Available online at ScienceDirect. Procedia Computer Science 103 (2017 )

Transcription

1 Avalable onlne at ScenceDrect Proceda Computer Scence 03 (207 ) XIIth Internatonal Symposum «Intellgent Systems», INTELS 6, 5-7 October 206, Moscow, Russa Retral queueng systems n seres of space experments Kontur O. Zayats, M. Korenevskaya, A. Ilyashenko*, A. Lukashn Peter the Great St.Petersburg Polytechnc Unversty, 29, Polytechncheskaya str., Sant Petersburg 9525, Russa Abstract Ths artcle descrbes queueng systems model of data transmsson system for remote control of robot from board of ISS usng publc networks. Model has two ncomng flows, one servce channel, lmted buffer sze and randomzed push-out mechansm. Also model of a retral queueng system and lost packets wth specfed probablty are able to get back on servce. Two parameters: retral and pushng-out probabltes of randomzed mechansm have extremely hgh nfluence on model parameters lke loss probablty and average queue length and allow changng them on tens of percents. Also shown that retral queueng models are havng areas of lnear behavor and blockng too, as model wthout retral. 207 The Authors. Publshed by by Elsever B.V. B.V. Ths s an open access artcle under the CC BY-NC-ND lcense ( Peer-revew under responsblty ofthe scentfc commttee of the XIIth Internatonal Symposum «Intellgent Systems». Peer-revew under responsblty of the scentfc commttee of the XIIth Internatonal Symposum Intellgent Systems Keywords: remote control; randomzed push-out mechansm; retral queueng systems.. Introducton: In descrbed n detals the jont Russan-German space experment "Kontur", performed snce 2009 at the Internatonal Space Staton (ISS). From the begnnng, ths experment gave a number of mportant and practcally sgnfcant results and has been extended several tmes up to the present tme, settng off a seres of smlar studes (experments "Kontur-2", "Kontur-3"). The most mportant part of all the works n the seres "Kontur" s a soluton to the problem of processng nformaton flows, as well as the management of these flows. It s well known that the man analytcal method of mathematcal modelng of such systems s to consder them as specfc queueng systems (QS).But QS models that can adequately descrbe the network of nteractons are qute complex 2. Correspondng author. E-mal address: lyashenko.alex@gmal.com The Authors. Publshed by Elsever B.V. Ths s an open access artcle under the CC BY-NC-ND lcense ( Peer-revew under responsblty of the scentfc commttee of the XIIth Internatonal Symposum Intellgent Systems do:0.06/j.procs

2 O. Zayats et al. / Proceda Computer Scence 03 ( 207 ) In the experment man goal was to control remotely a robotc object usng nformaton about the operaton whch conssts of two qualtatvely dfferent components: the telemetry data wth addcton of force-feedback joystck data and vdeo stream. Both are transmtted through the broadband publc networks. Control commands broadcast va TCP transport protocol, and the results of vsual observaton of the vdeo stream s formed. The ntensty of the TCP-packet transmsson control and telemetry s 00 Kbt/s, and for UDP-packets of the vdeo stream, t reached.2 Mbt/s. Total channel bandwdth s about 256 Kbt/s. It s logcal that n the sense of the problem beng solved telemetry data should have preemptve prorty. However, only prortzaton s not enough flexble to provde wde qualty control method. For a gven experment arrval rates of hgh-prorty and low-prorty traffc buffer s flled wth mostly low-prorty packets, and the majorty of hgh prorty wll be lost, whch wll sgnfcantly reduce the effcency of the robot control. Also ths approach of data transfer system can be used n systems of quantum electronc. For example, detector of mechancal rotaton contans feed-back element, whch need a rapd block for nformaton processng. New methods of retral queueng systems wth randomzed push-out have possblty to mprove some characterstcs of ths detector: ts precson and effcency. To overcome ths dffculty n the theory of prorty queueng developed specal technques. In the late sxtes G.P. Basharn suggested usng a determnstc push-out mechansm, whch allows hgh-prorty packets to push-out of buffer low-prorty packets when t's full 3. Unfortunately, n our problem, ths approach s not very effectve, as hgh prorty packets wll domnate and fll whole storage qute fast. In ths case vdeo sgnal wll be sgnfcantly truncated, and control the robot wll become extremely dffcult. To make more precse tunng of telematc devce could be added a probablstc pushng-out mechansm when hgh-prorty packets aren't pushng-out low-prorty packets wth probablty equal to, but only wth some probablty α, whch plays the role of the control parameters of the system. Such mechansm has been proposed n the late nnetes by N.O. Vlchevsky and worked out n detal wth reference to a sngle-channel system wth nonpreemptve prorty n 4,5. The authors of ths artcle resolved problem smlar to 4,5 n case ofpreemptve 6,7 and alternatng 8 prorty. These results allowed us to buld model of telematcs devce, the probablty of choosng ratonally push-out probabltyα based on the propertes of the network envronment and to effectvely manage the robots aboard the ISS. At the same tme t remans unused another mportant approach for ncreasng the qualty of remote control. We are talkng about the possblty of re-sendng prevously lost n the packet network. Usng TCP-connectons allows to check the fact of recept of the package recever and, f necessary, re-send t agan. The theory of retral QS s well studed and currently s beng developed ntensvely. In ths paper, methods of ths theory 9 appled to the study of queueng models wth preemptve prorty, consdered n 6,7. 2. Queueng model of data transfer system As a man model for remote control n case of lmted bandwdth was used model wth two Posson dstrbuted ncomng flows, sngle servce channel and randomzed push-out mechansm from class M2 / M // k/ f. Model 2 was studed n steady state. Arrval rates of ncomng flows are and 2. Servce ntensty s μ.forgettng model closer to real devces add lmted buffer sze k. Buffer s lmted and t can get flled sometmes. In ths case we can add to the model pushng-out mechansm, whch allows to replace low-prorty packets n system buffer by hghprorty packets. Dfferent types of pushng-out mechansms where consdered by authors n 4-8. Such models are sutable when for sendng data UDP protocol s used, but n case of TCP such models are not workng. In ths case we add to model case when lost packet can get on servce agan wth specfed probabltyq for frst flow and q 2 for second. Such queueng systems are called retral systems. Theory of these queueng systems studed well n works of Stepanov 9. Lot s of queueng models can be consdered n combnaton wth retral. In these models when packet s comng to the system and gettng lost, t can try to get servced agan. It takes place n specal queue and watng random tme before gong to servce channel agan. Ths queue of packets, tryng to get on servce agan, s called an orbt 9.

3 564 O. Zayats et al. / Proceda Computer Scence 03 ( 207 ) To make model more flexble add probabltes of packet gettng nto orbt queue. Let t be for frst flow equal to q and packets from both flows are gettng lost. Schema of retral M / M // k/ f model presented n fgure. q, and for second q 2. Out of these queues packets are gong on servce agan. Else, wth probabltes ( ) ( q 2 ) 2 2 Fg.. Schema of retral M / M // k / f queueng system 2 2 Assume that tme nterval between packets comng from frst hgh-prorty and second low-prorty flows wth ntensty 0, are dstrbuted as 0, τ () τ = 0,,( =,2) a e Servce tme s equal for both type of packets and dstrbuted as b ( x) = b ( x) = μe μx. 2 Also n ths model we assume that tme whch packets spend n orbt s dstrbuted as c() τ = γ e γτ,( =,2) And we added probablty q of beng servced agan for packet from orbt. So, when t's tryng to be servced agan after awatng n orbt queue t's passng to servce channel only wth ths probablty. Total flow from orbt has more complex structure, because t s a superposton of a random flows number wth the ntensty γ. In 9 shown, that these flow has Posson dstrbuton wth ntensty rep, = γ norb,,( =,2), () where, orb n s an average retral queue length of -th type packets. Also ths flow statstcally ndependent from ncomng flow of ntal packets. From 9 obtan that average queue length of -th type orbt packets s equal to

4 O. Zayats et al. / Proceda Computer Scence 03 ( 207 ) n orb P q, =,( =, 2), () ( ) () 0, loss Ploss γ (2) () where Ploss s total probablty of -th type packet beng lost. By substtuton (2) n (), obtan P q rep, =,( =,2), () () 0, loss Plossq then actual ntensty of -th flow on queueng model entrance s = 0, + rep,,( =,2), and can be extracted as =,( =,2) () P q 0, loss So actual ntensty can be hgher than ntensty of ntal flow. In works 6-8 authors shown that loss probabltes depend on four parameters P = φ(,, k, α),( =,2), () loss 2 where, 2 -load factors by frst and second lows accordngly, k sze of buffer and α s a probablty of pushng out low prorty packet from buffer by hgh-prorty packet. Usng defnton of load factors obtan system of equatons for gettng unknown, 2,0 = = = μ φ(, 2, k, α) q,(,2), (3) where,0- ntal frst flow load factor, and φ (, 2, k, α) can be obtaned from 6-8 by gettng soluton for queueng model wthout retral. It s easy to see that ths system always has only one soluton. To obtan t rewrte (3) as = = (4),0 φ(, 2, k, α) q,(,2), and show on one chart dependences of left and rght parts of (4) from and fxed other parameters (fgure 2).

5 566 O. Zayats et al. / Proceda Computer Scence 03 ( 207 ) Numercal results Fg. 2. Left () and rght (2) parts of equaton (4) In addton to obtaned results n 6-8 can be found how loss probabltes depend on probablty of beng servced agan after loss q and q 2. Loss probabltes can be found usng (5). P p ( ) p, P p p p. k k k () (2) loss = 0 + α loss = + α + k = = 0 2 = 2 (5) As can be seen from fg.3, the dependence of the probablty of loss at weak hgh-prorty packets payload s close to lnear, regardless of the packet type. Ths effect also was found n 7-9 for model wthout retral and called lnear behavor effect. Moreover, t s monotoncally ncreasng as a functon of parameters q and q 2. In the transton to a strong hgh-prorty packets payload loss probablty changes only at low values of α close to 0. But when α s gettng close to, there s the effect of system blockng (fgure 4), when system buffer s flled wth hgh-prorty packets and can t servce all of them. Also by changng probablty α loss probablty of lowprorty packets can be reduced and some of them can reach servce channel. Usng ths effect, we proposed to change qualty of remote robotc control to fnd balance between telemetry and vdeo data. 4. Concluson: Numercal results obtaned n fgures 3-4 approved that effects from 6-8 whch were called areas of lnear behavor and areas of closng could be obtaned and for queueng system wth retral. Also from these chart can be seen that changng retral probablty for both types of packets can be used as one more effectve way of loss control n queueng model. Durng experment Kontur-2 all these effects were used and allowed to mprove react tme of changng frewall parameters to obtan better qualty of robot remote control from board of ISS.

6 O. Zayats et al. / Proceda Computer Scence 03 ( 207 ) Fg. 3.Dependence of both packets types loss probabltes from α and dfferent values of q and q 2 n case of weak hgh-prorty packets payload ( = 0.2, = 0.9 ). 2 Acknowledgements Ths work was fnancally supported by the Mnstry of Educaton and Scence of the Russan Federaton n the framework of the Federal Targeted Programme for Research and Development n Prorty Areas of Advancement of the Russan Scentfc and Technologcal Complex for ( , ID RFMEFI5786X02)

7 568 O. Zayats et al. / Proceda Computer Scence 03 ( 207 ) Fg. 4. Dependence of both packets types loss probabltes from α and dfferent values of q and q 2 n case of strong hgh-prorty packets payload ( =.2, = 0.2 ). References 2. Zaborovsky V, Mulukha V, Ilyashenko A. Cyber-Physcal Approach n a Seres of Space Experments Kontur. Lecture Notes n Computer Scence 205; 9247, p Vshnevsky VM. Theoretcal bascs of computer networks. Moscow: Tekhnosfera, Basharn GP. Some results for queueng systems wth prortes(n Russan). Queueng models n data transmsson systems. Moscow: Nauka; 969. p Avrachenkov KE, Shevlyakov GL, Vlchevsky NO. Randomzed push-out dscplnes n prorty queueng. Journal of mathematcal scence 2004; 22(4), p Avrachenkov KE, Vlchevsky NO, Shevlyakov GL. Prorty queuengwth fnte buffer sze and randomzed push out mechansm. Performance evaluaton 2005; 6(),p Ilyashenko A, Zayats O, Mulukha V, Laboshn L. Further Investgatons of the Prorty Queung System wth Preemptve Prorty and Randomzed Push-Out Mechansm. Lecture Notes n Computer Scence 204; 8638, p Mulukha V, Ilyashenko A, Zayats O, Zaborovsky V. Preemptve Queung System wth Randomzed Push-Out Mechansm. Communcatons n Nonlnear Scence and Numercal Smulaton 205; 2( 3), p Ilyashenko A, Zayats O, Mulukha V, Lukashn A. Alternatng prortes queueng system wth randomzed push-out mechansm. Lecture notes n computer scence 205; 9247, p Stepanov SN. Numercal methods for retral queung systems (n Russan). Moscow: Nauka;983.