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3. A trade-off approach based predictive function 
We consider that each charging station is composed of several charging points. All information regarding 
charging stations (including their status, provided charging power, location, etc.) are collected and stored into the 
platform database as explained in [6]. Furthermore, the collaborative platform regularly updates the information 
about the charging process, such as charging station status, driving range, and number of charging requests. Using 
these parameters, we developed an approach: i) to optimally handling the charging requests received from EVs, and 
ii) to allow assisting drivers in choosing an adequate charging station with eventual desired interest points. 
In this approach, an integrated predictive function is introduced to predict average charging rates for forthcoming 
requests. The differential properties of the predictive function are described in [19]. In the case of the charging 
process, the basic parameters of the predictive function are given as follows: 𝑃𝑃
!"#
is the maximum value of charging 
rate. In the most cases, this value is fixed at 100 %; 𝑃𝑃
!"#
represents a minimum threshold, which corresponds to the 
accepted minimum value of charging rate. The expression of the predictive function is given by the function (1) and 
other parameters are defined hereafter. 
𝜆𝜆 =
𝑃𝑃
!
1 + 𝑃𝑃
!
∙ 𝑒𝑒
!
!
.!
+ 𝑃𝑃
!"#
(1) 
where 𝜆𝜆 represents the average charging rate (given in %) and varies between 𝑃𝑃
!"#
and 𝑃𝑃
!"#
. 𝑃𝑃
!
is the difference rate 
between 𝑃𝑃
!"#
and 𝑃𝑃
!"#
. 𝑃𝑃
!
and 𝑃𝑃
!
are constants, which are calculated according to the number of charging points, 
charging requests and arrival times of charging requests. The parameter 𝑥𝑥 of the function (1) can be expressed as 
follows: 
𝑥𝑥 =
𝑛𝑛
!"
𝑛𝑛
!"
∙ ∆𝑘𝑘 
(2) 
where 𝑛𝑛
!"
is the number of EVs, which is accepted by available charging points ( 𝑛𝑛
!"
≥ 1), 𝑛𝑛
!"
is the number of 
available charging points (𝑛𝑛
!"
≥ 1),∆𝑘𝑘 is the inter-arrival between the 𝑘𝑘
!!
and (𝑘𝑘 − 1)
!!
charging requests 
expressed as follows: ∆𝑘𝑘 = 𝑈𝑈
!
𝑘𝑘 − 𝑈𝑈
!
𝑘𝑘 − 1
The following cases are considered to determine the average charging times according the number of EVs demands 
and the numbers of available charging points, where 𝐶𝐶𝐶𝐶
!"#
is the corresponding charging time to 𝑃𝑃
!"#
, and 𝐶𝐶𝐶𝐶
!"#
is 
the corresponding charging time to 𝑃𝑃
!"#
. In the equation (4), 𝑡𝑡
!
is the corresponding charging time to the average 
charging rate 𝜆𝜆. 
Case 1. 𝑛𝑛
!"
≤ 𝑛𝑛
!"
; 
Case 2. 𝑛𝑛
!"
> 𝑛𝑛
!"
; 
(a) 𝑛𝑛
!"
< 2 ∙ 𝑛𝑛
!"
; 
𝑡𝑡
!
=
𝜆𝜆 ∙ 𝐶𝐶𝐶𝐶
!"#
100
(3) 

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130 
A. Nait-Sidi-Moh et al. / Procedia Computer Science 141 (2018) 127–134
4 
NaitSidiMoh et al./ Procedia Computer Science 00 (2018) 000–000 
𝑡𝑡
!
=
𝑛𝑛
!"
𝑛𝑛
!"
∙ 𝐶𝐶𝐶𝐶
!"#
+ 𝑛𝑛
!"
− 𝑛𝑛
!"
𝑛𝑛
!"
∙ 𝑡𝑡
!
𝑛𝑛
!"
(4)
(b) Otherwise 
𝑡𝑡
!
=
𝐶𝐶𝐶𝐶
!"#
∙ 2 ∙ 𝑛𝑛
!"
𝑛𝑛
!"
+ 𝑛𝑛
!"
∙ 𝑛𝑛
!"
𝑛𝑛
!"
− 1 − 𝑛𝑛
!"
𝑛𝑛
!"
!
𝑛𝑛
!"
(5)