Process control solutions for congestion control in computer networks

The 7 h In e na ional Symposium on Design, Ope a ion and Con ol o Chemical P ocesses (PSE ASIA 2016) PROCESS CONTROL SOLUTIONS FOR CONGESTION CONTROL IN COMPUTER NETWORKS Te esa ALVAREZ*, and Jo ge SANDOVAL Depa men o Au oma ic Con ol, Uni e si y o Valladolid, 47002 Valladolid, Spain Co esponding Au ho ’s E-mail: [email p o ec ed] ABSTRACT: The use o P ocess Con ol ideas o he solu ion o conges ion con ol p oblems is discussed he e. Conges ion appea s in mode n da a ne wo ks when ou e s ecei e mo e da a han hey can p ocess. I his conges ion is no p ope ly ea ed conges i e collapse occu s, wi h he ou e p o iding e y low h oughpu , as packages ha e o be esen mul iple imes. This p oblem is no dissimila o some luid con ol p oblems in P ocess Con ol, whe e lows ha e o be con olled o a oid o e lows. Thus, i can be modelled using luid models, so i is discussed in his pape how s anda d p ocess con ol ideas can be adap ed o deal wi h hese conges ion con ol p oblems. A case s udy in ol ing a se o AQM-based ou e s unde TCP p o ocol is ca ied ou , using a non-in e ac ing PID con olle p e iously p oposed o P ocess Con ol. Equi alen luid models a e p o ided and i s con ol ca ied ou . The esul s show how p ocess con ol ideas make possible o a oid conges ion when he con olle is adequa ely uned, despi e inhe en a ia ions. Keywo ds: Fluid Models, P ocess Con ol, PIDs, Conges ion Con ol. 1 In oduc ion Rou e s a e main componen s o mode n da a ne wo ks: hey a e esponsible o mo ing da a be ween di e en ne wo ks, being esponsible o ensu ing ha da a ge s whe e i needs o go. As hey connec di e en ne wo ks, hey a e equen ly a ec ed by conges ion, when hey ecei e mo e da a han hei a ailable capaci y, so some da a a e disca ded (see, o example, Azuma e al., 2006). This is a pa allel p oblem o o e lows in P ocess Con ol, agg a a ed by he ac ha da a no ecei ed a he ecep o is esen by he emi e : I his conges ion is no p ope ly ea ed so called conges i e collapse would appea (Jacobson, 1988), which is a pa allel p oblem o Wind-up in P ocess Con ol. I is discussed in his pape how s anda d p ocess con ol ideas (such as hose condensed in As öm and Hägglund, 2006; and O’Dwye , 2009) can be adap ed o co ec his p oblem by ca e ully egula ing he da a ha is disca ded. This pa allelism is based on he ac ha da a ne wo ks can be app oxima ed by dynamic luid models. As explained in Do Young (2005) luid modelling cap u es he a e age a e o how each low e ol es and i is use ul o know con e gence condi ions, ne e heless as ne wo ks ha e an inhe en andomness some imes a s ochas ic model can be usu ul. Bu as s a ing poin luid modelling is a well-es ablished and obus app oach o unde s anding ne wo ks and uning con olle s. The possibili y o using algo i hms de i ed om p ocess con ol sys ems has al eady being sugges ed (see, o example, Hollo e al., 2002; Bolaj a e al., 2010; Al a ez and Ma ínez, 2013 and e e ences he ein). This will be illus a ed o a speci ic case s udy in ol ing a se o AQM-based ou e s (p esen ed in Figu e 2). Mo e p ecisely, unde a s anda d TCP p o ocol i is shown ha a PID-like con olle ( he so-called non-in e ac ing con olle ype 5 p oposed o p ocess con ol p oblems by Hansen (1995), and u he s udied by O’Dwye , 2009, pp. 370), is an adequa e solu ion o his p oblem; a con olle is hen uned and es ed based on his s uc u e. To de elop he con olle , i s equi alen luid models a e discussed ( ollowing Bolaj a e al., 2010) and i s con ol ca ied ou using he selec ed PID-like con olle . In summa y, his shows how p ocess con ol ideas make possible o a oid conges ion when he con olle is adequa ely uned, despi e inhe en a ia ions in ne wo k pa ame e s (Figu e 3). 2 Fluid Models in Conges ion Con ol Many di e en models ha e been p oposed in he li e a u e o conges ion con ol p oblems (see, o example, Ve es and Boda, 2000, he book by S ikan , 2012 and e e ences he in). This pape solely concen a es on luid models, ha ha e he ad an age o p o iding a se o nonlinea di e en ial equa ions ha ep esen ai h ully he main dynamics o hese p ocess. F om hese nonlinea di e en ial equa ions i is hen possible o ca y ou analysis o he p oblem (see, o example, he s abili y analysis by Mazenc and Niculescu, 2003), and o ob ain app oxima e linea models in ans e unc ion o m, ha can be di ec ly use o design and une con olle s using P ocess Con ol ideas (see, o example, Hollo e al., 2002 o Bolaj a e al., 2010). July 24-27, 2016, Tokyo, Japan  2  Figu e 1: Dumbbell opology 2.1 TCP/IP NewReno dynamic model Now, he TCP/IP NewReno ne wo k dynamics is p esen ed. The dynamics o an AQM ou e a e complex due o he numbe o a iables ha come in o play: packe sou ces, p o ocols, e c. Ne e heless, i is possible o ob ain a nonlinea model ha ep esen s he dynamics o he sys em (See Hollo e al., 2002) conside ing ha he p o ocol used is TCP. The model ela es o he a e age alue o he ne wo k a iables and is desc ibed by he ollowing coupled, nonlinea di e en ial equa ions: 1 ()((())) () ( ()) () 2 ( ()) () (), 0 () () () max 0, ( ) , 0 () TCP TCP W W R R W p R R R R N CW q R q N CW q R               & & , (1) whe e W: a e age TCP window size (packe s), q  : a e age queue leng h (packe s), R: ound- ip ime = q/C+Tp (secs), C: link capaci y (packe s/sec), Tp: p opaga ion delay (secs), NTCP: load ac o (numbe o TCP sessions) and p: p obabili y o packe ma k. As explained by Hollo e al. (2002), he i s di e en ial equa ion in (1) desc ibes he TCP window con ol dynamic, and he second equa ion models he bo leneck queue leng h, as an accumula ed di e ence be ween he packe a i al a e and he link capaci y. The queue leng h and window size a e posi i e, bounded quan i ies, i.e.,  qq ,0 and  WW ,0 , whe e and W deno e bu e capaci y and maximum window size, espec i ely. In his o mula ion, he conges ion window size W( ) is inc eased by one e e y ound- ip ime i no conges ion is de ec ed, and is hal ed when conges ion is de ec ed. 2.2 Linea ized model Al hough an AQM ou e is a non-linea sys em, in o de o analyse ce ain ypes o p ope ies and design con olle s, a linea ized model is used. To linea ize (1), i is assumed ha he numbe o ac i e TCP sessions and he link capaci y a e cons an , i.e., NTCP( )= N and C( )=C. Figu e 2: Block diag am o AQM as a eedback con ol sys em q The 7 h In e na ional Symposium on Design, Ope a ion and Con ol o Chemical P ocesses (PSE ASIA 2016) To simpli y he de elopmen o a model adequa e o con olle design, he dependence o he ime delay a gumen −R on queue leng h q is igno ed, so i is assumed o be −R0. This app oxima ion is accep able when he ound- ip ime is domina ed by he p opaga ion delay (see Chen e al., 2006), which occu s when he capaci y C is la ge. R0 should be chosen such ha he abo e hypo hesis can be ensu ed, so a alue ha wo ks in he wo s case scena io should be ad isable. When he model is linea ized, he same supposi ion is made. I canno be denied ha calcula ions a e signi ican ly simpli ied, bu u he esea ch in he ma e would be ad isable. Local linea iza ion o (1) a ound he ope a ing poin esul s in he ollowing di e en ial equa ions:                      )( 1 )()( 2 1 00 0 2 2 0 0 2 0 0 2 0 q R W R N q R p N CR R q q CR R W W CR N W   , (2) whe e 0 )( WW W  , 0 qqq  and 0 ppp  , ep esen he pe u bed a iables. The ope a ing poin o a desi ed equilib ium queue leng h q 0 is gi en by: p T C q R 0 0, 0 0 TCP RC WN  and 2 0 0 2 W p . (3) The linea ized model (2) can be ew i en by sepa a ing he low equency (‘nominal’) beha iou P(s) o he window dynamic om he high equency beha iou ∆(s) which is conside ed as pa asi ic.   2 2 00 (2 ) () , (2 ) ( ) 1 TCP TCP CN Ps s NRCsR   0 2 3 0 2 () 1 Rs TCP N se RC    (4) Taking (4) as a s a ing poin , Hollo e al. (2002) gi e a eedback con ol desc ip ion o AQM (Fig. 1). The ac ion implemen ed by an AQM con ol law is o ma k packe s wi h a disca d p obabili y p( ), as a unc ion o he measu ed queue leng h q( ). The la ge he queue, he g ea e he disca d p obabili y becomes. 3 Con olle Design o he Case S udy I can be seen om (4) ha he linea ized model co esponds o a sys em wi h a delay and wo eal poles: (5) whe e he pa ame e s a e gi en by: ߬ ௠ ൌܴ ଴ ܶ ௠ଵ ൌ ோ బ మ ஼ ଶே ೅಴ು ܶ ௠ଶ ൌ ଵ ோ బ I has been p oposed by O’Dwye (2009) ha o he class o sys ems desc ibed by (5) he mos adequa e PID-like con olle is he one p esen ed in Figu e 3, which co esponds o he ollowing s uc u e: (6) Some uning ules a e sugges ed in O’Dwye (2009) o his con olle based only on he alue o he delay and ime cons an . As he models in (1) and (4) co espond o app oxima ions o he dynamics o he sys em, a ull es was ca ied ou using he simula ion ool ns2 (see Issa iyakul, and Hossain 2011 o a gene al desc ip ion o his ool). ns2 p o ides disc e e-e en da a ne wo k simula o s, which a e ex ensi ely used in da a ne wo k esea ch. Nex sec ion desc ibes in de ail hese es s. July 24-27, 2016, Tokyo, Japan  4   Figu e 3: Non-in e ac ing PID-like con olle 5 [3] 4 Simula ion esul s This sec ion desc ibes a se o expe imen s ha ha e been ca ied ou o show he p oposed app oach. Fi s , a non-in e ac ing PID-like con olle ha ollows he s uc u e p esen ed in Figu e 5 was uned using he linea model in (4). The PID con olle was uned o he nominal case ha co esponds o N TCP =325 links, delay R 0 =100ms; he link be ween he sou ces and Rou e 1 has a capaci y o C=20 Mb/s. The con olle uned o he nominal case had he ollowing nominal pa ame e s (in adequa e uni s): b=0.143, c=-0.00078, K c =-0.0015, T i =0.9889, T d =-0.00018. Once uned, i was implemen ed using Simulink ollowing he diag am block shown in Figu e 3 . Then he co esponding disc e e con olle was ob ained and compa ed o he con inuous PID. These simula ions ga e some insigh in he sys em pe o mance and con i med he adequacy o he con olle s ( esul s a e no p esen ed he e due o lack o space). Then, he non-linea simula ion ool ns2 was in oduced o simula e mo e ealis ic scena ios, based on he opology p esen ed in Figu e 4. Fo his de ailed simula ions s anda d blocks om ns2 lib a ies we e used, ha a e known o ai h ully ep oduce eal da a ne wo ks. The PID p oposed in Figu e 3 was no a ailable in hose lib a ies, so i was coded. This makes possible o es he designed con olle in se e al scena ios wi h di e en a ic pa ame e s, changing numbe o sou ces and di e en delays, using exponen ial dis ibu ions o he gene a ion o da a by he sou ces. Some esul s a e p esen ed in Figu es 5-8 and a e now discussed in de ail. Figu e 4: Dumbbell opology and ne wo k pa ame e s Figu e 5 and Figu e 6 show he queue and p obabili y e olu ion. Ou con ol a iable is he p obabili y o disca ding a packe and he con olled a iable he queue size in packe s. I is shown in he same plo he simula ion esul s o N=175, 325 and 500 sou ces when he e e ence is cons an and equal o 200 packe s. E en when he ne wo k condi ions a e di e en , he esul s a e adequa e wi h he designed con olle . Table 1 gi es a summa y o each o he h ee scena ios in e ms o mean, s anda d de ia ion and wo me ics widely used in communica ions. The QACD (Quad a ic A e age o Con ol De ia ion) is a me ic o measu e how well is he con olle wo king. I gi es a measu e o how much he eal alue is de ia ed om he desi ed alue. The lowe he alue he be e he esul . The 7 h In e na ional Symposium on Design, Ope a ion and Con ol o Chemical P ocesses (PSE ASIA 2016) Figu e 5: E olu ion o he queue leng h wi h di e en numbe o sou ces Figu e 6: E olu ion o he ma king p obabili y wi h di e en numbe o sou ces Numbe o Sou ces N Queue: Mean leng h Queue: S anda d de ia ion QACD: mean QACD: s anda d de ia ion 175 201.1 26.1 92.2 82.2 325 199.3 29.8 70.0 57.0 500 199.5 31.3 80.9 67.5 Table 1: Summa y o Resul s o di e en numbe o sou ces wi h he p oposed con olle The con olle gi es pe ec esul s o he nominal case (N=325), and adequa e esul s o he o he wo scena ios. I should be no ed ha om he obse a ion o Figu e 6 we can conclude ha he lowe ma king p obabili y belongs o he case when he e a e 175 sou ces. Figu e 7: E olu ion o he queue leng h when he e e ence changes Ano he se o expe imen s consis ed in changing he e e ence a a ious ime poin s. Some esul s a e p esen ed in Figu e 7 and Figu e 8: good pe o mance was ob ained in he h ee di e en si ua ions s udied. Figu e 7 shows he queue e olu ion and Figu e 8 depic s he p obabili y o ma king packe s. I can be seen ha he con olle is well uned as he e e ence is co ec ly acked.  July 24-27, 2016, Tokyo, Japan  6   Figu e 8: E olu ion o he ma king p obabili y when he e e ence changes 5 Conclusions I has being shown in his pape how p ocess con ol ideas can be adop ed o he conges ion con ol p oblem in compu e ne wo ks, by de eloping PID-like con olle s de eloped om equi alen dynamic luid models. This has being illus a ed o a speci ic case s udy, based on he non-in e ac ing con olle ype 5 used o p ocess con ol. When his PID-like con olle is adequa ely uned, i makes possible o obus ly a oid conges ion, as shown by de ailed simula ions in expec ed ope a ing condi ions. Acknowledgemen s Funded by MiCInn DPI2014-54530-R and FEDER unds. Re e ences As öm K.J. and T. Hägglund (2006), Ad anced PID con ol. ISA. NC. Azuma, T., T. Fuji a, T. and Fuji a, M. Conges ion con ol o TCP/AQM ne wo ks using S a e P edic i e Con ol, Elec ical Enginee ing in Japan, 156, 1491-1496 (2006) Bolaj a , M., Tadeo, F., Al a ez, T., & Rami, M. A. (2010). S a e- eedback wi h memo y o con olled posi i i y wi h applica ion o conges ion con ol. IET Con ol Theo y & Applica ions, 4(10), 2041-2048. Chen, J., F. Paganini, M.Y. Sanadidi, R. Wang and M. Ge la (2006). Fluid- low analysis o TCP Wes wood wi h RED. Compu e Ne wo ks, 50, 132-1326. Do Young Eun (2005). On he Limi a ion o Fluid-based App oach o In e ne Conges ion Con ol. ICCN, San Diego, USA. Hansen, Pe e D. Sel - uning con olle ha ex ac s p ocess model cha ac e is ics. U.S. Pa en No. 5,394,322. 28 Feb. 1995. Hollo , C.V., V. Mis a, D. Towsley, W. Gong (2002). Analysis and Design o Con olle s o AQM Rou e s Suppo ing TCP lows. IEEE T ansac ions on Au oma ic Con ol, 47, 945-959. Issa iyakul, T., & Hossain, E. (2011). In oduc ion o ne wo k simula o ns2. Sp inge Science & Business Media. Jacobson, V. (1988). Conges ion a oidance and con ol. ACM SIGCOMM'88. O'Dwye , Aidan. Handbook o PI and PID con olle uning ules. London: Impe ial College P ess, 2009. S ikan , R. (2012). The ma hema ics o In e ne conges ion con ol. Sp inge Science & Business Media. Te esa Al a ez, Diego Ma ínez (2013), Handling he Conges ion Con ol P oblem o TCP/AQM Wi eless Ne wo ks wi h PID Con olle s, IAENG T ansac ions on Enginee ing Technologies, 365- 379. Ve es, A., & Boda, M. (2000). The chao ic na u e o TCP conges ion con ol. In P oceedings o he Nine een h Annual Join Con e ence o he IEEE Compu e and Communica ions Socie ies (INFOCOM 2000), 3, 1715-1723). 