IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 73, NO. 10, OCTOBER 2024 15125
Delay-Awa e Link Scheduling in IAB Ne wo ks
Wi h Dynamic Use Demands
Yeka e ina Sado aya , G adua e S uden Membe , IEEE, Olga Vikh o a , Membe , IEEE,WeiMao ,
Shu-ping Yeh ,OmidSemia i, Membe , IEEE, Hosein Nikopou ,
Shilpa Talwa , Senio Membe , IEEE, and Se gey And ee , Senio Membe , IEEE
Abs ac —In eg a ed Access and Backhaul (IAB) is a cos -
e icien ne wo k densi ica ion echnology o imp o ing he
co e age and capaci y o he millime e -wa e (mmWa e) cellula
ne wo ks. In IAB sys ems, use a ic is o wa ded o/ om he
wi ed base s a ion by one o mo e elay s a ions, known as IAB
nodes. Due o he mul i-hop elaying, hese sys ems may be subjec
o la ge packe delays and poo pe o mance when he load is
une enly dis ibu ed among nodes. Add essing his limi a ion ia
delay-awa e access and backhaul link scheduling in IAB ne wo ks
is challenging due o po en ially la ge ne wo k scale, complex opol-
ogy, hal -duplex, and in e e ence cons ain s. In his pape , he
opical link scheduling p oblem is o mula ed as a Ma ko decision
p oblem (MDP) o a single-dono IAB sys em wi h a gene al
opology ha allows o use s wi h di e en delay equi emen s
and a ic dynamics. The p oposed link scheduling s a egy join ly
op imizes (i) use a ic ou ing and (ii) mul iplexing o access and
backhaul links unde hal -duplex cons ain s and non-negligible
in e e ence ha may a ise in dense IAB sys ems e en wi h high
beam di ec ionali y. To add ess he complexi y o ou o mula ed
MDP, we conside se e al app oxima ion me hods, namely, Q-
lea ning, Mon e Ca lo T ee Sea ch (MCTS), and gene ic algo i hms
(GAs). Then, we p opose a cus omized e sion o he GA, which
p o ides he p e e ed op imali y–complexi y ade-o and o e s
a 15% packe delay educ ion as compa ed o he s a e-o - he-a
backp essu e algo i hm.
Index Te ms—IAB, millime e -wa e, link scheduling, ou ing,
hal -duplex cons ain , in e e ence, use dynamics.
I. INTRODUCTION
A. Resea ch Mo i a ion
INTEGRATED Access and Backhaul (IAB) echnology p o-
posed by he Thi d Gene a ion Pa ne ship P ojec (3GPP)
Manusc ip ecei ed 27 Feb ua y 2023; e ised 10 Janua y 2024 and 21 Ma ch
2024; accep ed 4 May 2024. Da e o publica ion 21 June 2024; da e o cu en
e sion 17 Oc obe 2024. This wo k was suppo ed in pa by In el Co po a ion,
and in pa by he Resea ch Council o Finland (P ojec s RADIANT, ECO-
NEWS, SOLID, and ALL-ON) . The e iew o his a icle was coo dina ed by
D . Xiaohu Ge. (Co esponding au ho : Yeka e ina Sado aya.)
Yeka e ina Sado aya and Olga Vikh o a a e wi h Tampe e Uni-
e si y, 33720 Tampe e, Finland (e-mail: yeka e ina.sado [email p o ec ed];
olga. ikh o [email p o ec ed]).
Wei Mao, Shu-ping Yeh, Omid Semia i, Hosein Nikopou , and Shilpa
Talwa a e wi h In el Co po a ion, San a Cla a, CA 95054 USA (e-mail:
[email p o ec ed]; [email p o ec ed]; [email p o ec ed]; ho-
[email p o ec ed]; shilpa. alw[email p o ec ed]).
Se gey And ee is wi h Tampe e Uni e si y, 33720 Tampe e, Finland, and
also wi h B no Uni e si y o Technology, 601 90 B no, Czech Republic (e-mail:
se gey.and ee[email p o ec ed]).
Digi al Objec Iden i ie 10.1109/TVT.2024.3409179
in [1] has ecei ed subs an ial a en ion om bo h academia and
indus y as a cos -e icien solu ion o ex ending he co e age
and imp o ing he pe o mance o u u e cellula ne wo ks
ope a ing a mmWa e equencies [2]. Due o o e ing la ge
bandwid hs han sub-6 GHz sys ems, mmWa e adio is c ucial
o he i h gene a ion and beyond (5G/B5G) sys ems o mee
he an icipa ed a ic g ow h and mo e s ingen equi emen s o
eme ging in e ac i e and imme si e applica ions [3]. Howe e ,
mmWa e links a e known o ha e signi ican ly highe pa h and
pene a ion losses and a e mo e p one o a mosphe ic abso p ion
as compa ed o, e.g., mic owa e links [4]. E en hough he
impac o losses can be e ec i ely educed by using ad anced
signal p ocessing and mul iple-inpu mul iple-ou pu (MIMO)
communica ions o o m highly di ec ional links, he esul ing
co e age is in e io o ha o sub-6GHz deploymen . Hence,
mmWa e sys ems equi e ul a-dense base s a ion deploymen s
o alle ia e co e age gaps caused by blockage and di ec ional
ansmissions. The s aigh o wa d densi ica ion by inc easing
he numbe o 5G New Radio (NR) nodeBs (gNBs) pe squa e
me e is cos ly and challenging in some loca ions. Ins ead, IAB
o e s apid and low-cos on-demand ne wo k densi ica ion by
deploying mul iple IAB nodes whe e addi ional co e age o
capaci y is needed.
IAB nodes a e wi eless elays in e connec ed wi h each o he
and wi h a dono gNB (DgNB) o e wi eless backhaul links.
The e o e, any new IAB node can be quickly added o he exis -
ing deploymen , while he al eady deployed nodes can be mo ed
o a new loca ion. Acco ding o he IAB a chi ec u e, which is
de ined in 3GPP TS 38.401 [5], an IAB node accommoda es bo h
dis ibu ed uni (DU) and mobile e mina ion (MT) unc ions as
shown in Fig. 1. MT unc ion de e mines IAB node as a child
node ha is con olled by he o he IAB nodes o dono , while
DU unc ion makes IAB node beha e as a pa en o he o he
IAB nodes and use equipmen (UE). IAB nodes and DgNBs can
o m di ec ed acyclic g aph (DAG) and spanning ee opologies
acco ding o 3GPP TR 38.874 [1]. Following he p inciples
o he open adio access ne wo k (O-RAN), cen al uni (CU)
and DU can u ilize a ious in elligen mic ose ices ( Apps o
xApps) implemen ed a he non- eal- ime and nea - eal- ime
adio access ne wo k (RAN) in elligen con olle s (RICs) [6] o,
e.g., p edic a ic demands, op imize opology, manage ou es,
and alloca e esou ces [7],[8] in IAB ne wo ks.
While 3GPP speci ica ions conside he possibili y o imple-
men ing backhauling in ou -o -band mode, mul iplexing access
© 2024 The Au ho s. This wo k is licensed unde a C ea i e Commons A ibu ion 4.0 License. Fo mo e in o ma ion, see
h ps://c ea i ecommons.o g/licenses/by/4.0/
15126 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 73, NO. 10, OCTOBER 2024
Fig. 1. Example IAB ne wo k wi h mul i-hop opology [1].
and backhaul links a he same equency p o ides a ac i e
cos bene i s due o ha dwa e and equency euse. This also
makes IAB nodes lowe in p ice han con en ional elays due o
he euse o mos o he 5G access in e aces a he backhaul
links [9]. Mo eo e , IAB sys ems can signi ican ly imp o e
ne wo k capaci y and delay pe o mance due o dynamic ime-
di ision duplexing (TDD) con igu a ion, which is enabled by
he lexible 5G NR ame pa e n s uc u e. The pe o mance o
IAB ne wo ks is elian on he ame pa e n es ablished by he
CU and announced by he dono a he beginning o e e y ame.
This pa e n indica es he sequence o uplink (UL) and downlink
(DL) slo s o he dono in a ame and canno be changed un il
he end o his ame. F ame pa e n along wi h use scheduling
and ou ing algo i hms p o ide mo e de ailed ins uc ions o
IAB nodes on how ime slo s can be used o p e en hal -duplex
misma ch and in e e ence [10].
Despi e he p omising bene i s o he IAB echnology, IAB
ne wo ks a e subjec o undamen al cons ain s o wi eless
mul i-hop ne wo ks. Fi s , in-band ope a ion in oduces se e al
challenges o op imizing esou ce alloca ion and link schedul-
ing due o he hal -duplex cons ain . The la e does no allow
IAB nodes o ansmi and ecei e signals simul aneously due
o signi ican sel -in e e ence a he node, he cancella ion o
which is challenging and cos ly. Second, use h oughpu and
packe delay pe o mance apidly de e io a es as he numbe o
hops be ween he dono and use s g ows [11],[12]. Mo eo e ,
UE mobili y and a ic demand changes lead o unbalanced
a ic ac oss UL and DL ansmissions.
The e o e, i is essen ial o p o ide e icien delay-awa e
a ic ou ing and use scheduling solu ions o mmWa e IAB
ne wo ks o imp o e he use -cen ic pe o mance and balance
he load in he ne wo k subjec o he hal -duplex and in e -
e ence cons ain s and dynamic UL and DL a ic. Speci i-
cally, ou wo k ocuses on a join op imiza ion o he ame
pa e n, ou ing, and use alloca ion in he o m o e icien
link scheduling ha conside s delay-sensi i e and delay- ole an
use applica ions. Since he pa e n is announced in ad ance, we
ope a e wi h a cen alized ame-based link scheduling solu ion
in IAB ne wo ks unde p edic ed a ic demands.
B. Rela ed Wo ks
Wi eless mul i-hop ne wo ks ha e been an ac i e a ea o
esea ch o a ew decades [13],[11]. Howe e , due o spe-
ci ic echnology limi a ions and applica ion use cases, no all
app oaches can be applied o he IAB sys ems. Fo example, he
complexi y o he link scheduling p oblem in wi eless mul i-hop
ne wo ks la gely depends on he unde lying opology and is
NP-ha d in gene al due o a la ge numbe o possible link
combina ions o scheduling. I is wo h no ing ha ou ing and
link scheduling p oblems a e ypically add essed sepa a ely in
pas wo ks. Fo ins ance, s a e-o - he-a nea -op imal delayed
column gene a ion me hod [14] o sol ing he link scheduling
p oblem in low-based wi eless mul i-hop ne wo ks has inspi ed
se e al da a-d i en app oaches [15],[16] o educe he size o
he link sea ch space o as e and mo e s able lea ning o he
op imal link scheduling s a egy. The wo k in [17] o e s an
elegan semi-cen alized amewo k o a ic ou ing in IAB
sys ems ha aims a minimizing end- o-end communica ion
la ency. Howe e , i does no op imize use scheduling a IAB
nodes and canno p o ide delay gua an ees.
To add ess he scheduling and ou ing p oblems join ly, back-
p essu e ou ing [18] and he maximum weigh ed ma ching
(MWM) i e a i e algo i hm o ins an aneous link schedul-
ing [19] a e widely employed. E en hough MWM algo i hms
a e highly a ac i e as app oxima e solu ions o he NP-ha d
weigh ed link scheduling p oblem due o hei simple concep ,
hey equi e con inuous bu e and channel s a e in o ma ion
upda es in e e y slo , which p oduces eno mous o e head i
implemen ed in eal-wo ld sys ems. Mo eo e , hese algo i hms
only op imize he h oughpu pe o mance o he sys em wi hou
conside ing delay-awa e me ics. In addi ion, hei complexi y
is ei he polynomial in he numbe o nodes o , in he bes case,
linea in he p oduc o he numbe o nodes and links, which
apidly g ows wi h he inc easing ne wo k size o he numbe o
communica ion links.
The complexi y issues associa ed wi h he backp essu e and
MWM algo i hms in IAB sys ems a e ackled by he adop ion o
da a-d i en me hods [17],[20],[21]. Speci ically, ein o cemen
lea ning (RL) a ac s g owing a en ion due o i s abili y o
lea n e icien policies ia in e ac ion wi h he en i onmen
when he a ic o channel s a is ics is unknown [22].The
wo k in [21] u ilizes RL o lea n he op imal scheduling policy
in IAB ne wo ks. I in eg a es a ame-based a ic p edic ion
module o minimize he eedback o e head o online lea ning.
Howe e , he lea ned policy is sub-op imal and ou pe o ms
he backp essu e al e na i e only unde some a ic egimes.
Se e al ecen wo ks on IAB p opose scalable semi-cen alized
and dis ibu ed link scheduling solu ions [23],[24],[25], which
na u ally s em om he backp essu e concep and, he e o e,
ocus on he ne wo k h oughpu op imiza ion a he han on he
sa is ac ion o use demands.
SADOVAYA e al.: DELAY-AWARE LINK SCHEDULING IN IAB NETWORKS WITH DYNAMIC USER DEMANDS 15127
Fig. 2. Illus a ion o op imal scheduling and ou ing solu ion and a ame
pa e n alloca ion ha can be de i ed om i .
C. Ou Con ibu ion
Ou wo k add esses impo an gaps in he exis ing esea ch
on scheduling and ou ing in IAB sys ems. Speci ically, he
majo i y o pas s udies conside ou ing and use scheduling
sepa a ely and/o dis ega d p ac ical sys em conside a ions, e.g.,
hal -duplex cons ain s. On he o he hand, he wo ks whe e
hese cons ain s a e accoun ed o ocus on he ne wo k u ili y
a he han on delay-awa e o use -cen ic me ics. On op o his,
pas known solu ions such as widely-employed backp essu e
and MWM algo i hms encoun e implemen a ion challenges
because a global con ol ac ion needs o be compu ed a e e y
ime s ep [18]. The e o e, ou con ibu ions in his pape can be
summa ized as ollows.
We de elop a no el 3GPP-complian op imiza ion ame-
wo k ha accoun s o he speci ic ea u es o IAB ne -
wo ks wi h he goal o sa is y di e se use demands wi hou
any pa icula assump ion on he a ic model. Speci ically,
we o mula e a new delay-awa e link scheduling p oblem
as MDP ha accoun s o ealis ic hal -duplex cons ain ,
non-negligible in e e ence, and UL and DL di ec ions o
communica ion.
We p opose a p ac ical cus omized gene ic algo i hm (GA)
ha deli e s desi able sys em pe o mance in e ms o se -
ice sa is ac ion and packe delay o delay-sensi i e lows.
I con e ges o he p e e ed pe o mance egion h ee
imes as e han he e e ence Mon e Ca lo T ee Sea ch
(MCTS) algo i hm. Mo eo e , i imp o es he packe delay
by 15% on a e age as compa ed o he baseline backp es-
su e algo i hm.
We assess he pe o mance o IAB sys ems unde a wide
ange o a ic load, deploymen , and opology con igu a-
ions. Based on hese obse a ions, we o mula e p ac ical
ecommenda ions o link scheduling in IAB ne wo ks
subjec o a gi en sys em se up.
The es o his pape is o ganized as ollows. Sec ion II
desc ibes he sys em model, while Sec ion III in oduces he
p oblem o mula ion. Sec ion IV p o ides de ails on he RL
amewo k used o o e come he complexi y o a gi en MDP,
while Sec ion Vou lines he employed app oxima e solu ions.
Essen ial simula ion assump ions and nume ical esul s a e dis-
cussed in Sec ion VI. Finally, Sec ion VII summa izes his wo k
and men ions i s po en ial ex ensions.
II. SYSTEM MODEL
This sec ion ou lines he assump ions adop ed o modeling a
mmWa e IAB ne wo k. We s a by desc ibing ne wo k deploy-
men and use a ic dynamics. This is ollowed by a summa y
o he channel and an enna modeling p ocedu e. Finally, he
in e e ence calcula ions a e explained.
A. Topology, Rou ing, and Use Demand Assump ions
We conside an IAB ne wo k wi h a single dono , VIAB
nodes, and UUEs. The opology is assumed o be gi en by a
g aph T={V,E}, whe e V={0,...,V} ep esen s he se o
IAB nodes including he dono and E={(eij)i,j∈V}deno es he
backhaul links. We conside wo ypes o opologies, namely,
DAG and spanning ee, which can be ob ained as explained,
e.g., in [26]. In spanning ee opology, each IAB node excep
he dono can ha e only one pa en , while in DAG opology,
IAB nodes can ha e up o Vppa en s.
Each UE can gene a e da a lows in UL and DL di ec ions. To
add ess delay equi emen s o di e en applica ions, we assume
ha UL and DL lows can be ca ego ized in o dis inc classes
o lows based on hei sensi i i y o packe delay. Wi hou loss
o gene ali y, we conside wo classes o lows, namely, delay-
sensi i e and delay- ole an lows. Le Fbe he o al numbe
o lows. F1deno es he se o lows wi h ame-based delay
equi emen s, while F0deno es he se o lows wi hou any
speci ic delay cons ain s. We le pa ame e δcon ol he a io
o delay-sensi i e and delay- ole an lows in he sys em. The
classes a e assigned andomly, such ha |F1|=δF, while1
|F0|=(1−δ)F.
Each low is associa ed wi h i s sou ce and des ina ion nodes
s and d om he join se o UEs U={1,...,U}and dono
node wi h index 0. Gi en he ne wo k opology T, he numbe
o pa hs be ween he sou ce and he des ina ion nodes can be
mo e han one. We le Kndeno e he se o lows, which ha e
node n∈Nin hei pa hs. When he numbe o pa hs om s
o d is highe han one, he ou ing decision o low is made
dynamically by he nodes depending on he queue backlogs.
Demand ∗
o low ∈Fis gi en as he numbe o packe s o
be deli e ed in a pa icula ame o sa is y he imely h oughpu
equi emen s. We assume ha low demands ( ∗
1,..., ∗
F)and
packe a i als a e known o he con olle a he beginning o a
ame and can be compu ed based on he p edic ed a ic load
and pe cei ed packe low a es.
The goal is o ind a scheduling and ou ing s a egy ha
ul ills he low demands and educes he delay o delay-sensi i e
1.and . ep esen loo ing and ceiling ope a o s, espec i ely.
15128 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 73, NO. 10, OCTOBER 2024
lows. As explained in Fig. 2, his s a egy p oduces a scheduling
pa e n, which se s he o de o link ac i a ions in space and ime.
B. Use Deploymen and Communica ion Model
1) P opaga ion: We conside he u ban mac ocell (UMa)
channel model as sugges ed o IAB ne wo ks in [1]. Acco d-
ingly, UEs a e uni o mly deployed o e he a ea o in e es ,
while he UE heigh s a e uni o mly dis ibu ed wi hin in e al
[1.5,20]m.
Le xand ybe he 2D and 3D dis ances be ween a UE and
an IAB node. A UE may all in o ei he line-o -sigh (LoS) o
non-LoS (NLoS) egion, he eby expe iencing di e en pa hloss
condi ions [27]. Speci ically, he LoS p obabili y in (1) shown
a he bo om o his page, depends on he 2D dis ance xand UE
heigh h, whe e
C(h)=0,h≤13 m,
(h−13)1.5
10 ,13 m <h. (3)
The pa h loss LdB(y) o he links in he LoS and NLoS
condi ions is p o ided by (2), shown a he bo om o his page,
whe e ωcis he ca ie equency in GHz, hBS deno es he heigh
o an IAB node, and he b eak-poin dis ance dBP is gi en by
dBP =4(h−1)(hBS −1)ωc,Hz
c,(4)
whe e cdeno es he speed o ligh and he ca ie equency
ωc,Hz is gi en in Hz.
Fo use associa ion, we assume ha each UE selec s a node
om Vwi h he maximum e e ence signal ecei ed powe
(RSRP). Fu he , la ge-scale link ading is assumed o be known
o he con olle a he beginning o a ame and does no change
du ing he ame du a ion.
2) An enna and In e e ence: In ou e e ence IAB de-
ploymen , he DgNB and IAB nodes comp ise o h ee
sec o ized an ennas wi h su icien spa ial sepa a ion o limi
sel -in e e ence [28]. We assume ha he beams in he ansmi
and ecei e di ec ions o he in ended communica ing pai a e
pe ec ly aligned. Beyond ha , we explici ly model an enna adi-
a ion pa e ns as ecommended by [27] o e alua e in e e ence,
since he beams o in e e ing ansmi e s and in ended ecei e
may o e lap. An example o in e e ence unde a pa icula
scheduling pa e n is shown in Fig. 3. Fo each link in he
scheduling pa e n, all o he links a e ea ed as in e e ing.
Acco ding o ou an enna model, he an enna adia ion pa e n
is ep esen ed as a supe posi ion o elemen adia ion pa e ns.
Fig. 3. Example in e e ing ansmissions and simul aneously ac i a ed links
a ime slo .
The e o e, he alues o he hal -powe beamwid h (HPBW) and
an enna gain depend on he numbe o an enna elemen s.
The adia ion pa e n A(φij,θ
ij)o an enna a node iseen a
node jis exp essed by
A(φij,θ
ij)=AE(φij ,θ
ij)
+10 log10 1+ρNH

m=1
NV

n=1|wmn mn|2−1,
(5)
whe e AE(φij,θ
ij)s ands o a single an enna elemen pa e n,
φij and θij a e he ho izon al and e ical angula shi s, espec-
i ely, wis he weigh ing ac o esponsible o he s eng h o
side lobes, is he phase shi , NHand NVa e he numbe s o
an enna elemen s in ho izon al and e ical planes, and ρis he
deg ee o co ela ion be ween he elemen s. The single an enna
elemen pa e n AE(φij,θ
ij)is compu ed as
AE(φij,θ
ij)=GE−min[−(AEH(φij )
+AEV(θij)),A
max],(6)
whe e GEis he gain o a single an enna elemen , Amax is
he on o back a io, while AEH(φij)and AEV(θij )a e he
a enua ion alues in ho izon al and e ical planes, co espond-
ingly [27],[29].
The gain in he main ansmi di ec ion o he in ended com-
munica ing pai is
G0
ij =A(0,0).(7)
PLoS(x)=1,x≤18 m,
18
x+exp(−x
63 )(1−18
x)1+C(h)5
4(x
100 )3exp (−x
150 ),18 m <x. (1)
LdB(x)=⎧
⎪
⎨
⎪
⎩
28 +22 log10(x)+20 log10(ωc),LoS,10 m ≤x≤dBP ,
28 +40 log10(x)+20 log10(ωc)−9log10(dBP )2−(hBS −h)2,LoS,d
BP ≤x≤5km,
32.4+30log10(x)+20 log10(ωc),NLoS.
(2)
SADOVAYA e al.: DELAY-AWARE LINK SCHEDULING IN IAB NETWORKS WITH DYNAMIC USER DEMANDS 15129
We no e ha he an ennas o he main ansmi ing– ecei ing pai
a e di ec ed owa d each o he . The e o e, he beam misalign-
men angle equals ze o, and he esul an gain in his di ec ion
is he bes achie able, which is compu ed ia (7). Fo ins ance,
Fig. 3shows an example link schedule, whe e UE 1 and UE
3 ansmi owa d he dono and IAB node 2, and IAB node 1
ansmi s owa d UE 2 and he dono . Fo ins ance, le us conside
he link be ween UE 2 and IAB node 1.
Howe e , he ho izon al and e ical beam misalignmen s φkj
and θkj be ween he a ge ecei e jand he in e e ing ans-
mi e ka e ypically non-ze o. Fo he example deploymen
in Fig. 3, he link om UE 3 o UE 2 is conside ed o be
an in e e ing one. Ha ing he coo dina es o he ansmi e
(xk,y
k,z
k)and he ecei e (xj,y
j,z
j), he di ec ion o a i al
can be compu ed as
(xkj,y
kj,z
kj)=⎧
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎩
(xj−xk)2
√(xj−xk)2+(yj−yk)2+(zj−zk)2)
(yj−yk)2
√(xj−xk)2+(yj−yk)2+(zj−zk)2)
(zj−zk)2
√(xj−xk)2+(yj−yk)2+(zj−zk)2).
(8)
The co esponding angula shi s φkj and θkj can be exp essed
by con e ing he Ca esian coo dina es in (8) in o he sphe ical
ones. Fu he , hese alues a e u ilized o weigh ing he incom-
ing signals acco ding o hei di ec ions o a i al and depa u e.
The e o e, he an enna gain in he in e e ing di ec ion o a
ecei ing an enna is gi en by
Gkj =A(φkj,θ
kj).(9)
A simila p ocedu e is pe o med o he compu a ion o he gain
o a ansmi ed signal.
III. PROBLEM FORMULATION
We assume ha he IAB ne wo k ope a es in slo ed ime and
o mula e a scheduling and ou ing p oblem o he du a ion o a
ame T.Le Q
n( )be he numbe o packe s o low queued a
node n∈N
a ime . The ne wo k o in e es has n∈N |Kn|
o o al queue leng h o di e en lows ac oss all nodes.
Le a
ij( )∈{0,1}be a scheduling decision ep esen ing
whe he he packe s o low a e ansmi ed o e he link
om node i o node ja ime . The join scheduling decision
p oduces a scheduling pa e n a( )=(a
ij( ))i,j∈N, ∈F.Due o
he hal -duplex cons ain , a node canno ansmi and ecei e
packe s a he same ime, whe eas i can ecei e om o ansmi
o se e al nodes. The e o e, he pa e n a( )should comply wi h
he ollowing hal -duplex cons ain :

∈F 
i∈P(n)
a
in( )·
∈F 
j∈P(n)
a
nj( )=0,n∈V,(10)
whe e P(n)is a se o immedia e neighbo s o node n. Owing o
he mul i-beam ansmission and ecep ion capabili ies a IAB
nodes [19], he maximum numbe s o simul aneously ac i e
ou going and incoming ansmissions a e limi ed by Nbas
ollows:

∈F 
i∈P(n)
a
in( )≤Nb,n∈V,(11)

∈F 
j∈P(n)
a
nj( )≤Nb,n∈V.(12)
Scheduling pa e n a( )is easible i cons ain s (10),(11),
and (12) a e me . We, hus, deno e by A he se o all easible
scheduling pa e ns o a gi en ne wo k deploymen .
Le PTij (a( )) be he ansmi powe o node i o node junde
he pa e n a( ). I node i∈N ansmi s o node j he packe s
o only one low, hen i sends hem wi h he maximum ansmi
powe Pi. O he wise, he powe Piis equally dis ibu ed ac oss
he lows yielding PTij (a( )) = Pi/j∈N  ∈F a
ij( ).
Le L(y)deno e he pa hloss (in he line scale) be ween
he nodes sepa a ed by dis ance y. As we demons a e in
subsec ion VI-B, o many scheduling pa e ns a∈A, he c oss-
link in e e ence is non-negligible [30]. The e o e, he signal- o-
in e e ence-plus-noise a io (SINR) o e link (i, j)deno ed by
Γ(yij,a( )) is gi en as ollows:
Γ(yij,a( )) = PTij (a( ))G0
ijG0
ji
(NW +Ij(a( )))L(yij),(13)
whe e Nis he he mal noise powe spec al densi y, Wis he
sys em bandwid h, Gij and Gji a e he co esponding linea
an enna gains a nodes iand j o he pe ec ly aligned beams,
and Ij(a( )) s ands o he in e e ence powe a he ecei e j
o a gi en pa e n a( ). The la e can be ob ained by
Ij(a( )) = 
k∈Kj(a( )) m∈N akm( )PTkm GkjGjk
L(ykj),(14)
whe e Kj(a( )) is he se o in e e ing nodes o node jgi en
he link scheduling pa e n a( ),Gis he an enna gain in he lin-
ea scale conside ing he co esponding ho izon al and e ical
angula shi s φkj and θkj o he cu en loca ions o he nodes.
The in e e ence can be compu ed independen ly o each node
once he pa e n a( )is known.
The capaci y o link (i, j)in slo exp essed as he numbe
o packe s is hen
Cij(a( )) = Fl(Wlog2(1+Γ(yij,a( )))) ,(15)
whe e Flis a unc ion ha de e mines he numbe o ansmi ed
packe s o a chosen modula ion and coding scheme [31].
We le b
ij(a( )) be he amoun o da a in low ansmi ed
om node i o node jin slo . The numbe o ansmi ed
packe s is de e mined by he capaci y Cij(a( )) and he numbe
o packe s in he backlog queue Q
i( ), so ha only he packe s
ha a e in he backlog queue can be ansmi ed subjec o he
capaci y:
b
ij(a( )) = a
ij( )minQ
i( ),C
ij(a( )).(16)
The numbe s o packe s in he queues as a esul o he
scheduling decision a( )a e gi en o all ∈F and ∈
{0,...,T −1}by he ollowing:
Q
n( +1)=Q
n( )+Λ
n( )
+
i∈P(n)
b
in(a( )) −
j∈P(n)
b
nj(a( )),(17)

15130 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 73, NO. 10, OCTOBER 2024
whe e Λ
n( )deno es he numbe o exogenously a i ed packe s
and, he e o e, Λ
n( )=0 o all IAB nodes n∈V {0}excep
o he dono . The ini ial sys em backlog Q
n(0) o n∈N
{d1,...,d
F} ollows om he dis ibu ion Q0, while Q
d (0)=
0 o ∈F.
Le =Q
d (T)be he sizes o he des ina ion queues o
lows ∈F a e Tslo s, which ep esen he numbe s o
deli e ed packe s du ing a scheduling in e al. The di e ence
∗
− indica es whe he a low demand is sa is ied. Conside a
case whe e he ini ial low backlog is g ea e han o equal o ∗
.
The demand o low is sa is ied i ∗
− ≤0 and is assumed
o be un ul illed i ∗
− >0 o ∈F. I is also possible
ha ∗
− <0 i all he packe s in he backlog queues o low
a e deli e ed o he des ina ion wi hin Tslo s. We, he e o e,
equi e ha ∗
− is always g ea e han 0. I he ini ial low
backlog is less han ∗
, he di e ence ∗
− always exceeds 0.
By minimizing ∗
− o e all lows, we aim a sa is ying he
low demands, bu canno imp o e he delay o delay-sensi i e
lows ∈F
1.
To educe he la e , we in oduce bina y penal y u (a( )),
∈F
1, o p io i ize he scheduling o packe s o delay-sensi i e
lows. I se es o impose a penal y i he size o he des i-
na ion queue Q
d ( )is no equal o he low demand ∗
o
delay-sensi i e lows ∈F
1. The penal y in slo equals 1 i
Q
d ( +1)≤ ∗
and equals 0 o he wise:
u (a( )) = 0,Q
d ( +1)≥ ∗
,
1,Q
d ( +1)<
∗
.(18)
We le π=(a(0),...,a(T−1)) be a cen alized scheduling
and ou ing s a egy o mula ed as a sequence o scheduling
decisions om he se Πo all easible s a egies.
Ou goal is o ind a s a egy π∗∈Π ha minimizes he
expec ed demand dissa is ac ion max[ ∗
− ,0]o e all lows
and imp o es he delay o delay-sensi i e lows. This can be
achie ed by sol ing he ollowing op imiza ion p oblem:
Min:
π∈Π
EπT−1

=0
∈F0
u (a( )) + 
∈F max[ ∗
− ,0]2,
which is subjec o: (10),(11),(12),(16),(17),and (18).
(19)
IV. REINFORCEMENT LEARNING
The p oblem in (19) ep esen s a ini e ho izon MDP. The size
o Πin he wo s case is |A|T. Howe e , he numbe o p ac ical
scheduling pa e ns in e e y slo , which a oid scheduling om
emp y queues, is usually signi ican ly less han |A|,bu emains
exponen ially high. The e o e, we u ilize a single-agen RL
app oach o ind a close app oxima ion o he solu ion o (19).
In his sec ion, we de ine RL-speci ic o mula ions ha include
s a es, ac ions, ansi ion p obabili ies, and cos s.
a) S a es: Le s (Q
i( ))i∈N, ∈F be he s a e o he
MDP a ime . All queues Q
na e ini e and bounded by he
demand ∗
in a gi en ame. The s a e space Sand i s ca dinali y
|S| can be gi en by
S=∪F
=1S ,S =(Q
n)n∈N :Q
n=0,..., ∗
,
(20)
|S| =( ∗
+1)K.(21)
b) Ac ions: A he beginning o ∈{0,...,T −1}, he
MDP agen chooses a easible ac ion a a( ),a ∈A.
c) T ansi ion p obabili ies: Since he a i als Λ
n( )and
la ge-scale ading a e known o he MDP agen and do no
change wi hin a ame du a ion, any ansi ion om s a e s
o s a e s
a e aking ac ion a is de e minis ic. Hence, he
ansi ion p obabili ies P(s
|s ,a
)=1 i s a e s
is p oduced
ia (16) and (17) om s by aking ac ion a ; o he wise,
P(s
|s ,a
)=0.
d) Cos s: Le g (s ,a
)and gT(sT)be he cos o aking
ac ion a in s a e s and he cos o being in s a e sTa he
end o he p oblem ho izon, espec i ely. The cos g (s ,a
)=
 ∈F0u (a ), while u (a )is gi en by (18). The cos o being
in s a e sTa e Tslo s gT(sT)= ∈F(max[ ∗
− ,0])2
ep esen s demand dissa is ac ion.
The e u n Rπ(s0) ep esen s he o al cos ob ained by ol-
lowing he s a egy π∈Π om s a e s0and is gi en by
Rπ(s0)=EπT−1

=0
g (s ,a
)+gT(sT).(22)
Minimiza ion o Rπ(s0)is equi alen o he p oblem in (19)
subjec o s ∈S and a ∈A. I is known as sho es pa h
p oblem [32] and can be sol ed i e a i ely h ough he Bellman
equa ion i he s a e and ac ion spaces a e small enough.
I is wo h no ing ha o a gi en ini ial s a e s0 he e migh
be se e al pa hs wi h he same cos , i.e., he op imal s a egy πis
no unique. Fo de e minis ic p oblems, in con as o s ochas ic
ones, minimizing he cos o e admissible ac ions a in e e y
decision epoch esul s in he same op imal cos as minimizing
o e sequences o ac ions π=(a(0),...,a(T−1)), since he
u u e s a es and con ol a e de e mined ia dynamic equa ions.
V. APPROXIMATE SOLUTIONS
In his sec ion, we desc ibe he algo i hms, which can be
adop ed o sol ing he o mula ed MDP o a ealis ic ne wo k
size and ame du a ion. We conside di e en algo i hms o
iden i y hei ad an ages in ela ion o he add essed p oblem.
A. Q-Lea ning
Fi s , we conside he Q-lea ning me hod, which uses a lookup
able o ind he bes ac ion in a gi en s a e. The so-called Q-
able [33] speci ies he alue o an ac ion aken in a pa icula
s a e. The Q- able is ini ialized wi h ze os; hen, he elemen s
q(s ,a
)o he able a e i e a i ely upda ed as
q(s +1,a
+1)=q(s ,a
)
+α(−g(s ,a
)+max
aq(s +1,a)−q(s ,a
)),
(23)
SADOVAYA e al.: DELAY-AWARE LINK SCHEDULING IN IAB NETWORKS WITH DYNAMIC USER DEMANDS 15131
Algo i hm 1: Q-Lea ning.
Ini ialize Q- able, α,Ne,T
o n=1,...,N
edo
Rese he en i onmen s0∼S
0
o =0,...,T −1do
Sample ac ion a using ε-g eedy policy
Take ac ion a and obse e g(s ,a
),s +1
i s /∈Q- able hen
Add q(s ,a
) o Q- able
end i
Upda e Q- able ia (23)
end o
end o
whe e αis he lea ning a e. No e ha we use nega i e ewa d
−g (s ,a
), which is de ined in Sec ion IV, since he o iginal
p oblem aims a minimizing he expec ed e u n. The solu ion
is summa ized in Algo i hm 1, whe e Ne e e s o he numbe
o aining episodes.
The lea ning o a Q- able is execu ed ia he ollowing s eps.
A e he ini ializa ion o he able, he lea ning a e, and he
numbe o aining episodes, he ini ial s a e s0is d awn om
a known dis ibu ion S0∈S. A e e y i e a ion, he ac ions
a e chosen andomly om Aacco ding o he ε-g eedy pol-
icy. Speci ically, ac ion a =a gmax
aq(s ,a)is selec ed wi h
p obabili y 1 −ε, while a andom ac ion om Ais selec ed wi h
p obabili y ε. Then, a e he co esponding cos is de i ed, he
Q- able is upda ed by ollowing (23). The algo i hm uns o a
ixed numbe o episodes, each o which is e mina ed a e T
s eps. In ou case, he e minal s a e co esponds o he queue
s a es Q(T).
The ime complexi y o his me hod depends on he ca di-
nali ies o ac ion and s a e spaces as O(T|A||S|). Mo eo e ,
bu e u iliza ion unde his algo i hm inc eases o e ime as new
ac ions and s a es a e disco e ed. The use o deep Q-lea ning
(DQL) helps ackle he p oblem o a g owing Q- able. Howe e ,
he p ocess emains memo y-hea y as i equi es s o ing he
s a es and ac ions in he eplay bu e . As he lea ning agen
may no encoun e he majo i y o he s a es du ing he lea ning
p ocess, we u he conside a Q-lea ning algo i hm wi h p io -
i ized sweeping ha can signi ican ly imp o e he pe o mance
o Q-lea ning in de e minis ic en i onmen s.
B. Q-Lea ning Wi h P io i ized Sweeping
In con en ional Q-lea ning, Q- alues a e upda ed in he o de
o agen expe ience, i.e., as hey a e encoun e ed. In con as ,
p io i ized sweeping upda es a e based on he impo ance o he
s a e–ac ion pai s [34]. The espec i e s eps a e summa ized in
Algo i hm 2.
We in oduce Pp io i ies o he encoun e ed s a es and
a p io i y queue PQ o s o e he mos p omising s a es. The
p io i ies a e compu ed ia a empo al di e ence e o be ween
he discoun ed es ima ed alue o he cu en s a e–ac ion pai
and he alue o he nex s a e–ac ion pai added o he ewa d
ecei ed. Howe e , e en hough he p io i ies a e upda ed o
Algo i hm 2: Q-Lea ning wi h P io i ized Sweeping.
Ini ialize q(s, a),Model(s, a),PQ,θ,∀s∈S,
∀a∈A(s)
o n=1,...,N
edo
s ←cu en non- e minal s a e
Sample ac ion a using ε-g eedy policy
Take ac ion a , obse e ewa d g(s ,a
)and s a e s +1
Model(s ,a
)←g(s ,a
),s
+1
P←|g(s ,a
)+γmaxaq(s +1,a)−q(s ,a
)|
i P>θ hen inse s ,a
in o PQwi h p io i y P
while PQis no emp y do
s ,a
← i s (PQueue)
g(s ,a
),s
+1←Model(s ,a
)
Upda e elemen s o Q- able ia (23)
o ∀¯s, ¯ap edic ed o yield s :do
¯g(s ,a
)←p edic ed ewa d o ¯s, ¯a, s
P←|¯g(s ,a
)+γmaxaq(s ,a)−q(¯s, ¯a)|
i P>θ hen inse ¯ain o PQwi h p io i y P
end o
end while
end o
e e y s a e–ac ion pai , only hose ha a e abo e he h eshold
θa e s o ed in he p io i y queue PQ. The nex s a e and ewa d
o each s a e–ac ion pai abo e he p io i y h eshold a e s o ed
in he Model a ay. Du ing he Q- able upda e p ocess, he las
s a e–ac ion pai om he p io i y queue is used o an upda e.
P io i ized sweeping allows o a mo e di ec ed sea ch o e
he p oblem sea ch space as i calcula es he impac o a new
s a e–ac ion pai on all i s p edecesso s and keeps ack o only
he impo an ones.
The heo e ical complexi y o he p io i ized sweeping
scheme is as high as ha o he con en ional Q-lea ning me hod.
Howe e , se e al s udies, such as he one in [35], demons a ed
empi ically ha he enhanced algo i hm con e ges as e as
compa ed o he con en ional op ion due o i s p io i ized sea ch.
C. Mon e Ca lo T ee Sea ch
The MCTS [36] scheme seeks he bes s a egy by combining
he ee sea ch me hod and he sampling echnique [37] o build a
decision ee om he ini ial s a e. In his algo i hm, he p oblem
is ep esen ed ia a g aph whe e s a es a e g aph nodes. The
ini ial s a e S0is named he oo node, while a node ex ending
om he oo o ano he node is named a child node.
This me hod has become a s a e-o - he-a echnique o de-
e minis ic combina o ial games and p oblems [38]. The unda-
men al challenge o balancing explo a ion and exploi a ion in
MCTS is add essed in he same way as in mul i-a med bandi
(MAB) p oblems. The algo i hm ea s each s a e o he sea ch
ee as a MAB and selec s an ac ion ha maximizes he uppe
con idence bound (UCB) heu is ics. In pa icula , he algo i hm
consis s o ou main s eps:
Selec ion: A he ini ial s ep, all g aph weigh s ˆ a e ini-
ialized as in ini e. The e o e, a child node in a g aph is
selec ed andomly. Then, he child node is chosen based
15132 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 73, NO. 10, OCTOBER 2024
on he maximiza ion o he UCB sco e, which is gi en by
max
aN (s ,a)
k=1(−Rπ)
N (s ,a)+CUCBlog(N (s0))
N (s ,a),
(24)
whe e N (s ,a)is he numbe o imes ac ion ahas been
selec ed in s a e s , while N (s0)is he o al numbe o is-
i s, N
k=1(−Rπ)is he ewa d accumula ed o e N (s ,a)
when ac ion ahas been selec ed in s a e s , and cUCB is
a pa ame e esponsible o he explo a ion–exploi a ion
ade-o .
Expansion: The sea ch ee is expanded ia all possible
ac ions by adding child nodes o he lea nodes.
Roll-ou : F om a selec ed child node, he sequence o
ac ions is chosen andomly a each dep h o he ee un il
he e minal s a e is eached. Then, o his sequence o
ac ions, an in e media e e u n is conduc ed o es ima e he
pe o mance o he selec ed child node.
Backp opaga ion: The ewa d e u ned om he p e ious
s ep is backp opaga ed all he way up o e e y node by
upda ing he accumula ed ewa ds, he numbe s o isi s,
and he co esponding UCB alues.
These s eps a e epea ed as many imes as ime o compu a-
ional esou ces allow. A s a egy is o med ei he a e a ixed
numbe o i e a ions o when a compu a ional limi is eached.
The complexi y behind a single upda e o he MCTS algo i hm
is O(T|A|). On he o he hand, he o e all complexi y o he
me hod depends on he o al numbe o i e a ions. In u n, he
numbe o i e a ions is a unc ion o mul iple ac o s, such as,
e.g., he ini ial s a e and deploymen pa ame e s.
D. Gene ic Algo i hm
GA ep esen s a policy-based app oach inspi ed by he bi-
ological e olu ion p ocess [39]. I s a s wi h an ini ial pop-
ula ion, whe e an indi idual ep esen s a scheduling policy
π=(a(0),...,a(T−1)) o all a( )∈A, while he gene o an
indi idual ep esen s a single pa e n a( ) o he ime slo .The
i ness sco e o an indi idual, hus, co esponds o he expec ed
e u n Rπ(s0)s a ing om s a e s0and ollowing policy π.
The size o he popula ion Npop is chosen a he ini ializa ion
s ep and does no change. The e o e, he algo i hm complexi y
depends on his pa ame e as O(TNpop). Fu he , he memo y
u iliza ion o GA is mo e e icien as compa ed o Q-lea ning
because i depends only on he popula ion size Npop, which
emains unchanged h oughou he simula ion ime.
The ini ial popula ion is gene a ed andomly, and he i ness
sco e o e e y indi idual is hen e alua ed. The i ness sco e
o he en i e popula ion is equi alen o he bes i ness sco e
among i s indi iduals. A new popula ion is ob ained om he
cu en one ia he ollowing s eps:
Selec ion: A he selec ion s ep, Npindi iduals wi h he
bes i ness sco e a e agged wi hin he popula ion. These
indi iduals a e named pa en s, while o he s a e named
child en. Fu he , wo pa en s wi h he bes i ness sco e
Algo i hm 3: Cus omized Gene ic Algo i hm.
Ini ialize popula ion o size Npop andomly
E alua e ini ial popula ion
o n=1,...,N
edo
o i=1,...,N
pop/2do
Pick wo pa en s wi h he bes i ness sco e
Rep oduce
Mu a e
end o
o j=Npop/2,...,N
pop do
Pick an indi idual Pbwi h he bes e u n Rπ
Iden i y lows wi h sa is ied demands Fsin Pb
Exclude a∈F
s om ac ion space A
o ac ion a( )in Pbdo
i a( )∈Ao sa is ied low queue is emp y hen
Compa e queues o unsa is ied lows
Change a( )
end i
end o
end o
E alua e popula ion
end o
a e selec ed om he cu en popula ion o ep oduce a
he nex s ep.
Rep oduc ion: A he ep oduc ion s ep, c osso e is pe -
o med o all pai s o pa en s o p oduce o sp ing. The
c osso e p ocedu e is execu ed by selec ing a c osso e
poin wi hin he pa en sequences and by exchanging hei
genes beyond ha poin . The c osso e poin o a pa en
is selec ed andomly om [0,...,T −1].
Mu a ion: O sp ing indi iduals can be subjec o a mu-
a ion, when pa e n a a a andomly selec ed posi ion o
policy πis o be changed. No e ha he newly p oduced
indi iduals always accoun o he hal -duplex cons ain ,
because a( )is selec ed om he se o ac ions A.
Bo h c osso e and mu a ion p ocedu es a e pe o med wi h
ce ain p obabili ies Pcand Pm, which a e se a he ini ial s ep
o he algo i hm execu ion. The abo e s eps a e epea ed un il
he ime/compu a ional limi o a gi en numbe o i e a ions is
eached.
E. Cus omized Gene ic Algo i hm
E en hough GA demons a es adequa e ope a ion in com-
bina o ial sea ch p oblems, i s pe o mance may d op due o
he andomized popula ion ini ializa ion, selec ion, c osso e ,
and mu a ion s eps [40],[41]. To o e come his sho coming,
we de elop a cus omized e sion o he GA o ou p oblem.
The pseudo-code o ou cus omized GA is summa ized in Al-
go i hm 3.
In he modi ied GA, he popula ion is gene a ed ia wo di e -
en me hods. Speci ically, he i s hal o he popula ion ollows
he ules o he classical GA me hod, while he o he hal is
p oduced ia a cus omized app oach. A he same ime, he bes
SADOVAYA e al.: DELAY-AWARE LINK SCHEDULING IN IAB NETWORKS WITH DYNAMIC USER DEMANDS 15133
indi idual is de e mined a each s ep. The second hal ep esen s
a modi ica ion o he bes indi idual (scheduling policy) being
ob ained by execu ing lines 10-19 in Algo i hm 3.I iswo h
no ing ha such a popula ion spli o e s mo e di e si y and
dec eases he p obabili y o alling in o a local minimum.
The complexi y o he modi ied GA e sion is simila o
ha o he classical implemen a ion in he wo s -case scena io.
Howe e , he cus omized algo i hm may con e ge as e han
he basic GA o he p oblem o in e es . This is because he
numbe o i e a ions ha he GA needs o con e ge is subjec
o andom mu a ions and c osso e s, which may no gua an ee
easonable con e gence. On he con a y, ou cus omized GA
has mo e con ol o e how he scheduling pa e ns a e upda ed,
because i aims o imp o e he cu en schedule as much as
possible a he han upda e he links in a pa e n andomly.
The links wi hin he scheduling pa e n a ha can be changed
a e selec ed based on he bu e s a es. Speci ically, o he
cu en bes policy, he numbe o ansmi ed packe s is com-
pa ed o he a ge equi emen s ∗
. Those links, which con ain
lows whe e he equi emen s we e sa is ied a e conside ed o
be ixed, while all o he links can be changed. No e ha i is
also necessa y o compa e no only he equi emen s bu also
he bu e s a es o hese lows o a oid scheduling a packe
ansmission om an emp y bu e . A e iden i ying he links
ha can be modi ied, we educe he ac ion space by excluding
hose ac ions, which in ol e only ‘sa is ied’ lows. Mo eo e ,
be o e an ac ion change, we ack he queues o ’unsa is ied’
lows o de e mine he numbe o po en ial changes in policy π
needed o sa is y he equi emen s as well as which lows should
be p io i ized o he change. In he ollowing sec ion, we p esen
a compa a i e assessmen o he discussed algo i hms.
VI. NUMERICAL RESULTS
A. Simula ion Assump ions
We conside a la ge numbe o IAB ne wo k deploymen s,
which esul s in many di e en ealiza ions o spanning ee and
DAG opologies. In pa icula , he DgNB is placed a he cen e
o a he edge o he cell, while UEs a e uni o mly dis ibu ed
wi hin he cell, and IAB nodes a e posi ioned wi hin he cell by
ensu ing su icien dis ance be ween each o he and he DgNB
as ecommended in [1]. Examples o he IAB deploymen s wi h
ealis ic ee and DAG opologies a e gi en in Fig. 4(a) and (b),
espec i ely.
We u ilize ou cus om simula ion so wa e w i en in Py hon
p og amming language o assess he pe o mance o he con-
side ed s a egies [42]. The modeling pa ame e s a e 3GPP-
complian and can be ound in Table II. The pa ame e s o
he app oxima ion algo i hms a e selec ed empi ically, i.e., a e
e alua ion o di e en alues, he p e e ed ones a e chosen. We
assume ha o he selec ed nume ology, he ime slo Δ is 1 ms
and i is ep esen ed by 14 OFDM symbols. This is a easonable
assump ion due o he p ac ical limi a ions o beam o ming.
Howe e , one can assume ha Δ is equal o he du a ion o
an OFDM symbol o a sequence o OFDM symbols o conduc
scheduling wi h a desi ed g anula i y.
Fig. 4. Examples o IAB ne wo k deploymen s. (a) Spanning ee opology.
(b) DAG opology.
Wi hou loss o gene ali y, we assume ha Λ
n(0)= ∗
and
Λ
n( )=0 o ∈[1,...,T −1]and ∈F. The low de-
mand ∗
can ei he be ob ained om eal da a o sampled as
ollows. In o de o unde s and he impac o he e ogeneous
demands on he sys em pe o mance, we in oduce pa ame e
σ∈{0.1,...,0.9,1} ha cap u es how a he low demands a e
om he capaci y egion [19] o a gi en opology and numbe
o use s. He e, σ=0 means ha all he demands a e wi hin
he ne wo k capaci y egion and σ=1 means ha each demand
exceeds he capaci y. Fo e e y alue o σ, we gene a e di e en
combina ions o low demands and hen a e age he esul s o
simula ion uns collec ed o each combina ion.
Wi h espec o unseen opologies, he scheduling s a egy is
upda ed e e y ame as he ini ial s a e o he MDP S0changes.
The la e means ha he ini ial queue backlogs and channel
s a es migh be upda ed. Howe e , all he conside ed algo i hms
u ilize p e iously lea ned s a is ics and s a egy, which acili-
a es inding a new s a egy. Whene e he ne wo k deploymen
changes, one needs o upda e s a e space Sand ac ion space A
wi h espec o he new numbe o IAB nodes, UEs, and ne wo k
opology be o e sol ing he a ge p oblem again.