Page 76 - 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



          Next, we consider the preference of SP     ∈     for the re‑   Similarly, at the SP‑MVNO hierarchical layer, the utility
          sources of MVNO    ∈   . If we denote preference factor by     of SP    ∈    playing the multi‑domain multi‑tenant
                                                                   
          Pr   ,  ,   , then                                   game is of the form given as:
                      Pr    ,  ,    ≤ 1, ∀   ∈   , ∀   ∈   ,  (13)     = arg max         ,1  ,       ,2  , ⋯ ,       ,  
                                                                                     ′
                                                                                               ′
                                                                                                           ′
                      ∈ℒ                                                           ,1  +      ,1       ,2  +      ,2           +      ,  
                                                                                                            (18)
         The bid      ,    placed by an SP    ∈    to an MVNO    ∈    is
         such that      ,    ≥ 0. With Pr   ,  ,    = 0, then SP    ∈    does  s.t.
         not place a bid for MVNO    ∈    resources. Besides,          C4:         ,    ≤        ∀   ∈   
         is such that it is IC for MVNO    ∈   , otherwise, the bid is    ∈  
         rejected. Hence, resource price of the MVNO    ∈    is such  C5:            ,    ≥          ∀   ∈   
                                                                           
         that:                                                         ∈           ∈       
                       ,    =        ,   Pr   ,  ,   ,    ∈   ,    ∈ ℒ  (14)  C6:      ≥ 0  ∀   ∈   ,  ∀   ∈   
                           ∈                                           ,  
          Thus, the share of resource type      ,  ,    an SP    ∈    receives
                                                                                                   ′
          from an MVNO    ∈    is given as:                    where the sum of bids of other SPs     ≠     is denoted by
                                                                 ′
                                                                    ,   .  We guarantee that the bid budget of an SP is not ex‑
                                      ,                           
                               ,  ,    =  Pr   ,  ,   .  (15)  ceeded in Constraint C4. In constraint C5, the demands of
                                      ,                        the respective subscribers are met by their SP. Lastly, in
                                                               constraint C6, a bid value is ensured to be non‑negative
          If we denote the bidding vector of an SP    ∈    as    =
                                                        
          (     ,1 ,      ,2 , … ,      ,   ) owing to the ability of an SP to bid for  and  also  an  SP  can  decide  not  to  place  a  bid  such  that
          resources from several MVNOs, thus:                       ,     = 0.
                                                               5.   RESOURCE ALLOCATION FRAMEWORK
                                 ,    ≤    , ∀   ∈       (16)
                                     
                         ∈                                     In  this  section,  we  describe  the  service  provider‑slice
                                                               users’ communication layer, the latency and delay model
          where    denotes the bidding budget of an SP. This im‑  employed in this work and the resource allocation frame‑
                   
          plies that the utility of the MVNO is based on the revenues  work.
          accrued from the auction of network resources to SPs. On
          the other hand, SPs provide different slice use‑cases con‑  5.1  Service Provider‑slice user layer
          tracts to subscribed users. It is important to reiterate that
                                                               In this work, without loss of generality, it is assumed that
          InPs, MVNOs, and SPs are individually rational and con‑  a slice user     ∈  {ℰ  ∪ ℳ  ∪ ℛ} is subscribed to one SP
          sider the IC of a bid offered before they release their re‑        ,  
                                                                  ∈    at a time. Moreover, this assumption is downplayed
          sources.                                             by  the  ability  of  SPs  to  bid  for  resources  from  different
          For ease of exposition, an MVNO    ∈    in the InP‑MVNO  MVNOs, and by extension InPs as the case may be. To this
          hierarchical stage maximises its utility    derived from  end, the QoS requirements of the respective slice users are
                                               
          its bidding vector    in the form given as:          satisfactorily met. Furthermore, the QoS requirements of
                            
                               ,1         ,2           ,       the slice users are dynamically met by taking into consid‑
             = arg max         ′  ,      ′  , ⋯ ,     ′
              
                             ,1  +      ,1       ,2  +      ,2       ,    +      ,    eration the cell load, tier load, bid budget, associated in‑
                                                               terference, slice users’ distribution and location, slice use‑
                                                      (17)
          s.t.                                                 case QoS requirement, delay and latency thresholds.
          C1:         ,    ≤    ,  ∀   ∈   
                           
                                                               5.2  Latency and delay model
                 ∈ℐ
          C2:    ℬ       ≥      ,   ∀   ∈                      In  a  similar  trend  with  the  work  in  [68],  the  link  layer
                        ,  
                                 
                 ∈ℐ          ∈                                 model and effective capacity theory in the seminal work
                                                               of [60,  61] are employed in addressing latency and ser‑
          C3:       ,    ≥ 0,  ∀   ∈   ,  ∀   ∈ ℐ
                                                               vice rate requirements of slice users. The link layer model
                                                       ′
          where the sum of the bids of other MVNOs    ≠    is  [60, 61] gained wide acceptance due to the ease of imple‑
                     ′
          denoted by    . Constraint C1 ensures the sum of the  mentation, and uncomplicated translation of decisive QoS
                       ,  
          bids of an MVNO for the resources of the respective InPs  requirements such as delay bounds, probability of packet
          does not exceed its budget    . Constraint C2 ensures that  loss,  and  packet  arrival  rate.  While  the  effective  capac‑
                                   
          the total load demand for a set of SPs bidding for the  ity of a slice ensures that the QoS requirements are met
          resources of the MVNO is met by the sum of resources  at a maximum packet arrival rate,  it leverages the aver‑
          purchased by the MVNO from the respective InPs. Con‑  age packet      ,ℎ,   , maximum delay bound threshold           ,
          straint C3 ensures that a bid value is non‑negative and  a delay‑bound violation probability   .  Thus, the effective
          also an MVNO can decide not to place a bid such that  capacity for a slice user      ,  ,     ∈  {ℳ ∪ ℛ} is given as [68, 61]:
               ,    = 0.



          64                                 © International Telecommunication Union, 2021
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