Novel radio frame design for efficient integration of wireless links into time-sensitive networks

No el Radio F ame Design o E icien In eg a ion
o Wi eless Links in o Time-Sensi i e Ne wo ks
Yousse El Kaisi, Ja ie Villa es, and Olga Mu˜
noz
Dep . o Signal Theo y and Communica ions
Uni e si a Poli `
ecnica de Ca alunya (UPC), Ba celona, Spain
E-mail: {yousse .el.kaisi, ja ie . illa es, olga.munoz}@upc.edu
Abs ac —This pape p esen s a no el adio ame design
o wi eless links ha allows e icien scheduling o mul iple
ime-sensi i e lows wi h bounded delay and a bi a ily small
packe ji e equi emen s. The p oposed design is compa ible
wi h he IEEE 802.1 s anda ds o Time Sensi i e Ne wo ks
(TSN) and pe mi s he e icien in eg a ion o wi eless links in o
newly a i ed wi ed TSN in as uc u e. Wi h his aim, we ha e
e o mula ed he window ese a ion mechanism in oduced in
s anda d 802.1Qb o deal wi h he a iable ansmission a e o
wi eless links. The new adio ame is o ganized in a sequence o
pa ially-o e lapped windows. I he in ended low does no use
i s window comple ely, he unconsumed ime can be scheduled o
o he lows in o e lapped windows. The bene i s o his app oach
a e e alua ed nume ically in an illus a i e indus ial scena io
showing subs an ial gain in e ms o bo h educed con ol
cycle ( lows’ pe iodici y) and enhanced ansmission h oughpu
(numbe o admi ed lows).
Index Te ms—Time-Sensi i e Ne wo king (TSN), adio e-
sou ce managemen , scheduling, low-la ency communica ions,
packe ji e .
I. INTRODUCTION
The au oma ion o many indus ies demands he de el-
opmen o de e minis ic communica ion ne wo ks ha allow
he exchange o c i ical da a wi h bounded and p edic able
la ency. Wi h his goal in mind, he IEEE 802.1 Time-
Sensi i e Ne wo king (TSN) Task G oup has de eloped a se
o s anda ds ha enable he deploymen o b idged E he ne
ne wo ks wi h bounded delay [1]. The adop ed p emise is
o minimize bu e ing in he ne wo k b idges by ese ing
ansmission windows a he b idge eg ess po s. This allows
an incoming low a i ing a an ing ess po o be immedia ely
w i en o he des ina ion eg ess po wi hou wai ing in a
queue. The a chi ec u e elies on wo s anda ds: 802.1as [2],
which enables p ecise synch oniza ion o all ne wo k nodes,
and 802.1Qb [3], which de ines he me hod o pe o ming
windowing.
Recen ly, he e has been a signi ican in e es in in eg a ing
wi eless connec ions in o eme ging TSN wi ed ne wo ks.
Va ious s anda diza ion g oups and indus ial conso ia a e
Wo k suppo ed by p ojec s MAYTE (PID2022-136512OB-
C21) and 6-SENSES (PID2022-138648OB-I00) unded by
MCIN/AEI/10.13039/501100011033 and ”ERDF A way o making Eu ope”,
EU, PREDICT-6G (g an 101095890) by EU’s Ho izon Eu ope, TIMING
(TSI-063000-2021-145) by MINECO UNICO5G and, g an s 2021 SGR
01033 and 2021 SGR 00772 by he Ca alan Go e nmen (AGAUR)
wo king on new mechanisms o o e delay gua an ees h ough
wi eless links [4] [5]. The p ima y obs acle o his goal is
he inhe en andomness o he wi eless channel. While wi ed
links can easily sus ain s able high ansmission a es, he
ansmission a e luc ua es andomly when connec ing wo
nodes o e he ai due o channel ading and ime- a ying
pa hloss.
Al hough de e minism is no s ic ly possible wi h wi eless
links, a cle e design o adio ames allows o bounded la-
ency wi h high p obabili y. This means ha , we ha e o accep
ine i ably ha , wi h non-ze o p obabili y, some packe s will
no be decoded co ec ly o in ime and will be decla ed los .
Unde his p emise, he s aigh o wa d design o minimize
packe loss is o ese e a sepa a e window in he adio ame
o e e y low and adjus i s du a ion o p o ide su icien ime
o ansmi ing he incoming packe s a he lowes a ailable
da a a e. While simple, his conse a i e design is ine icien
because windows a e no ully occupied when he channel
ealiza ion is a o able, and he ansmi e is allowed o selec
as e modula ion and coding schemes (MCS).
To imp o e e iciency, in his a icle we s udy he design o
adio ames wi h o e lapped windows, a oiding spa e ime
and, he eby, subs an ially inc easing he sys em h oughpu .
The design is ocused on he downlink o a gene ic wi eless
link, al hough he app oach is ex ensible o he uplink. The
p oposed design is assessed nume ically in he simula ion
sec ion o a wi eless local a ea ne wo k ope a ing in a ypical
indus ial en i onmen .
II. PROBLEM STATEMENT
We conside ha Kwi eless e minals, a ached o he
same access poin (AP), a e connec ed simul aneously o a
se e om which hey download indi idual da a lows. In
indus ial applica ions, he se e is ypically a p og ammable
logic con olle (PLC) ha pe iodically sends ins uc ions
o a se o Kmobile machines o obo s ha ing wi eless
connec i i y. These ins uc ions a e encapsula ed in o laye 2
ames, e e ed o as packe s he eina e , wi h a leng h o Bk
bi s and a pe iodici y gi en by he con ol cycle, Tkslo s, o
k=1,...,K. This ype o a ic is commonly known as
isoch onous in he li e a u e [6]. I is wo h no ing ha ime is
assumed o be slo ed so ha all ime in e als a e mul iple o
he slo ime Tslo , de ined as he minimum scheduling uni .
Accep ed e sion o he a icle published in he IEEE 35 h In e na ional Symposium on Pe sonal, Indoo and Mobile Radio Communica ions (PIMRC)
Sep embe 2024. DOI: 10.1109/PIMRC59610.2024.10817459. A ailable a : h p://ieeexplo e.ieee.o g
© 2024 IEEE. Pe sonal use o his ma e ial is pe mi ed. Pe mission om IEEE mus be ob ained o all o he uses, in any cu en o u u e media,
including ep in ing/ epublishing his ma e ial o ad e ising o p omo ional pu poses, c ea ing new collec i e wo ks, o esale o edis ibu ion o
se e s o lis s, o euse o any copy igh ed componen o his wo k in o he wo ks.
Access
Poin
Wi eless link
(Downlink)
E he ne
TSN
Swi ch
PLC
E he ne
TSN
Swi ch
E he ne
ime
ime
ime
ime
1 2 3 4
1 2 3 4
1 2 3 4
1 2 k=3 4
!!
"!,#$%&$ "!,'()
Te minal 4 Te minal 2
Te minal 3
Te minal 1
end- o-end delay (k=3)
Fig. 1. End- o-end delay example. A window in he eg ess po o a node
canno be opened un il he associa ed window in he ing ess po is closed.
Ou objec i e is wo old. Fi s ly, packe s should be ans-
e ed om he PLC o he des ina ion e minals wi h he
minimum end- o-end delay. Secondly, he end- o-end delay
should emain as s able as possible h oughou he connec ion,
he eby minimizing packe delay a ia ion (ji e ). The end- o-
end delay o a packe is de ined as he sum o he delays
incu ed a e e y link in he ou e om he PLC o he des-
ina ion e minal. Following he 802.1Qb ecommenda ion,
we assume ha a ansmission window opens in he eg ess
po o e e y b idge as soon as he packe en e s he b idge.
This app oach ensu es ha wai ing imes in queues become
negligible and he end- o-end delay is p ima ily de e mined
by he ansmission ime. Howe e , while ansmission ime is
de e minis ic and small in wi ed links, i ends o be a iable
and o en longe in wi eless links due o he andomness o
he p opaga ion channel.
Fig. 1 illus a es a simpli ied scena io wi h K=4 lows
ollowing he same ou e om he PLC o he wi eless access
poin . As depic ed in Fig. 1, he con ibu ion o he wi eless
link o he end- o-end delay is usually dominan . Consequen ly,
i is necessa y o design an e icien adio ame o anspo
he maximum numbe o isoch onous lows om he AP o he
e minals wi h bounded delay and p ede ined con ol cycles
{Tk}.
The s uc u e o he adio ame is as depic ed in Fig. 2. A
!!
!
!,#$ !
#$ !
%$
!
&= !
!,#$+ !
#$+ !
%$
#',()*+) #',,-. = #',()*+)+ $'
%'
1. . . k-1 k+1 . . . K
Fig. 2. Radio ame s uc u e. The ame p eamble (Tp,UL slo s) and he
uplink sec ion (TUL slo s) a e ma ked using a blued do ed pa e n. The
downlink is di ided in o Kindependen windows wi h K he numbe o
ac i e lows. The bu s ansmi ed in he k h window, wi h du a ion skslo s,
is indica ed using a ed s iped pa e n.
empo al window is assigned o e e y low in he downlink.
The k h window s a s a ime k,s a , has a du a ion o Nk
slo s, and ends a ime k,end. In Fig. 2, windows a e indepen-
den (no o e lapped). Howe e , o mul iplex mo e lows and
imp o e e iciency, we will allow windows o o e lap la e ,
i.e., k+1,s a <
k,s a +Nk. The objec i e is o design he
op imum alues o k,s a and Nk o k=1,...,K and
implemen a dynamic scheduling algo i hm o mul iplex in
ime (Time-Di ision Mul iple Access) he ac i e K lows using
he p ede ined windows as a e e ence. The ole o windows
in he schedule p ocedu e will be u he explained in Sec.
IV.
As highligh ed in Fig. 2, he ime equi ed o ansmi he
packe o low kis
sk=Bk/Rk, (1)
which a ies o e ime because i depends on he ime- a ying
ansmission a e Rk, gi en in bi s pe slo . To compensa e o
his a iabili y and a oid packe ji e , e minals can e ain he
ecei ed packe un il he end o he window, k,end, be o e
using i . This de-ji e ing p ocedu e is a well-known concep
in he li e a u e and is o en e e ed o as hold-and- o wa d
in he con ex o 5G [8].
The ( adio) ame du a ion T is adjus ed o he g ea es
common di iso (GCD) o all he low pe iods {Tk}.To
simpli y he analysis, we conside om now on ha all he
lows ha e he same pe iod (Tk=T) and, he e o e, he ame
leng h is se o his alue: T =T.
III. NON-OVERLAPPED WINDOWS DESIGN
In his sec ion, we conside a simple ame design ha
ese es an exclusi e window o each low, wi h no o e lap
among windows, so ha he ansmission o he low’s packe s
is no a ec ed by o he lows. Typically, he ansmission a e
in a wi eless link is selec ed acco ding o he Signal- o-Noise-
Ra io (SNR) a he ecei e o ensu e ha he e o p obabili y
due o ansmission e o s is negligible. The SNR is epo ed
pe iodically o he ansmi e and s ongly depends on he
p opaga ion channel. As he channel is andom, so a e he
ansmission a e and ime needed o send each packe , e en
o packe s co esponding o he same low. Consequen ly, he
du a ion o each window shall be de ined s a is ically.
The delay o packe s in he wi eless link implemen ing non-
o e lapped windows is di ec ly p opo ional o sk, hus, i is
also andom. Neglec ing he p opaga ion ime, he delay is
exp essed as
dk= k,s a  wi ed
k,end +sk. (2)
The i s e m in (2) is he ime be ween he closing ins an
o he window om he p e ious wi ed node, wi ed
k,end , and he
ins an a which he window in he wi eless link opens, k,s a .
These ins an s a e ixed and de e mined by how he ne wo k
a anges he windows along he connec ion pa h. We conside
ha he ne wo k p io i izes he design o he wi eless link,
as i is he c i ical one, and hen o ganizes he p e ious links
acco dingly so ha wi ed
k,end = k,s a and hence he delay only
depends on he second e m, dk=sk.
The window o each low has a limi ed du a ion, Nk=
k,end  k,s a . Packe s wi h skNkwill gene ally ex-
pe ience di e en delays, which would cause ji e . To a oid
i , he ecei e can make use o he p e iously men ioned
hold-and- o wa d mechanism [8] o inc ease he delay o all
ecei ed packe s so ha hey ma ch he window du a ion Nk.
Fo somewha ji e - ole an applica ions, i is also possible o
ma ch he delays o a alue lowe han Nkand allow some
ji e a ecep ion. The decision is up o he ecei e and does
no a ec he ame design wha soe e .
Howe e , he e will also be packe s wi h ansmission imes
la ge han he window du a ion, sk>N
k, which will be
los because hei delay is conside ed excessi e. Thus, lows
will su e a non-null packe loss a e pk. We expec use
applica ions o ha e a ce ain ole ance o packe loss ˘pk, such
ha , as long as he pk˘pk he applica ion will pe o m as
expec ed:
pk=p ob (sk>N
k)˘pk. (3)
The window du a ion Nkmus be la ge enough o ul il (3).
Indeed, he la ge Nk, he lowe pk, bu also he longe he
ame. Thus, Nkis selec ed as he smalles alue ha obeys
(3), which in p inciple is he one ha achie es he equali y.
In p ac ice, he e is a ini e numbe o a ailable ansmission
a es Rk(and consequen ly ansmission imes sk), so he
possible alues o he window du a ion Nka e limi ed o
hese op ions, which will in gene al no include he solu ion
ha eaches he equali y in (3). Bea ing his in mind, he
window du a ion has o be ob ained as ollows:
Nk= a gmax
N
p ob (sk>N), s. . pk˘pk. (4)
No e ha he esul ing packe loss p obabili y will be, in
gene al, lowe han he equi ed alue (pk<˘pk).
IV. OVERLAPPED WINDOWS DESIGN
The ame design in Sec ion III consis s o con iguous,
non-o e lapped windows. The window leng h depends on
he co esponding low’s channel s a is ics. Due o channel
andomness, mos ansmi ed packe s will in gene al no use
he whole window, lea ing some slo s emp y. In his sec ion,
we p esen an al e na i e ame design ha makes use o hese
emp y slo s o educe adio ame leng h. We achie e his by
designing windows ha open be o e he p e ious ones close.
Fig. 3. Window con igu a ion o he o e lapped windows design
Fig. 3 shows he gene al s uc u e o he window designed
o he k h low. We will e e o his window as he k h
window hence o h. The window is composed o wo egions.
The i s egion, Region A, goes om he opening o he
window k,s a un il he closing o he p e ious window
k1,end. The second egion, Region B, is he po ion o he
window beyond k1,end and un il k,end. Al hough mo e han
one window could close a e k,s a , o keep he explana ion
simple, we will assume ha k2,end  k,s a .
In Region A, low k1occupies as many slo s as i equi es
du ing each packe ansmission, and low kis hen allowed o
make use o he le o e slo s in he egion. This educes he
amoun o emp y slo s in window k1while no dis u bing
he ope a ion o he p e ious low, which is unawa e o he
o e lap. In Region B, he k h low does no o e lap wi h
p e ious windows and hus can use he esou ces wi hou
es ic ions. The ollowing window k+1 will o e lap wi h
window k, bu his o e lap will no a ec he scheduling o
low k.
The occupancy o slo s in egion A by p e ious lows is an-
dom, cha ac e ized by a andom a iable Mk. I s dis ibu ion
is pa ame e ized by he opening ins an k,s a . The ac ual
alue o Mka ec s he delay o he k h low’s packe s in he
ollowing manne :
dk=sk+Mk. (5)
The packe loss a e condi ion is hus gi en by:
pk=p ob (sk+Mk>N
k)˘pk. (6)
As k,s a dec eases, Region A becomes la ge and Region
B ends o dec ease, educing o e all ame leng h. Indeed,
he ame is a i s minimum when k,s a = 1,s a .We
e e o his con igu a ion as ull o e lap, since each window
o e laps comple ely wi h all he p e ious ones. Wi h his
se ing, window leng hs {Nk}inc ease wi h k, and he window
associa ed o he las low k=Kis as long as he whole ame.
This makes his con igu a ion gene ally no p ac ical, since i
esul s in lows wi h e y di e en delays, mos o hem being
in ole ably la ge. To keep he delays unde accep able alues,
we impose a second condi ion when designing he windows:
Nk˘
dk, whe e ˘
dkis he maximum ole able delay by low
k. No e ha ˘
dkNmin
k, whe e Nmin
kis he non-o e lapped
window du a ion o low k(window du a ion i Mk=0).
The pa icula case whe e ˘
dk=Nmin
kis e e ed o as he
minimum delay con igu a ion.
Fig. 4. F ame design example wi h 3 lows, highligh ing he o e lapped
egion o each window and showcasing he skslo s used by he k- h low
o ansmi ing i s packe .
The design o each window equi es knowing he leng hs
and opening ins an s o p e ious windows. Thus, i is nec-
essa y o design windows ecu si ely in ascending o de as
gi en by hei indexa ion k. No e ha low 1does no ha e
any p e ious windows and hus is designed as i i was non-
o e lapped (N1=Nmin
1). In p ac ice, he ollowing i e a i e
p ocedu e is used o design he k h window wi h as much
o e lap as allowed by he design cons ain s:
1: k,s a k1,end ˘
dk
2: i k,s a <0 hen
3: k,s a 0
4: end i
5: Nk 1
6: while Nk>˘
dkdo
7: k,s a k,s a +1
8: F(x) CDF(sk+Mk)
9: Nk min(x):F(x)1˘pk
10: end while
In Fig. 4 we p o ide a g aphical example o he o e lapped
design. O e all, his design p esen s an in insic ade-o
be ween delay and ame leng h, whe e he ex emes a e he
minimum delay con igu a ion ( ˘
dk=Nmin
k), esul ing in a
long adio ame, and he ull o e lap con igu a ion, yielding
minimum ame leng h bu la ge delays. I is necessa y o
highligh ha e en he minimum delay Nmin
kis al eady
subs an ially la ge han he delay in he wi ed links, so i is
impo an o weigh he imp o emen on ame leng h e sus
delay inc ease when designing he ame.
V. SIMULATION RESULTS
This sec ion p o ides a quan i a i e e alua ion o he p o-
posed ame design h ough so wa e simula ion. The simula-
ions po ay he pe o mance o he design in e ms o con ol
cycle ( ame du a ion) and h oughpu as he numbe o ac i e
lows g ows.
1) Wi eless ne wo k: A wi eless access ne wo k ounded
on he s anda d 802.11ax [7] is conside ed in his sec ion o
e alua ing he p oposed windows design. To a oid he andom
delay in legacy WiFi (con en ion-based access), we adop he
s anda dized O hogonal F equency Di ision Mul iple Access
(OFDMA) [9], mi o ing he medium access in 5G ne wo ks.
The ime slo du a ion is se o Tslo = 13.6µs, which
co esponds o one OFDM symbol wi h a 800 ns gua d
in e al. The ansmission bandwid h is se o BW = 20 MHz
and is di ided in o 256 subca ie s spaced 78.125 kHz, 234
o which a e used o da a ansmission. Fo simplici y, in
e e y slo , he schedule is compelled o assign all he da a
subca ie s o he same low, hence mul iplexing lows solely
in ime.
Fo he ansmission o each packe , he MCS is selec ed
based on he e ec i e SNR, a link quali y indica o ha is a
unc ion o he SNR o all he da a subca ie s. F om he MCS
able in he s anda d, comp ising 11 schemes, we selec he
highes MCS ha gua an ees a Block E o Ra e (BLER) no
highe han 104 o a LDPC-encoded block o 1458 by es. A
low BLER is adop ed because e ansmissions a e no easible
o he s udied delay-cons ained sys em. The e ec i e SNR is
e alua ed using he Recei ed Bi In o ma ion Ra e (RBIR), a
mu ual in o ma ion measu e ha was adop ed by he 802.11ax
ask g oup o physical-laye abs ac ion [10] [11].
2) Wi eless channel: We conside a andom ading channel
wi h exponen ially-decaying powe -delay p o ile and delay
sp ead ⌧= 50 ns [12]. Assuming Rayleigh ading, he disc e e
channel impulse esponse is gi en by
h[n]=Ce
nTs
2⌧a[n], (7)
whe e {a[n]}n0⇠CN(0,2) a e complex- alued ze o-
mean Gaussian-dis ibu ed andom a iables o uni a y (pe -
componen ) a iance, Ca no maliza ion cons an ixing
P1
n=0 E{|h[n]|2}=1, and Ts=1/BW he sam-
pling pe iod. We assume also unco ela ed sca e ing, i.e.,
E{h[n1]h⇤[n2]}=0 o any n16=n2.
The abo e delay sp ead (⌧= 50 ns) esul s in a cohe ence
bandwid h o a ound 1.6 MHz, de ined as he equency sepa-
a ion o which he au oco ela ion o he channel equency
esponse H( )=P1
n=1 h[n]ej2⇡ nTsdec eases by a
ac o o 0.9. Fu he mo e, he cohe ence ime is assumed o
be longe han he con ol cycle ( ame leng h), so he esul ing
ading channel is la in ime, bu equency selec i e.
The SNR o a gi en subca ie a equency is exp essed
as ollows:
SNR( )=·|H( )|2, (8)
wi h E{|H( )|2}=P1
n=0 E{|h[n]|2}=1and  he a e age
ecei ed SNR pe subca ie .
3) T a ic: Fo he sake o simplici y and cla i y, in he
simula ions we con igu e he lows o be iden ical, i.e., hey
sha e he same pe iodici y (T ), he associa ed channels a e
independen and iden ically dis ibu ed, and hey all sha e he
ollowing pa ame e s:
•= 20 dB
•B= 1500 By es
•˘p=2·103
A. Con ol cycle simula ion
The con ol cycle is de e mined by he ame du a ion
T . As shown in Fig. 2, he o al ame leng h depends on
he downlink and uplink po ions and he ame o e head.
In he simula ion, we compu e he ime equi ed o alloca e
he designed downlink windows in he downlink sec ion and
1 2 3 4 5 6 7 8 9 10
0
1
2
3
4
5
6
7
8
Fig. 5. Con ol cycle o di e en delay cons ain s. Delay cons ain s a e
no malized by he non-o e lapped window leng h Nmin =52slo s.
assume ha he uplink pa will be o equal leng h, i.e.,
TUL =TDL. This assump ion co esponds o a scena io wi h
balanced a ic load in bo h di ec ions. Acco dingly, he ame
du a ion is gi en by
T =Tp,DL +TDL +TUL =2
0.9TDL. (9)
In his equa ion, we a e also assuming ha he o e head Tp,DL
app oxima ely accoun s o a 10% o he ame leng h T
( ac o 1 o e 0.9 in (9)), which is a widely-accep ed o e head
in adio packe communica ions.
Fig. 5 shows he minimum allowed con ol cycle as he
numbe o lows inc eases o he non-o e lapped design and
he o e lap design case wi h di e en delay cons ain s ˘
d.
The non-o e lapped window du a ion Nmin is equal o 52
slo s (707.2 µs), which is he ansmission ime associa ed
o MCS1 (QPSK modula ion and code a e 1/2). This MCS
is selec ed by sol ing (4). The delay cons ain s ha e been
selec ed based on Nmin and exp essed no malized by his
alue in he igu e. Speci ically, he chosen delay cons ain s
a e 1 (minimum delay), 1.5, and 2 imes Nmin, espec i ely.
All con igu a ions show a linea inc ease wi h he numbe
o lows, al hough wi h di e en slopes. Fo cons ain s ˘
d=2
and ˘
d=1.5, hei cu es coincide wi h each o he and ba ely
di e om he ull o e lap case. Mo e in e es ing is ha he
minimum delay cons ain , ˘
d=1, e en hough i esul s in
a no able inc ease in con ol cycle wi h espec o he ull
o e lap case, s ill p o ides a much sho e con ol cycle han
he non-o e lapped windows design, all while cons aining he
delay o he same minimum alue.
B. Th oughpu simula ion
The o e all h oughpu is he amoun o in o ma ion ans-
mi ed pe uni o ime. In his simula ion we e alua e he
20 40 60 80 100 120 140 160 180 200
15
20
25
30
35
40
45
50
Fig. 6. Suppo ed h oughpu o di e en delay cons ain s. Delay cons ain s
a e no malized by he non-o e lapped window leng h Nmin =52slo s.
h oughpu ha he con igu a ions in Fig. 5 p o ide. The
h oughpu is es ima ed as:
TH =2K·B
T
=0.9K·B
TDL
, (10)
wi h Kbeing he numbe o downlink lows. As in (9), we
assume ha TUL =TDL o balanced DL and UL a ic loads.
Fig. 6 shows he h oughpu o he con igu a ions simu-
la ed in Fig. 5. The non-o e lapped design shows a cons an
h oughpu along K, p opo ional o he ansmission a e
o he MCS selec ed by sol ing (4), which yields a bi a e
Rk= 16.97 Mbps. The o e lapped windows designs ini ially
show a apidly g owing endency, bu as Kg ows la ge ,
he slope dec eases un il he h oughpu eaches a p ac ically
cons an alue. In e es ingly, he alue ha he ull o e lap
cu e ends o is he h oughpu ha would esul i he
ansmission ime o e e y packe was equal o i s a e age,
i.e., sk=E{sk}. This uppe bound is shown in he igu e
as a dashed line. As a e e ence, his h oughpu is o e 3
imes la ge han he non-o e lapped one. Howe e , he uppe
bound can only be (nea ly) achie ed by implemen ing ull
o e lap wi h an un easonable amoun o lows. Looking a a
ealis ic numbe o lows, o ins ance K= 10, i minimum
delay is desi ed, he h oughpu gain wi h espec o he non-
o e lapped case is 82%. In cases wi h mo e delay ole ance,
his gain could each up o 127%.
C. Packe loss a e simula ion
In his subsec ion we show he e ec o he packe loss a e
equi emen (˘
p) on he pe o mance o he ame design. The
simula ion shown in Fig. 7 compu es he minimum con ol
cycle o suppo 10 lows wi h he pa ame e s es ablished in
subsec ion V-3, excep o he packe loss ole ance ˘
p which
is now a iable.

10-3 510-3 10-2 510 -2 10-1
2
3
4
5
6
7
8
Fig. 7. Con ol cycle o di e en delay cons ain s. Delay cons ain s a e
no malized by he non-o e lapped window leng h. Numbe o lows is K=
10.
Fig. 7 p esen s he cu es o he same con igu a ions shown
in he p e ious simula ions. The non-o e lapped windows
cu e ollows a s ep unc ion, ha ing wo d ops a he alues
o ˘phighligh ed wi h dashed lines in he igu e. These wo
d ops coincide wi h he p obabili ies a which i is possible o
commu e o a highe ansmission a e Rk(i.e., highe MCS
index) in (4) and hus educe he window leng h Nmin. As in
he p e ious simula ions, delay cons ain s ˘
da e e e enced o
he minimum window leng h Nmin. Howe e , as his alue is
no cons an h oughou he ange o scanned p obabili ies,
he igu e is spli in h ee sepa a e sec ions, one o each
Nmin alue: Nmin =52, 35, and 26 slo s, espec i ely. In
each sec ion, he o e lap con igu a ions gene ally show sho e
con ol cycles han in he non-o e lapped case, and he gap
widens as ˘pinc eases. In pa icula , in he le mos sec ion
o he igu e (˘p<1.2·102), he con ol cycle can be
oughly di ided by wo, e en in he minimum o e lap case
(˘
d=Nmin). As shown in he igu e, when he delay cons ain
is elaxed, esul s a e no so a ec ed by he disc e iza ion o
Rk( ini e MCS able) and quickly con e ge o he smoo h
cu e achie ed wi h ull o e lap.
VI. CONCLUSION
In his pape , we ha e p oposed a no el ame design o
he wi eless segmen o TSN ne wo ks based on an enhanced
e sion o he window ese a ion mechanism o s anda d
802.1Qb . In ou design, he window designed o each
speci ic low o e laps wi h hose designed o o he lows.
The in ended low has he lowes scheduling p io i y in he
egion whe e he window o e laps wi h o he windows ha
s a be o e in ime. On he o he hand, he in ended low
has he highes scheduling p io i y in he egion ha does no
o e lap wi h p e ious windows.
While a ame design based on non-o e lapped windows
ha can be used only by he co esponding low (baseline
app oach) can be ine icien , ou app oach, combined wi h
scheduling and link con ol, can e icien ly use adio esou ces.
This e iciency ansla es in o a smalle con ol cycle o
ime-sensi i e applica ions, such as communica ing con ol
in o ma ion be ween a cen al se e and se e al wi eless
e minals. The con ol cycle educ ion compa ed o he base-
line app oach is mo e signi ican as he numbe o e minals
inc eases. This imp o emen in con ol cycle di ec ly ela es
o a subs an ial inc ease in h oughpu , up o 127% speci ically
o 10 e minals in he case o ou simula ions.
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