Page 76 - 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

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.

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