Page 17 - ITU Journal Future and evolving technologies Volume 2 (2021), Issue 5 – Internet of Everything

ITU Journal on Future and Evolving Technologies, Volume 2 (2021), Issue 5

Fig. 2 – FL framework for the VFs placement

In problems (4)‑(10), constraint (9) expresses the fact
= ∑ ∑( + ,ℎ ) ,ℎ ,ℎ +(1− ,ℎ ) , ( + , ), that each SR with a high priority has to be served, while

∈ ℎ∈ constraints (10) and (11) represent that the VFs allocation
(7) has to respect the storage limit of CNs and cloud, respec‑
where and are the execution time spent by the SR tively.

on the CPU of a CN and of the cloud, respectively. It is im‑ 4. FEDERATED LEARNING FRAMEWORK
portant to note that both the execution times and

mainly depend on the size of the SR , the CPU frequency 4.1 The learning problem
of the node hosting its elaboration, and the time spent by
The aim of ML is the exploitation of some data used for
the SR on that node waiting for the actual computation.
Therefore, ,ℎ and , represent the queuing time ex‑ training, to learn models. In order to do that, typically,
ML involves the de inition of a loss function representing
perienced by the the SR waiting for its execution on the
CN ℎ and cloud, respectively Furthermore, ,ℎ is a bi‑ the error implicitly resulting from the model training [8].
2
nary value equal to 1 if the SR is executed on the CN ℎ, The loss function depends on the data sample and a pa‑
0 otherwise. Similarly, ,ℎ is equal to 1 when the VF is rameter vector w, and it is named hereafter as (w). As

present on CN ℎ, 0 otherwise. Finally, , is equal to 1 if previously introduced, this paper supposes the presence
of SRs, with = + ℳ, deriving from an underlying
the VF is loaded on cloud, 0 otherwise. It is important to
level of EUs, each of which disposes of a local dataset Θ ,
make evident that the TSA in (7) strongly depends on the
= 1, … , . Therefore, as assumed in [8, 20], we suppose
queuing time experienced by the SR on the service provi‑
the collective loss function equals to
sion sit In fact, a proper deployment of VFs on the ECN
may drastically reduce the TSA time. 1
(w) = ∑ (w), (12)
In formal terms, the aim of this paper is the maximization |Θ |
∈Γ
of the SP revenue by providing decision making on the VFs
placement, in order to satisfy the SRs. Therefore, the main where |Γ | is the number of elements belonging to Γ , re‑

goal of the paper is given by ferred as the cardinality of the Γ set. Respectively, the

global function evaluated at the central server site, the
min ∑ ( , ) + ∑ ( , ), (8)

q,z global loss function, based on the distributed local dataset
=1,…, =1,…,ℳ
Θ and de ined as [8, 20], is expressed by the following re‑

lation
s.t. ∑ |Θ | (w)
≤ , ∀ = 1, … , , (9) =1,…,

(w) = . (13)
∑
≤ , ∀ℎ ∈ ,
∑ ,ℎ (10) =1,…, |Θ |

∈ ⋆
Therefore, the objective here is to ind w such that [8]
∑ , (11) ⋆ (14)
≤ .
∈ w = argmin (w).
2
The CPU queue has been modeled with the irst‑in‑ irst‑out service
policy.
© International Telecommunication Union, 2021 5