Page 79 - 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

For ease of exposition, we give an in‑depth breakdown
′
of (P1 ) by employing hierarchical decomposition [74] m i m k
in Appendix A. We proceed by addressing the slice user ...
multi‑tier multi‑domain association problem ingrained in
′
(P1 ).
f
7.1 Slice user multi‑tier multi‑domain associ‑ i
ation problem ... f k

Furthermore, we address the slice user multi‑tier multi‑
domain association problem in an M‑TTSD network by
adopting the following approaches: (i) QoS in multi‑ p i ... p
domain networks [75], and (ii) association of users in k
heterogeneous networks [76, 77]. To this end, we for‑
mulate the association problem in an M‑TTSD network
as a maximisation optimisation problem given in sub‑
problem (P3) as:
... pf
pf i k
(P3) ∶ max Υ , , Ω , ,
Υ,Ω
∈ℐ ∈{ , , , } ∈{ℰ∪ℳ∪ℛ}
s.t.: Υ , , Ω , , ≤ 1, ∀ , ∀
∈ℐ ∈{ , , , }
(25)a InP i InP k
Υ , , ∈ {0, 1} ∀ , ∀ , ∀ (25)b Fig. 6 – Multi‑tier multi‑domain slice user matching game.
Ω , , ∈ {0, 1} ∀ , ∀ , ∀ (25)c

In addressing sub‑problem (P3), we consider the pecu‑ ⎡ Ω 1 Ω 1 Ω 1 ⎤ ⎡ Υ 1, 1 Υ 1, 1 Υ 1, 1 ⎤
liarities of each tier such as slice types it can accommo‑ = ⎢ Ω 2 Ω 2 Ω 2⎥ ⊙ ⎢ Υ 2, 2 Υ 2, 2 Υ 2, 2⎥ (26)
date, coverage radius, transmit power. We ensure that a ⎢ ⋮ ⋮ ⋮ ⎥ ⎢ ⋮ ⋮ ⋮ ⎥
slice user can only associate with one tier and by exten‑ ⎣Ω Ω Ω ⎦ ⎣Υ , Υ , Υ , ⎦
sion associate with only one domain network by ensur‑
ing constraint (25)a is enforced. Moreover, constraints Solving the multi‑tier multi‑domain user association
sub‑problem (P3) gives room to further address the
(25)b and (25)c help to relax constraint (25)a by ensur‑ utility maximisation problem stated in (P1 ). To this
′
ing the sum of the products in (25)a equals one for a slice end, we further transform (P1 ) to re lect variables of
′
user to be admitted to a tier in a particular domain net‑ the utility function given in expressions (21)‑(22) and
work. It is important to note that the expressions (50)‑ user association carried out in solving sub‑problem (P3).
(53) were employed in the breakdown of the objective Therefore, we rewrite (P1 ) to give (P1 ) in (27). It is
′
′′
function in sub‑problem (P3). Additionally, the many‑ important to note that logarithmic rule is applied to the
to‑one concept in matching theory [78, 79] is adopted expression (22) to reduce the complexity of solving (P1 ),
′′
in our proposed multi‑tier multi‑domain slice user algo‑ thereby splitting the decision variables of and .
rithm. This is a result of the practicability in M‑TTSD , , , , ,
networks. Fig. 6 illustrates the multi‑tier multi‑domain
slice user matching algorithm proposed to solve sub‑
problem (P3). Moreover, we give the pseudo‑code of
the multi‑tier multi‑domain slice user algorithm in Alg.1.
For ease of exposition, expression (26) gives an insight
into the mathematical representation of matching ma‑
trix for a slice ∈ {ℰ , , ∪ ℳ , , }. In Alg.1, =
{ , , , , , , , , , , , , , , , , , , , , , , , }.
Additionally, = { , , , , , , , , , , , , , , , }, =
{ , , , , , , , , , , , , , , , }, = { , , , , , , , }.
For ease of exposition, expression (26) gives an insight
into the mathematical representation of matching matrix
for a slice ∈ {ℰ , , ∪ ℳ , , }.

© International Telecommunication Union, 2021 67