Page 78 - ITU Journal Future and evolving technologies Volume 2 (2021), Issue 6 – Wireless communication systems in beyond 5G era

ITU Journal on Future and Evolving Technologies, Volume 2 (2021), Issue 6

(P1) ∶ max Υ , , Ω , , ( , , , )
Υ,Ω,
∈ℐ ∈{ , , , } ∈{ℰ∪ℳ∪ℛ}
s.t.: Υ , , Ω , , [ , , , − ℎ ] ≥ 0 ∈ {ℰ ∪ ℳ ∪ ℛ}, ∈ { , , , } (23)a
, ,
Υ , , Ω , , ≤ 1 ∈ , ∈ {ℰ ∪ ℳ ∪ ℛ} (23)b
∈ℐ ∈{ , , , }
Υ , , ∈ {0, 1} ∈ {ℰ ∪ ℳ ∪ ℛ}, ∈ ℐ, ∈ (23)c
Ω , , ∈ {0, 1} ∈ { , , , }, ∈ {ℰ ∪ ℳ ∪ ℛ} (23)d
Υ , , Ω , , , , , = 1, ∈ , ∈ ℐ (23)e
∈ ∈{ℰ , , ∪ℳ , , ∪ℛ , , }
Υ , , Ω , , , , , = 1, ∈ , ∈ ℐ (23)f
∈ℱ ∈{ℰ , , ∪ ℳ , , }
Υ , , Ω , , , , , = 1, ∈ , ∈ ℐ (23)g

∈ ∈{ℰ , , ∪ ℳ , , }
Υ , , Ω , , , , , = 1, ∈ , ∈ ℐ (23)h
∈ ∈ ℱ ∈{ℰ , , ∪ ℳ , , }
, , , = (0, 1) ∈ {ℰ , , ∪ ℳ , , ∪ ℛ , , } (23)i
, , , = (0, 1) ∈ {ℰ , , ∪ ℳ , , } (23)j
, , , = (0, 1) ∈ {ℰ , , ∪ ℳ , , } (23)k
, , , = (0, 1) ∈ {ℰ , , ∪ ℳ , , } (23)l

(P2) ∶ max , ∇ , ℬ

Υ,Ω
∈ ∈ℐ
s.t.: ≤ ∈ ℐ, ∈ (24)a
∈
∇ , ∈ {0, 1} ∈ , ∈ ℐ (24)b
, ∈ (0, 1) ∈ , ∈ ℐ (24)c
, ≥ ∈ (24)d
∈ ∈ℐ

7. PROPOSED SOLUTIONS ′
(P1 ) ∶max Υ , Ω , ( , , )
Υ,Ω
∈ℐ ∈ ∈{ℰ∪ℳ∪ℛ}
In this section, we give an in‑depth description of the pro‑
posed solutions to the latency and bid aware dynamic re‑ + Υ , Ω , ( , , )
source allocation problem in an M‑TTSD network stated in
∈ℐ ∈ℱ ∈{ℰ∪ℳ}
(P1) and (P2). First, the objective function in (P1) is re‑
formulated for tractability and complexity reduction us‑ + Υ , Ω , ( , , )
ing the hierarchical decomposition technique [74]. For ∈ℐ ∈ ∈{ℰ∪ℳ}
clarity, readability, and without the abuse of notations, in
the reformulation of (P1), we drop indexes in Υ , , , Ω , , + Υ , Ω , ( , , )
′
and ( , , , ). (P1) is transformed into (P1 ) taking into ∈ℐ ∈ ∈ ℱ ∈{ℰ∪ℳ}
consideration the physical network described in
Subsection in
Subsection 3.3.

66 © International Telecommunication Union, 2021