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
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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:
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଴
ܶ
௠ଵ
ൌ
ோ
బ
మ
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ଶே
೅಴ು
ܶ
௠ଶ
ൌ
ଵ
ோ
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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.
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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
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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.
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July 24-27, 2016, Tokyo, Japan
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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.
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