Page 77 - 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

In order to fully maximise the utility of the respective SP
1 1
( , , ) = lim log , , , , (19) in the M‑TTSD network, we formulate a joint tier‑domain
→∞ , , user‑association SP‑slice user resource allocation prob‑
where the QoS exponent is denoted by , , , and the lem in the (P1).
source packet arrival rate over the time interval [0, ) is Constraint (23)a guarantees that the minimum achievable

denoted by , , . By employing the theory of large devi‑ rate for each slice use‑case is met for all the slice users de‑
ations [69] and the application of a moment generating scribed in the categorisation in Subsection 3.3 and for the
function [70] to (19), the work in [68, 61], shows that the respective tiers and domains. Constraint (23)b ensures
ℎ
minimum achievable rate , , of a slice , , ∈ {ℳ∪ℛ} that a slice user is associated with only one access net‑
can be expressed as: work in a tier and by extension, can only be associated
with one domain network. Constraint (23)c ensures the
, , log( ) domain‑slice user association restriction such that, a user
ℎ
, , = − log( ) (20) subscribed to SP is associated with domain when
log (1 − ) Υ , , = 1, and otherwise not associated with the do‑

, ,
main with Υ , , = 0. A user can only be associated with
where the packet size and delay bound violation proba‑ one domain only. Similarly, Constraint (23)d enforces the
bility threshold are denoted as , , and , respectively. tier‑slice user association restriction. A slice user sub‑
scribed to SP is associated with a tier when Ω , , = 1,
5.3 Resource allocation model and otherwise when Ω , , = 0. Moreover, constraints
(23)e ‑ (23)h highlight that the sum of slice user ratio
Herein, to meet slice users’ demands, the resources from
of a resource does not exceed the resource size for
the respective MVNOs and by extension, the InPs, are , , ,
respective tiers. Besides, constraints (23)i ‑ (23)l indicate
pooled by an SP and then allocated to slice users in a dy‑
the slice user ratio which is the fractional allocation of re-
namic manner similar to the work in [68]. However, un‑
sources allocated to a slice user. To this end, the slice user
like [68], we consider a distributed resource allocation
ratio lies between 0 and 1, hence, it is a positive value.
framework in which an SP has control over its allocation
Furthermore, we investigate the resource allocation chal‑
process rather than a centralised approach. Moreover,
the utility of a slice user ( , , , ) is expressed as [71, 20, 67]: lenge in the MVNO hierarchical layer. We formulate a
utility maximisation optimisation problem in MVNO‑SP
1− layer by employing additive utility similar to the SP‑slice
⎧ , , , , ≠ 1
( , , , ) = 1 − (21) user utility maximisation problem in (P2). The total util‑
⎨ ity of MVNO is the aggregation of the utility of SPs re‑
⎩log( , , , ), = 1 lated to the resources of MVNO . Constraint (24)a guar‑
antees that aggregation of resource allocated to SP
,
where ( , , , ) is expressed as: by MVNO does not exceed the resource bid for by
MVNO from InP . Besides, constraint (24)b estab‑
, , , = , ⋅ , , ⋅ , , , ⋅ , , , . (22) lishes the Business‑to‑Business (B2B) relationship ∇ ,
The weight of a resource type belonging to InP allocated between an SP and an InP . When a slice user sub‑
to SP is denoted by . We represent the tier‑slice ra‑ scribed to SP is associated with a domain network man‑
,
tio of the resource by , , , and , , , denotes the slice aged by an InP , ∇ , = 0, otherwise resources of InP
user ratio. The spectrum ef iciency , , , is given in (2) cannot be utilised. In addition, constraint (24)c ensures
and the spectrum ef iciency , , , is strictly concave and the resource share , of MVNO resource allocated to
strictly increases i.e., non‑decreasing values of ≥ 0. In SP lies between 0 and 1. Moreover, the IC for MVNOs is
guaranteed in constraint (24)d. To this end, the sum bids
this work, we adopt logarithmic utility in (22) when = 1.
of SPs associated with MVNO must exceed the sum
The logarithmic utility ensures proportional fair rate allo‑ ,
cations. of the bids placed by MVNO for the resources of
InPs associated with it.
6. PROBLEM FORMULATION

In this section, a latency‑aware, bid‑aware, and dis‑
tributed resource allocation problem in the hierarchical
layers of an M‑TTSD network is examined. First, the over‑
all utility of an SP is investigated by formulating a utility
maximisation problem in the SP‑user hierarchical layer.
We adopt additive utility given in [72, 73] to determine
the overall utility of an SP. Additive utility assumes pref‑
erential independence between attributes such that the
total associated utility of an SP is the aggregation of the
utility of individual slice users.

© International Telecommunication Union, 2021 65