Page 82 - ITU Journal Future and evolving technologies Volume 2 (2021), Issue 6 – Wireless communication systems in beyond 5G era
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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
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