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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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A. Nait-Sidi-Moh et al. / Procedia Computer Science 141 (2018) 127–134 
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implementation and production capacity to meet demands’ fluctuations, which could not be entirely predictable. 
Furthermore, the integration of electric vehicles in the power grid network generates new additional issues that need 
to be also considered. 
In the past few years, great research efforts have been dedicated to developing the power engine of electric 
vehicles and batteries. However, little attention has been paid so far to their charging process and infrastructure. This 
is due to their charging process, which is completely different from the refueling process of conventional engines 
powered vehicles. Mainly, the uncertainty of drivers to get suitable and vacant places at a charging station 
constitutes one of the major obstacles to the large deployment of electric vehicles [1]. Recently, several scheduling 
and assignment approaches have been proposed to tackle this issue ([2], [3], [4] and [5]). For example, the 
charging/discharging process has been formulated in [3] as a global scheduling optimization problem, in which 
powers of charging are considered to minimize the total cost of all EVs. Authors in [4] propose a distributed 
scheduling approach for minimizing the waiting time for EV charging in large-scale road networks.
In our previous work, an assignment approach for charging EVs is proposed in [6] and [7]. It can be used to 
predict the charging rate and charging time for EVs requests. A Time Event Graph-based model (TEG) was 
proposed to describe the behavior of the system components. This model is basically used to study some qualitative 
properties of the system. In order to complete this study and evaluate some quantitative properties of the system, a 
(max, +) - model derived from the TEG model, was developed and analyzed. This model allows expressing and 
studying the system behavior. The work presented in this paper introduces a predictive function-based model for 
handling multiple charging demands and predicting average charging rates and charging times. The main aim is to 
minimize simultaneously the waiting time of each received request and the occupation time of charging stations.
The remainder of this paper is organized as follows. Section 2 presents a survey of exiting work from literature. 
Section 3 is dedicated to the description of the trade-off approach based on the introduced predictive function. In 
Section 4, we present the predictive approach with obtained simulations results. The last section concludes the paper 
and gives some future research directions.