 300x300 1.5859e+010 4.7334e+008 33.5045 400x400 2.9722e+010 8.8201e+008 33.6981 500x500 4.7904e+010 1.4273e+009 33.5640 600x600 7.0405e+010 2.1130e+009 33.3197 700x700 9.7225e+010 2.9425e+009 33.0412 800x800 1.2836e+011 3.9185e+009 32.7581 Table 16: Practcal speed up for tme delay neural networks (2D-complex values ). Sze of (n=20) (n=25) (n=30) 100x100 38.33 46.99 62.88 200x200 39.17 47.79 63.77 300x300 38.44 48.86 64.83 400x400 37.92 47.23 65.99 500x500 37.32 46.89 64.89 600x600 36.96 46.48 64.01 700x700 36.67 46.08 63.31 800x800 36.38 45.78 62.64 ISSN: 1790-2769 816 ISBN: 978-960-474-124-3