Page 82 - 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

Therefore, the average traf ic demand is given as: , = , , , ∀ ∈ , ∈ ℐ (36)
∈ , , ,
= ⋅ (35)
The mean traf ic load of the macro‑tier , , is expressed
as:
Algorithm 2 Distributed recursive backtracking for
multi‑player multi‑domain game. , , = , , Ω ,
Υ
Input: , , , , , : ∈ ℐ, ∈ , ∈ , ∈ ∈{ℰ ∪ℳ ∪ℛ }
# SP Network Layer
Υ Ω
1: for ← 1 to | | do + , , ,
2: Estimate The Weight S , of Each InP ∈ℱ ∈{ℰ ∪ℳ }
,
S , = + , , ,
Υ Ω
, ∈ ∈{ℰ ∪ℳ }
∈ℐ
3: for ← 1 to | | do + , , , (37)
Υ Ω
4: for ← 1 to |ℐ| do ∈ ∈ ℱ ∈{ℰ ∪ℳ }
5: Determine SP Request Mat = , ⋅ , ⋅ S ,
6: end for In the similitude of (36) and (37), the mean traf ic demand
7: end for of the femto‑tier is given by
8: end for
# MVNO Network Layer
Υ Ω
9: for ← 1 to | | do , , = , , , (38)
10: Estimate the Weight of Each InP Associated with an ∈ℱ ∈{ℰ ∪ℳ }
MVNO
The mean traf ic load of an SP ∈ , , , in the pico‑tier
, is given by
∈
S , =
Υ Ω
, , , = , , ,
∈ ∈{ℰ ∪ℳ }
∈ ∈ℐ
11: for ← 1 to |ℐ| do
Υ Ω
12: Determine MVNO Req. Mat.= , ⋅ , ⋅ S , + , , , (39)
13: end for ∈ ∈ ℱ ∈{ℰ ∪ℳ }
14: end for Lastly, for the clustered femto‑tier, the mean traf ic demand
# InP Network Layer is given by
15: for ← 1 to |ℐ| do , ,
16: for ← 1 to | | do , , = , , , (40)
Υ Ω
17: # InP Resource Alloc. to MVNO
, ∈ ∈ ℱ ∈{ℰ ∪ℳ }
=
, 7.3 Monte Carlo method
∈
18: end for Numerical methods are broadly classi ied into two cate‑
19: end for gories [86]: (1) deterministic and (2) stochastic methods.
20: for ← 1 to | | do The Monte Carlo method has been widely used for ran‑
21: for ← 1 to | | do domised numerical computing owing to its simple struc‑
22: # MVNO Resource Alloc. to SP , ture and ease of implementation [87]. The Monte Carlo
, method is a technique for inding approximate solutions
, = to mathematical and physical problems by the simulation
, of stochastic entities [88]. Alg. 3 shows the pseudo‑code
∈ for the Monte Carlo method employed in this work. To
23: end for
24: end for solve the optimisation problem in (P1) and (P2), we em‑
ploy Alg. 1 and Alg. 2. In Alg. 3, we run several thousand
With the aid of Lemma 1, the average traf ic demand of an runs of Alg. 1 and Alg. 2 to increase the con idence levels
M‑TTSD network can be determined via Theorem 1. in the total network utility.
For instance, let the outcomes of several iterations of a
Theorem 1. Let the mean user throughput given in (20) simulation be denoted by , such that
be the same as in Lemma 1. Then, the mean traf ic load
…
of an SP ∈ wrt an InP ∈ ℐ is the sum of the mean = 1 2 3 (41)
traf ic load of all the tiers and is of the form: 1 2 3 …

70 © International Telecommunication Union, 2021