Page 19 - ITUJournal Future and evolving technologies Volume 2 (2021), Issue 1

ITU Journal on Future and Evolving Technologies, Volume 2 (2021), Issue 1

ʹǤ {S i (t)} ”‡’”‡•‡– –Š‡ Šƒ‡Ž •–ƒ–‡ ˆ‘” ‡ƒ Š —•‡” i
i∈N
†—”‹‰ •Ž‘– tǤ Ž•‘ǡ –Š‡ Šƒ‡Ž ƒ „‡ ‡‹–Š‡” ‹ Dz ƒ†dz •–ƒ–‡
‡ ‘•‹†‡” N —•‡”• –”ƒ•‹––‹‰ ’ƒ ‡–• –‘ ƒ •‹‰Ž‡ ”‡Ǧ ȋ†‡‡’ ˆƒ†‹‰Ȍ ‘” ‹ Dz ‘‘†dz •–ƒ–‡ ȋ‹Ž† ˆƒ†‹‰ȌǤ Š‡ ’‘••‹Ǧ
‡‹˜‡” ‘˜‡” ™‹”‡Ž‡•• ˆƒ†‹‰ Šƒ‡Ž•Ǥ ‡– N {1,...,N} „Ž‡ Šƒ‡Ž •–ƒ–‡• ‘ˆ ‡ƒ Š —•‡” i ƒ”‡ †‡• ”‹„‡† „› –Š‡ •‡–
„‡ –Š‡ •‡– ‘ˆ –Š‡ –‘–ƒŽ —•‡”• ‹ –Š‡ •›•–‡Ǥ ‹‡ ‹• ƒ••—‡† S { , }ǡƒ† S i (t) ∈Sǡ ∀i ∈NǤ ‘” •‹’Ž‹ ‹–›ǡ ™‡
–Š
–‘ „‡ •Ž‘––‡†ǡ ƒ† t ∈ Z †‡‘–‡• –Š‡ t •Ž‘–Ǥ ƒ••—‡ –Šƒ– –Š‡ ”ƒ†‘ ˜ƒ”‹ƒ„Ž‡• ‘ˆ –Š‡ Šƒ‡Ž ’”‘ ‡••
(t) ƒ”‡ ‹Ǥ‹Ǥ†Ǥ ˆ”‘ ‘‡ •Ž‘– –‘ –Š‡ ‡š–Ǥ
‡– p(t) [p 1 (t),...,p N (t)] †‡‘–‡ –Š‡ ’‘™‡” ƒŽŽ‘ ƒ–‹‘
–Š
˜‡ –‘” ‹ –Š‡ t •Ž‘–Ǥ ‡ ‘•‹†‡” ƒ •‡– ‘ˆ †‹• ”‡–‡ ’‘™‡”
( ‘™) ( ‹‰Š)
Actuation/Control Ž‡˜‡Ž• 0,P ,P Ǥ Š‡ ”‡“—‹”‡† ’‘™‡” –‘ Šƒ˜‡ ƒ
VR/AR •— ‡••ˆ—Ž –”ƒ•‹••‹‘ —†‡” Dz ƒ†dz ƒ† Dz ‘‘†dz Šƒ‡Ž
‘†‹–‹‘• ‹• †‡‘–‡† „› P ‹‰Š ƒ† P ‘™ ǡ ”‡•’‡ –‹˜‡Ž›Ǥ –
Tactile Internet
‡ƒ Š –‹‡ •Ž‘–ǡ –Š‡ •‡– ‘ˆ •‡Ž‡ –ƒ„Ž‡ ’‘™‡” Ž‡˜‡Ž• P i (t) ˆ‘”
‡ƒ Š —•‡” ‹• ‘†‹–‹‘‡† ‘ –Š‡ Šƒ‡Ž •–ƒ–‡ S i (t)Ǥ ‘”
‡šƒ’Ž‡ǡ ‹ˆ –Š‡ —””‡– Šƒ‡Ž •–ƒ–‡ ‹• Dz ƒ†dzǡ –Š‡ P ȋ ‘™Ȍ
ƒ‘– „‡ •‡Ž‡ –‡†Ǥ Š—•ǡ ™‡ Šƒ˜‡

ȋ ‹‰ŠȌ
0,P ǡ‹ˆ S i (t)=
p i (t) ∈ ǡ ∀i ∈NǤ ȋͷȌ
0,P ȋ ‘™Ȍ ǡ‹ˆ S i (t)=
‡– μ i (t) „‡ –Š‡ ’‘™‡” ƒŽŽ‘ ƒ–‹‘ǡ ‘” ’ƒ ‡– •‡”˜‹‰ǡ ‹†‹Ǧ
‹‰Ǥ ͳ Ȃ šƒ’Ž‡ ‘ˆ –Š‡ •›•–‡ ‘†‡Ž ™‹–Š –‹‡Ǧ ”‹–‹ ƒŽ —•‡”• ™‹–Š ’ƒ Ǧ –Š
‡–• ™‹–Š †‡ƒ†Ž‹‡• ƒ† —•‡”• ™‹–Š ‹‹—Ǧ–Š”‘—‰Š’—– ”‡“—‹”‡‡–•Ǥ ƒ–‘” ˆ‘” –Š‡ —•‡” i ‹ –Š‡ t •Ž‘–ǡ ™‡ Šƒ˜‡

‡ ‘•‹†‡” –Š‡ —•‡”• –‘ „‡ •› Š”‘‹œ‡† ƒ† ‘–”‘ŽŽ‡† μ i (t) 1ǡ‹ˆ p i (t) > 0 ǡ ∀i ∈NǤ ȋ͸Ȍ
„› ƒ • Š‡†—Ž‡”Ǥ  ‘—” •›•–‡ ‘†‡Žǡ ƒ– ‘•– ‘‡ —•‡” ƒ 0ǡ ‘–Š‡”™‹•‡
–”ƒ•‹– ƒ– ‡ƒ Š –‹‡ •Ž‘–Ǥ ‡ ‘•‹†‡” –™‘ •‡–• ‘ˆ —•‡”•Ǥ
Š‡ ϐ‹”•– •‡– ‹ Ž—†‡• —•‡”• –Šƒ– Šƒ˜‡ ƒ””‹˜ƒŽ• ‘ˆ ’ƒ ‡–• – ‘•– ‘‡ ’ƒ ‡– ƒ „‡ –”ƒ•‹––‡† ‹ ƒ –‹‡•Ž‘– tǡ ‹Ǥ‡Ǥǡ
™‹–Š †‡ƒ†Ž‹‡•Ǥ ‡ †‡‘–‡ –Š‡ •‡– ‘ˆ —•‡”• ™‹–Š ’ƒ Ǧ –Š‡ ˜‡ –‘” ’(t) Šƒ• ƒ– ‘•– ‘‡ ‘Ǧœ‡”‘ ‡Ž‡‡–Ǥ Š‡ •‡–
‡–• ™‹–Š †‡ƒ†Ž‹‡• „› R⊆NǤ Š‡ •‡ ‘† •‡– ‘ˆ —•‡”•ǡ ‘ˆ ’‘™‡” ‘•–”ƒ‹–• ˆ‘” p(t) ‹• –Š‡ †‡ϐ‹‡† „›
U⊆ N ǡ ‘–ƒ‹• –Š‡ —•‡”• –Šƒ– Šƒ˜‡ –Š”‘—‰Š’—– ”‡“—‹”‡Ǧ N
‡–•Ǥ ‡ ‘•‹†‡” –Šƒ– ‡ƒ Š —•‡” u ∈U ‹• •ƒ–—”ƒ–‡† P(t) p(t): ͳ {μ i (t)=1} ≤ 1 ǡ ȋ͹Ȍ
ƒ† –Š‡”‡ˆ‘”‡ǡ ‹– Šƒ• ƒŽ™ƒ›• ’ƒ ‡– –‘ –”ƒ•‹–Ǥ ‘–‡ –Šƒ– i=1
U∪ R = N ƒ† U∩ R = ∅Ǥ  ‡šƒ’Ž‡ ‘ˆ ‘—” •›•–‡ ™Š‡”‡ ͳ {·} †‡‘–‡• –Š‡ ‹†‹ ƒ–‘” ˆ— –‹‘Ǥ ‘” ‡ƒ Š —•‡”
‘†‡Ž ‹• •Š‘™ ‹ ‹‰Ǥ ͳǤ r ∈Rǡ ƒ ’ƒ ‡– ‹• †”‘’’‡† ‹ˆ ‹–• †‡ƒ†Ž‹‡ Šƒ• ‡š’‹”‡†Ǥ
‘” –Š‡ †‡ƒ†Ž‹‡Ǧ ‘•–”ƒ‹‡† —•‡”•ǡ ‡ƒ Š ’ƒ ‡– –Šƒ– ƒ”Ǧ ‹ ‡ –Š‡ “—‡—‡ ˆ‘ŽŽ‘™• –Š‡ †‹• ‹’Ž‹‡ǡ ƒ ’ƒ ‡– ‹•
”‹˜‡• ‹ –Š‡ “—‡—‡ ‘ˆ –Š‡ —•‡”• Šƒ• ƒ †‡ƒ†Ž‹‡ „› ™Š‹ Š –Š‡ †”‘’’‡† —†‡” –Š‡ ˆ‘ŽŽ‘™‹‰ ‘†‹–‹‘•ǣ ͳȌ ‹– ‹• ƒ– –Š‡
’ƒ ‡– —•– „‡ –”ƒ•‹––‡†Ǥ –Š‡”™‹•‡ǡ ‹– ‹• †”‘’’‡† ƒ† Š‡ƒ† ‘ˆ –Š‡ “—‡—‡Ǣ ʹȌ –Š‡ ”‡ƒ‹‹‰ —„‡” ‘ˆ –Š‡ •Ž‘–•
”‡‘˜‡† ˆ”‘ –Š‡ •›•–‡Ǥ ‡ ƒ••—‡ –Šƒ– –Š‡ †‡ƒ†Ž‹‡• –‘ •‡”˜‡ –Š‡ ’ƒ ‡– ‹• 1Ǣ ƒ† ͵Ȍ ’‘™‡” ‹• ‘– ƒ••‹‰‡† –‘
‘ˆ–Š‡’ƒ ‡–• ‹ –Š‡•ƒ‡“—‡—‡ ƒ”‡–Š‡•ƒ‡Ǥ ‘™‡˜‡”ǡ —•‡” r ƒ– –Š‡ —””‡– •Ž‘–Ǥ ‡– D r (t) „‡ –Š‡ ‹†‹ ƒ–‘” ‘ˆ –Š‡
†‡ƒ†Ž‹‡• ‘ˆ †‹ˆˆ‡”‡– “—‡—‡• ƒ› ˜ƒ”›Ǥ ‡ †‡‘–‡ –Š‡ ’ƒ ‡– †”‘’ ˆ‘” —•‡” r ƒ– –‹‡ tǤ Š‡ “—‡—‡ ‡˜‘Ž—–‹‘ ˆ‘”
–Š
’ƒ ‡– †‡ƒ†Ž‹‡ ‘ˆ –Š‡ r “—‡—‡ ™‹–Š m r ∈ Z + ǡ ∀r ∈RǤ ‡ƒ Š —•‡” r ∈R ‹• †‡• ”‹„‡† ƒ•
‡– d r (t) „‡ –Š‡ —„‡” ‘ˆ •Ž‘–• Ž‡ˆ– ‹ –Š‡ t –Š •Ž‘– „‡Ǧ
ˆ‘”‡ –Š‡ ’ƒ ‡– –Šƒ– ‹• ƒ– –Š‡ Š‡ƒ† ‘ˆ “—‡—‡ r ‡š’‹”‡•Ǥ ‡– Q r(t +1) = ƒš [Q r(t) − μ r(t), 0] + α r(t) − D r(t)ǡ ∀i ∈RǤ
–Š
Q r (t) „‡ –Š‡ —„‡” ‘ˆ ’ƒ ‡–• ‹ “—‡—‡ r ‹ –Š‡ t •Ž‘–Ǥ ȋͺȌ
’ƒ ‡– ƒ””‹˜‡• ™‹–Š ’”‘„ƒ„‹Ž‹–› π r ƒ– ‡˜‡”› –‹‡ •Ž‘–
ǡ ™Š‡”‡
‹ –Š‡ “—‡—‡ ‘ˆ —•‡” rǤ ‡– α(t) {α r (t)} ‡ †‡ϐ‹‡ –Š‡ ’ƒ ‡– †”‘’ ”ƒ–‡ ˆ‘” ‡ƒ Š —•‡” r ∈Rǡ–Š‡
r∈R
α r (t) ∈{0, 1}ǡ ”‡’”‡•‡–• –Š‡ ’ƒ ‡– ƒ””‹˜ƒŽ ’”‘ ‡•• ˆ‘” ƒ˜‡”ƒ‰‡ ’‘™‡” ‘•—’–‹‘ ˆ‘” ‡ƒ Š —•‡” i ∈Nǡƒ† –Š‡
–Š
‡ƒ Š —•‡” r ‹ –Š‡ t •Ž‘–Ǥ Š‡ ”ƒ†‘ ˜ƒ”‹ƒ„Ž‡• ‘ˆ –Š‡ –Š”‘—‰Š’—– ˆ‘” ‡ƒ Š —•‡” u ∈U ƒ•
’ƒ ‡– ƒ””‹˜ƒŽ ’”‘ ‡•• ƒ”‡ ‹†‡’‡†‡– ƒ† ‹†‡–‹ ƒŽŽ›
†‹•–”‹„—–‡† ȋ‹Ǥ‹Ǥ†ǤȌǤ ‡– λ r †‡‘–‡–Š‡ƒ””‹˜ƒŽ”ƒ–‡ˆ‘” —•‡” D r Ž‹ D r (t)ǡ ∀r ∈Rǡ ȋͻȌ
r ƒ† E{α r (t)} = λ r Ǥ —”–Š‡”‘”‡ǡ ƒ– ‘•– ‘‡ ’ƒ ‡– t→∞
ƒ „‡ –”ƒ•‹––‡† ƒ– ‡ƒ Š –‹‡ •Ž‘– ƒ† ‘ ‘ŽŽ‹•‹‘• ƒ”‡ p Ž‹ p (t)ǡ ∀i ∈Nǡ ȋͼȌ
i
i
t→∞
ƒŽŽ‘™‡†Ǥ  ‡ƒ Š “—‡—‡ ‘ˆ ‡˜‡”› —•‡” r ∈Rǡ ’ƒ ‡–• ƒ”‡ μ = Ž‹ ¯μ u (t)ǡ ∀u ∈Uǡ ȋͽȌ
•‡”˜‡† ‹ –Š‡ ‘”†‡” –Šƒ– –Š‡› ƒ””‹˜‡ ˆ‘ŽŽ‘™‹‰ –Š‡ ‹”•–  u t→∞
‹”•– —– ȋ Ȍ †‹• ‹’Ž‹‡Ǥ t−1
”‡•’‡ –‹˜‡Ž›ǡ ™Š‡”‡ǡ D r (τ) = 1 D r (t)ǡ p (t) =
‡ ƒ••—‡ –Šƒ– –Š‡ Šƒ‡Ž •–ƒ–‡ ƒ– –Š‡ „‡‰‹‹‰ ‘ˆ ‡ƒ Š t τ=0 i
–‹‡ •Ž‘– ‹• ‘™Ǥ Š‡ Šƒ‡Ž •–ƒ–‡ ”‡ƒ‹• ‘•–ƒ– 1 t−1 1 t−1

™‹–Š‹ ‘‡ •Ž‘– „—– ‹– Šƒ‰‡• ˆ”‘ •Ž‘– –‘ •Ž‘–Ǥ ‡– (t) t p i (τ)ǡƒ† ¯μ u (t)= t μ u (τ)Ǥ Š‡ ’ƒ ‡– †”‘’
τ=0 τ=0

© International Telecommunication Union, 2021 3