Enhancing Service Continuity in Non-Terrestrial Networks via Multi-Connectivity Offloading

IEEE COMMUNICATIONS LETTERS, VOL. 28, NO. 10, OCTOBER 2024 2333 Enhancing Se ice Con inui y in Non-Te es ial Ne wo ks ia Mul i-Connec i i y O loading Yeka e ina Sado aya , G adua e S uden Membe , IEEE, Olga Vikh o a , Membe , IEEE, Se gey And ee , Senio Membe , IEEE, and Halim Yanikome oglu , Fellow, IEEE Abs ac — Non- e es ial ne wo ks (NTNs) ha e ecen ly eme ged as a p omising pa adigm o compu a ion-in ensi e six-gene a ion (6G) applica ions, which may ange om aug- men ed eali y o disas e elie . Mo eo e , NTNs can ca e o unin e up ed connec i i y needs in bo h u al and u ban a eas. In u ban se ings, unc ewed ae ial ehicles (UAVs) and high-al i ude pla o m s a ion (HAPS) play c ucial oles in sup- po ing delay-sensi i e compu a ion applica ions o e es ial use s when e es ial ne wo ks ace limi a ions. Gi en he eme ging in e es in mul i-connec i i y o NTNs, his le e in es- iga es UAV- and HAPS-assis ed mul i-connec i i y compu a ion o loading in u ban a eas. Speci ically, we p opose wo no el mul i-connec i i y o loading s a egies o imp o e he p obabili y o imely ask compu a ion, along wi h a amewo k o op imiz- ing he co esponding o loading p obabili ies on o HAPS and UAVs. Ou esul s demons a e ha u ilizing mul i-connec i i y in NTN-assis ed o loading can achie e a 75% educ ion in ask compu a ion delay as compa ed o scena ios wi h no o loading. Index Te ms— HAPS, UAV, NTN, mul i-connec i i y, MEC, o loading. I. INTRODUCTION MOBILITY o use de ices causes spa ial and empo al demand luc ua ions ac oss e es ial ne wo ks. To p e- en se ice ou ages, mobile ne wo k ope a o s (MNOs) o en o e -p o ision by inc easing he densi y o hei e es ial base s a ions (BSs). These BSs a e s a egically clus e ed in u ban a eas likely o expe ience peak demand. Howe e , he densi ica ion signi ican ly aises bo h capi al and ope a ional expendi u es o e es ial ne wo ks and he ne wo k’s ene gy consump ion due o he unde u iliza ion o BSs when demand is low. While a ious ne wo k ene gy sa ing echniques ha e been de eloped o add ess his issue, e es ial densi ica ion emains unsus ainable in he long un. This p oblem can be mi iga ed by in eg a ing non- e es ial ne wo k (NTN) wi h exis ing adio access ne wo ks (RANs). High al i ude pla o m s a ion (HAPS) and unc ewed ae ial ehicle (UAV) Manusc ip ecei ed 2 July 2024; accep ed 18 July 2024. Da e o publica ion 29 July 2024; da e o cu en e sion 11 Oc obe 2024. This wo k was sup- po ed by he Resea ch Council o Finland (P ojec s ALL-ON, ECO-NEWS, SOLID, and RADIANT). The associa e edi o coo dina ing he e iew o his le e and app o ing i o publica ion was M. Elha ab. (Co esponding au ho : Yeka e ina Sado aya.) Yeka e ina Sado aya and Olga Vikh o a a e wi h he Uni o Elec ical Enginee ing, Tampe e Uni e si y, 33014 Tampe e, Finland (e-mail: yeka e ina. sado [email p o ec ed]; olga. ikh o[email p o ec ed]). Se gey And ee is wi h he Uni o Elec ical Enginee ing, Tam- pe e Uni e si y, 33014 Tampe e, Finland, and also wi h he Depa men o Telecommunica ions, 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]). Halim Yanikome oglu is wi h he Non-Te es ial Ne wo ks (NTN) Lab- o a o y, Ca le on Uni e si y, O awa, ON K1S 5B6, Canada (e-mail: [email p o ec ed]). Digi al Objec Iden i ie 10.1109/LCOMM.2024.3434400 a e pa icula ly a ac i e o his aim as hey can be deployed on-demand o quickly espond o su ges in e es ial ne wo k load [1]. In addi ion o p o iding on-demand connec i i y, NTNs can hos mobile edge compu ing (MEC) se e s o p ocessing and analyzing in o ma ion om powe -cons ained de ices, he eby acili a ing he ansi ion owa d sa e and sma e en i onmen s [2]. NTNs can suppo MEC by allowing use equipmen (UE) and In e ne o Things (IoT) de ices o o load hei compu a ionally in ensi e asks such as objec de ec ion, ecogni ion, acking, o ajec o y p edic ion o , e.g., u ban augmen a ion, sma ci y, and public sa e y applica ions. P o- cessing hese asks on he de ice side is o en es ic ed by i s small ba e y capaci y. A c i ical equi emen o hese applica ions is he suppo o eal- ime la ency o ensu e imely decision making. Bo h HAPS and UAVs, as pa o an NTN, ha e he po en ial o such applica ions. HAPS sys ems a e ypically deployed a al i udes o 20 km, which educes p opaga ion la ency o less han 1 ms. They ha e a la ge enough payload o suppo a high capaci y MEC on boa d and can be equipped wi h powe ul ene gy sou ces, including sola and wind ene gy con e e s. Mo eo e , he a mosphe ic empe a u e a HAPS’s ope a ing al i udes helps sa e ene gy o cooling and allows o scaling up he compu- a ion capaci y. Di e en aspec s o HAPS-aided compu a ion o loading ha e been s udied including join o loading and caching o imp o ed o loading delay [3], as well as join o loading and esou ce alloca ion o educed UE ene gy consump ion [4]. Howe e , as poin ed ou in [1], agg ega ing all he load on a single HAPS may esul in conges ion and sig- ni ican pe o mance deg ada ion. This issue can be add essed ia o loading di e si y, by in oducing less powe ul bu mo e adap i e UAV-aided MEC [5]. Coope a ion be ween HAPS and UAVs alle ia es limi ed compu a ion esou ces and endu ance ime o UAVs, he eby sa is ying s ingen applica ion equi emen s. Ano he app oach o enhancing he o loading di e - si y is h ough mul i-connec i i y, which enables de ices o connec o mul iple BSs simul aneously. Recen wo ks on mul i-connec i i y in NTNs ha e demons a ed p omising esul s o load balancing [6] and enhanced se ice con inu- i y [7]. While mul i-connec i i y is s anda dized and widely used o e es ial ne wo ks, i s implemen a ion in NTN p esen s se e al challenges [8], one o which is e icien ask and a ic s ee ing be ween nodes. To he bes o ou knowledge, his is he i s s udy o mul i-connec i i y o loading ha add esses he compu a ion ask s ee ing challenge in NTNs. In his le e , we benchma k © 2024 The Au ho s. This wo k is licensed unde a C ea i e Commons A ibu ion-NonComme cial-NoDe i a i es 4.0 License. Fo mo e in o ma ion, see h ps://c ea i ecommons.o g/licenses/by-nc-nd/4.0/ 2334 IEEE COMMUNICATIONS LETTERS, VOL. 28, NO. 10, OCTOBER 2024 Fig. 1. Conside ed NTN deploymen wi h HAPS- and UAV-assis ed MEC. wo p oposed mul i-connec i i y-speci ic o loading s a egies agains a baseline app oach om [9] adap ed o ai com- pa ison. All he s a egies a e op imized o maximize he p obabili y o in- ime ask compu a ion based on he de eloped analy ical model, e alua ed, and compa ed h ough ex ensi e simula ions. Ou esul s demons a e ha mul i-connec i i y o loading imp o es in- ime compu a ion o UE asks a a ma ginal inc ease in UE ene gy consump ion. II. SYSTEM MODEL A. Deploymen and Sys em Assump ions We conside an NTN deploymen ea u ing a HAPS and NUAVs, which p o ide MEC se ices on demand [10] o e es ial UEs wi h delay-awa e and compu e-in ensi e appli- ca ions when he capaci y o e es ial RANs is insu icien . As illus a ed in Fig. 1, he a ea o in e es is modeled as a disk wi h a adius RHAP S , which co esponds o he co e age a ea o he HAPS. The on-demand UAV co e age a ea is modeled by a disk wi h a adius RUAV , which depends on he deploymen si e’s en i onmen . Ou a ge ed UEs, being se ed by he NTN, a e assumed o be uni o mly dis ibu ed wi hin he co e age a ea o he UAVs, hence ensu ing ha each UE is wi hin he co e age o a leas one UAV. The HAPS is s a iona y and accessible o any o he conside ed UEs. UEs selec senso y pe cep ion o he en i onmen acco ding o he gene a e-a -will model [11] wi h in ensi y ϵ. The la e means ha he samples a e gene a ed a he UEs acco ding o a Poisson p ocess. The senso y in o ma ion is ep esen ed as s acked ideo ames, which a e p ocessed as a ba ch, while he ba ches a e o he ixed size n[12]. Each ba ch equi es a cons an compu a ional load C o , e.g., objec de ec ion and ecogni ion ask, which has o be execu ed wi hin a deadline ∗. This deadline may co espond o he in e al be ween wo consecu i e en i onmen samplings. We assume ha UEs as well as MEC se e s a he HAPS and UAVs ha e di e en numbe s o cen al p ocessing uni s (CPUs) and CPU equencies. Speci ically, each UE is equipped wi h a single CPU [12], while HAPS and UAVs ha e cUAV and cHAPS CPUs onboa d, espec i ely [9]. The CPU equencies a UEs, UAVs, and HAPS a e deno ed by CUE, CUAV, and CHAPS, espec i ely, being measu ed in GFLOPs. The ask p ocessing ime, consequen ly, a ies ac oss he compu ing nodes and can be gi en as DUE =C/CUE,DUAV = C/CUAV, and DHAPS =C/CHAPS. UE can compu e i s asks locally o o load hem on o UAV and/o HAPS. We conside a compu a ion o loading s a egy om [9] as a baseline, by ex ending i o include he capabili y o ask o loading o UAVs. In his baseline s a egy, UEs o load hei asks o he associa ed UAV wi h p obabili y ξ, o he HAPS wi h p obabili y η, o compu e hem locally. We also p opose eplica ion and spli ing o loading s a egies ha le e age mul i-connec i i y capabili ies a he UEs. The eplica ion s a egy in ol es he UE sending ask eplicas o bo h HAPS and UAV, and he spli ing s a egy in ol es spli ing he asks equally be ween HAPS and UAV. In bo h cases, he p obabili y o o loading is deno ed by ξ. The ime ins ances o ask gene a ion a e iden ical and independen ac oss all UEs. When a new ask is gene a ed, a UE immedia ely makes an o loading decision, which esul s in he ask a i al a he HAPS and UAVs being a supe posi ion o se e al hinned Poisson p ocesses. Le µbe he a e age numbe o UEs wi hin he co e age o a UAV. Unde he baseline s a egy, asks a i e a his UAV wi h in ensi y ξµϵ and a he HAPS wi h in ensi y ηNµϵ. Fo he eplica ion and spli ing s a egies, he in ensi ies o ask a i als a he HAPS and UAV a e ξµϵ and ξNµϵ, espec i ely. Al hough he a e age numbe o asks o loaded on o UAVs and HAPS is he same o hese s a egies, he payload di e s because he asks a e di ided in he spli ing s a egy. B. T ansmission Delay The signal- o-noise a io (SNR) be ween a ansmi e and a ecei e in he conside ed sys em is gi en as Γ = PTX(G/N)RX kWL ,(1) whe e PTX is he e ec i e adia ed powe , (G/N)RX is he ecei e an enna-gain- o-noise- empe a u e, Lis he pa h loss in NTN gi en by [12],kis he Bol zmann cons an , and W is he sys em bandwid h. Le ΓUL UAV,ΓDL UAV,ΓUL HAPS, and ΓDL HAPS be he SNR o uplink (UL) and downlink (DL) communica ion channels be ween UE, UAV, and HAPS acco ding o he deploymen . The co esponding link capaci y he e o e yields Ri j=Wlog21+Γi j,(2) whe e i∈ {UL,DL}and j∈ {UAV,HAPS}. The communica ion delays be ween a UE i s associa ed UAV o he HAPS in he cases o he baseline and eplica ion s a egies can be exp essed as Ti j=n/Ri j. Fo he spli ing s a egy, he delay is Ti j=δjn/Ri j, whe e δjis he ask spli ing a io such ha δUAV +δHAPS = 1. SADOVAYA e al.: ENHANCING SERVICE CONTINUITY IN NTNs VIA MULTI-CONNECTIVITY OFFLOADING 2335 C. P opaga ion Delay Due o a signi ican di e ence in he deploymen al i udes be ween HAPS and UAVs, he p opaga ion delay o he HAPS may impac he o e all communica ion delay, he eby in luenc- ing he choice o an o loading s a egy. The e o e, we include he p opaga ion delay τ=d/clin o he compu a ion o he o e all ask compu e delay, whe e dis he a e age dis ance be ween UEs and HAPS and clis he speed o ligh . D. Task Compu e Delay Upon he UE o loading decision, asks a i e a a sha ed compu e queue and a e p ocessed acco ding o he i s come i s se ed (FCFS) discipline. I a newly a i ed ask inds an a ailable CPU, i immedia ely s a s being p ocessed; o he wise, i wai s in he queue [13]. 1) Onboa d Compu e: Delay o local ask compu e TUE includes wai ing and p ocessing imes a UE’s CPU TUE =WUE +DUE,(3) whe e WUE is he ask wai ing ime a he UE’s queue and DUE is he ask p ocessing ime. As DUE is de e minis ic and asks a i e acco ding o he Poisson p ocess, he wai ing ime can be modeled acco ding o he M/D/1queue [13]. The cumula i e dis ibu ion unc ion (CDF) o TUE is gi en by P{TUE ≤ }=FWUE ( −DUE)u( −DUE),(4) whe e u(·)is he Hea iside s ep unc ion, FWUE ( )is he CDF o he wai ing ime gi en by (9) o D=DUE,λ= (1−ξ−η)ϵ o he baseline s a egy and λ= (1 −ξ)ϵ o he eplica ion and spli ing s a egies. 2) UAV-Assis ed Compu e: Task o loading o UAVs equi es bo h UL and DL ansmissions, which may expe ience di e en delays. The e o e, he o e all compu e delay is gi en as ollows: TUAV =TUL UAV +TDL UAV +WUAV +DUAV,(5) whe e TUL UAV and TDL UAV a e UL and DL ansmission delays, DUAV is he p ocessing delay a a UAV. Since DUAV is de e minis ic, asks a i e acco ding o he Poisson p ocess, and UAV is equipped wi h se e al CPUs, he wai ing ime can be modeled as he M/D/c queue [13]. The CDF o he UAV-assis ed compu e delay TUAV is exp essed as P{TUAV ≤ }=FWUAV ( −DUAV −TUL UAV −TDL UAV)× u( −DUAV −TUL UAV −TDL UAV),(6) whe e he CDF o he wai ing ime FWUAV (x)is gi en by (10) o D=DUAV,λ=ξϵµ, and c=cUAV o all s a egies. 3) HAPS-Assis ed Compu e: I a ask is o loaded o HAPS, he compu e delay also includes he p opaga ion delay as de ined in subsec ion II-C. The e o e, he o e all delay o he HAPS-assis ed compu e can be w i en as ollows: THAPS = 2τ+TUL HAPS +TDL HAPS +WHAPS +DHAPS,(7) whe e TUL HAPS,TDL HAPS, and DHAPS a e he UL and DL ansmis- sion delays and he p ocessing delay a he HAPS, which a e assumed de e minis ic. Simila ly o he UAV-assis ed compu e case, he CDF o he HAPS-assis ed compu e delay THAPS is P{THAPS ≤ }=FWHAPS ( −DHAPS −TUL HAPS− TDL HAPS −2τ)×u( −DHAPS −TUL HAPS −TDL HAPS −2τ),(8) whe e he CDF o he wai ing ime FWHAPS (x)is gi en by (10) o D=DHAPS,λ=ηNµϵ o he baseline s a egy, λ=ξNµϵ o bo h spli ing and eplica ion s a egies, and c=cHAPS. III. ANALYSIS OF OFFLOADING STRATEGIES A. Wai ing Time Dis ibu ion Rema k 1: The CDF o he wai ing ime o an M/D/1queue wi h a i al a e λand se ice ime D is exp essed as FW(x) = (1 −λD) ⌊x D⌋ X k=0 (−λ(x−kD))keλ(x−kD) k!.(9) P oo : See he de i a ion in [14].□ Rema k 2: The CDF o he wai ing ime o an M/D/c queue wi h a i al a e λand se ice ime Dis gi en by FW(x) = eλ(x−kD) kc−1 X j=0 Qkc−j−1 (−λ(x−kD))j j!,(10) whe e Qm=Pm+c i=0 piand pj=e−λD (λD)j j! c X j=0 pk+ c+j X k=c+1 pkeλD (λD)j−k+c (j−k+c)!. P oo : See he de i a ion in [15].□ To ob ain he p obabili ies pjin a compu a ionally e icien manne , we employ he geome ic ail app oach. Fo mo e de ails on his me hod, we e e ou eade s o [16, p. 378]. B. Baseline S a egy The baseline s a egy assumes ha UEs o load hei asks o he associa ed UAVs wi h p obabili y ξ, o HAPS wi h p ob- abili y η, o compu e hem locally wi h p obabili y 1−ξ−η. Gi en he p obabili y P{Tk≤ ∗} o k∈ {UE,UAV,HAPS}, which deno es he p obabili y ha a ask is comple ed wi hin he deadline ∗ei he locally, a a UAV, o a he HAPS, he p obabili y P(ξ, η)o a ask being compu ed in- ime ollowing he baseline s a egy can be exp essed as ollows: P(ξ, η) = (1 −ξ−η)P{TUE ≤ ∗}+ ξP{TUAV ≤ ∗}+ηP{THAPS ≤ ∗}.(11) Since P{T≤ ∗}=FT( ∗)by de ini ion, one can compu e P(ξ, η)by e alua ing he CDF alues om (4),(6), and (8) a ∗, espec i ely. We seek ξ∗and η∗ ha maximize P(ξ, η): (ξ∗, η∗) = a g max P(ξ, η), 0≤ξ≤1,0≤η≤1, ξ+η≤1.(12) 2336 IEEE COMMUNICATIONS LETTERS, VOL. 28, NO. 10, OCTOBER 2024 The op imiza ion p oblem in (12) is NP-ha d, and he objec i e unc ion P(ξ, η)is non-di e en iable a e e y poin in i s domain due o he p esence o he piece-wise Hea iside unc ion. To ackle he p oblem in (12), we use a de i a i e- ee Nelde -Mead sol e [17] wi h di e en ini ial simpleces and he s opping condi ion o ϵs op = 0.01 o ensu e obus con e gence close o he global op imum. C. Replica ion S a egy Acco ding o he eplica ion s a egy, UEs send ask eplicas o he UAVs and he HAPS wi h p obabili y ξRand compu e asks locally wi h p obabili y 1−ξR. Due o ask eplica ion, he o e all sys em compu e load is highe as compa ed o he baseline scena io unde he same en i onmen sampling a e ϵ. The ask is comple ed i ei he he UAV o he HAPS e u ns a esul o he UE be o e he deadline ∗. The p obabili y P(ξ) o such an e en is gi en by PR(ξ) = (1 −ξR)P{TUE ≤ ∗} +ξRhP{TUAV ≤ ∗}+P{THAPS ≤ ∗}i.(13) To ind he op imal o loading p obabili y ξ∗ R, we nume i- cally sol e he ollowing op imiza ion p oblem: ξ∗ R= a g max PR(ξR), 0≤ξR≤1.(14) D. Spli ing S a egy Ins ead o sending ask eplicas o he UAV and he HAPS, a UEs can spli i s ask be ween hem. The ask is comple ed i he UE ecei es esul s in ime om bo h he UAV and he HAPS. The p obabili y o in- ime compu e o he spli ing s a egy is gi en by PS(ξS) = (1 −ξS)P{TUE ≤ ∗}+ ξSP{TUAV ≤ ∗}P{THAPS ≤ ∗}.(15) We ob ain he op imal o loading p obabili y ξ∗ Susing he Nelde -Mead sol e o he ollowing op imiza ion p oblem: ξ∗ S= a g max PS(ξS), 0≤ξS≤1.(16) The ask a i al a e a he UAVs and HAPS is he same as ha o he eplica ion s a egy, bu he ask sizes di e . Assuming a spli ing ac o δ, he p opo ion o asks o loaded o he UAV δUAV =δ, while he p opo ion o loaded o he HAPS is δHAPS = 1 −δ. IV. NUMERICAL RESULTS The pa ame e s used in ou nume ical assessmen a e p o ided in Table I. Each UE p oduces ideo ames by cap- u ing a senso y ep esen a ion o he en i onmen wi h a size o 0.375 MB a a ame a e o 5 ames pe sec- ond (FPS). We assume ha he deadline o p ocessing he asks is in e sely p opo ional o hei sampling a e, i.e., ∗= 1/ϵ, which is a easonable assump ion o he eal- ime ideo p ocessing applica ions [9]. Each ask has a TABLE I SIMULATION PARAMETERS Fig. 2. P opo ion o imely compu ed asks as a unc ion o he numbe o (a) UEs and (b) UAVs. The e a e 5 UAVs in (a) and 120 UEs in (b). cons an compu a ional load o C= 100 GFLOPs, which is ypical o applica ions such as objec de ec ion o seman ic segmen a ion [12]. We e alua e h ee e e ence o loading s a egies agains a s a egy wi h no o loading unde di e en sys em con igu a- ions. Fo he o loading s a egies, we de e mine he op imal o loading p obabili ies as desc ibed in Sec ion III and employ hem in ou ex ensi e simula ions. Fo each con igu a ion, we collec s a is ics om mul iple simula ion uns un il a 95% con idence le el in he es ima es is achie ed. In he simula ion, he channel ealiza ions be ween UEs, UAVs, and HAPS ollow he me hodology om [12]. Mul i-connec i i y can be implemen ed a a ious le els, including he PHY, MAC, PDCP, and co e ne wo k laye s [8]. In e es ial ne wo ks, mul i- adio dual connec i i y has been s anda dized as an appealing PDCP-laye solu ion due o i s adap abili y o changing adio condi ions. We conside his app oach o ou mul i-connec i i y se up, e en hough i has no ye been s anda dized o NTNs. Fig. 2shows he p obabili y o in- ime compu a ion as a unc ion o (a) he numbe o UEs and (b) he numbe o UAVs. This p obabili y emains abo e 0.7 o all he o loading s a egies and UE deploymen densi ies conside ed. As he numbe o UEs inc eases, he p obabili y o in- ime compu a ion wi hou o loading dec eases mo e apidly han ha wi h any o loading s a egy, by e en ually d opping below 0.4. Meanwhile, he a e age UE ene gy consump ion wi hou o loading, as illus a ed in Fig. 3, is consis en ly highe han he ene gy consump ion wi h any o loading s a egy. Fig. 2sugges s ha o deploymen s wi h ewe UEs, he eplica ion s a egy achie es he highes p obabili y o SADOVAYA e al.: ENHANCING SERVICE CONTINUITY IN NTNs VIA MULTI-CONNECTIVITY OFFLOADING 2337 Fig. 3. A e age UE ene gy consump ion. Fig. 4. CDF o he ask compu e delay. imely compu a ion due o he bene i s o compu e di e si y. This end pe sis s up un il he combined load on he UAVs and HAPS, along wi h he eplica ion o e heads, becomes su icien ly high. A his poin , bo h ask spli ing and base- line o loading become mo e p e e able solu ions, which is pa icula ly e iden when he e a e 180 UEs. While he ask eplica ion s a egy consis en ly consumes mo e ene gy han he baseline s a egy due o a lowe o loading p obabili y, his inc ease in ene gy consump ion is negligible as compa ed o he signi ican imp o emen in he numbe s o asks compu ed in ime. Simila ly, he eplica ion s a egy deli e s he highes p ob- abili y o imely compu a ion as mo e UAVs a e deployed, he eby o e ing addi ional compu e capaci y. The ask spli - ing s a egy pe o ms compa ably o he baseline s a egy and does no show a signi ican imp o emen e en wi h he deploymen o mo e UAVs. Fo ins ance, when he numbe o UAVs exceeds 2, he ask eplica ion s a egy o e s a 5-17% gain o e bo h he baseline and he ask spli ing o loading s a egies. Howe e , when he e a e ewe han 3 UAVs, as illus a ed in Fig. 2, he baseline s a egy ou pe o ms he eplica ion and he ask spli ing s a egies by 3-5% and 3-7%, espec i ely. Fig. 4p esen s he CDF o he ask compu e delay as de e mined by (3),(5), and (7) o 60 UEs and 5 UAVs as an example. In his deploymen , all asks a e compu ed be o e he deadline o 500 ms. O loading s a egies signi ican ly educe bo h he a e age and he wo s -case ask compu e delay. The eplica ion s a egy exhibi s he lowes delays among all s a egies, while he baseline s a egy, al hough being sligh ly in e io o he eplica ion s a egy, ou pe o ms he ask spli ing s a egy. By u ilizing mul i-connec i i y o loading mechanisms, he sys em can e icien ly dis ibu e asks ac oss a ailable esou ces, he eby educing compu a ion delay and mi iga ing se ice in e up ions. V. CONCLUSION Gi en he challenges o deploying dense e es ial ne wo ks and he g owing need o MEC, his le e o e s a no el analysis o di e en compu a ion ask o loading app oaches in UAV- and HAPS-assis ed NTNs. The conside ed o loading s a egies le e age mul i-connec i i y capabili ies be ween he a ge UEs and he NTN nodes o inc ease he p obabili y o imely compu a ion o he UE asks. Ou esul s indica e ha mul i-connec i i y o loading signi ican ly imp o es he p obabili y o in- ime compu e, by ensu ing ha 70% o asks a e comple ed be o e he deadline. The eplica ion s a egy achie es he highes p obabili y o imely compu a ion and he lowes ask compu e delay when he numbe o UEs is smalle . Con e sely, he baseline s a egy ou pe o ms bo h ask eplica ion and spli ing s a egies as he compu a ion load g ows. REFERENCES [1] C. E. Kemen e al., “Sus aining dynamic a ic in dense u ban a eas wi h HAPS,” IEEE Commun. Mag., ol. 61, no. 7, pp. 150–156, Jul. 2023. [2] G. K. Ku e al., “A ision and amewo k o he HAPS ne wo ks o he u u e,” IEEE Commun. Su eys Tu s., ol. 23, no. 2, pp. 729–779, 2nd Qua ., 2021. [3] Q. Ren, O. Abbasi, G. K. Ku , H. Yanikome oglu, and J. Chen, “Caching and compu a ion o loading in HAPS assis ed in elligen anspo a ion sys ems,” IEEE T ans. Wi eless Commun., ol. 21, no. 11, pp. 9010–9024, No . 2022. [4] D. S. Lakew, A.-T. T an, N.-N. Dao, and S. Cho, “In elligen o load- ing and esou ce alloca ion in HAP-assis ed MEC ne wo ks,” in P oc. In . Con . In . Commun. Technol. Con e g. (ICTC), Oc . 2021, pp. 1582–1587. [5] Z. Jia, Q. Wu, C. Dong, C. Yuen, and Z. Han, “Hie a chical ae ial compu ing o In e ne o Things ia coope a ion o HAPs and UAVs,” IEEE In e ne Things J., ol. 10, no. 7, pp. 5676–5688, Ap . 2023. [6] S. M. Shahid, Y. T. Seyoum, S. H. Won, and S. Kwon, “Load balancing o 5G in eg a ed sa elli e- e es ial ne wo ks,” IEEE Access, ol. 8, pp. 132144–132156, 2020. [7] M. López, S. B. Damsgaa d, I. Rod íguez, and P. Mogensen, “Con- nec ing u al a eas: An empi ical assessmen o 5G e es ial-LEO sa elli e mul i-connec i i y,” in P oc. IEEE 97 h Veh. Technol. Con . (VTC-Sp ing), Jun. 2023, pp. 1–5. [8] M. Majamaa, “Towa d mul i-connec i i y in beyond 5G non- e es ial ne wo ks: Challenges and possible solu ions,” IEEE Commun. Mag., ea ly access, Jan. 15, 2024, doi: 10.1109/MCOM.001.2300581. [9] A. T aspadini, M. Gio dani, G. Giambene, and M. Zo zi, “Real- ime HAP-assis ed ehicula edge compu ing o u al a eas,” IEEE Wi eless Commun. Le ., ol. 12, no. 4, pp. 674–678, Ap . 2023. [10] Z. Lou, R. Wang, B. E. Y. Belmekki, M. A. Kishk, and M.-S. Alouini, “Te ain-based UAV deploymen : P o iding co e age o ou doo use s,” IEEE T ans. Veh. Technol., ol. 73, no. 6, pp. 8988–9002, Jun. 2024. [11] N. Sa hya ageeswa an, R. D. Ya es, A. D. Sa wa e, and N. Mandayam, “Timely o loading in mobile edge cloud sys ems,” 2024, a Xi :2405.07274. [12] G. Pan, H. Zhang, S. Xu, S. Zhang, and X. Chen, “Join op imiza ion o ideo-based AI in e ence asks in MEC-assis ed augmen ed eali y sys ems,” IEEE T ans. Cogn. Commun. Ne w., ol. 9, no. 2, pp. 479–493, Ap . 2023. [13] Z. Xie e al., “A Ma ko ian queueing model o end- o-end delay anal- ysis in compu a ion o loading sys em,” IEEE Commun. Le ., ol. 27, no. 10, pp. 2687–2691, Oc . 2023. [14] A. K. E lang, “The heo y o p obabili ies and elephone con e sa ions,” Ny . Tidssk . Ma . Se . B, ol. 20, pp. 33–39, 1909. [15] G. J. F anx, “A simple solu ion o he M/D/cwai ing ime dis ibu ion,” Ope . Res. Le ., ol. 29, no. 5, pp. 221–229, Dec. 2001. [16] H. C. Tijms, A Fi s Cou se in S ochas ic Models. Hoboken, NJ, USA: Wiley, 2003. [17] S. Singe and J. Nelde , “Nelde –Mead algo i hm,” Schola pedia, ol. 4, no. 7, p. 2928, 2009.