Aymen Gammoudi
email: aymen.gammoudi@irisa.fr

Adel Benzina
email: adel.benzina@isd.rnu.tn

Mohamed Khalgui
email: khalgui.mohamed@gmail.com

Daniel Chillet

Energy-Efficient Scheduling of Real-Time Tasks in Reconfigurable Homogeneous Multi-Core Platforms

Keywords: Homogeneous multi-core architecture, Realtime system, Low-power scheduling, Reconfiguration, Task mapping

This paper deals with real-time scheduling of homogeneous multi-core platforms powered by a battery to be periodically recharged. A system is composed of reconfigurable real-time dependent and periodic tasks to be assigned to different cores interconnected by a network-on-chip (NoC). The system is subject to reconfigurations, which are automatic operations allowing the addition and/or removal of tasks as well as their exchanged messages on the NoC. Consequently, any reconfiguration can violate real-time and energy constraints on cores as well as the NoC when the energy is unavailable until the next recharge. A novel periodic task model based on elastic coefficients and a new scheduling strategy are proposed to compute useful temporal parameters allowing for tasks and messages to meet the related constraints while controlling the communication cost on the NoC. This strategy is compared with an ILP-based optimal solution, and a tool named OptimalMappingTasks is developed to run different simulations that prove the originality of the paper's contribution.

I. INTRODUCTION

The number of reconfigurable real-time embedded platforms powered by batteries is constantly increasing with applications in aeronautics, mobile communication systems, automotive, robotics, telecommunications, environmental monitoring, consumer electronics, and so on [START_REF] Houssein | Energy efficient scheduler of aperiodic jobs for real-time embedded systems[END_REF]- [START_REF] Meskina | Multiagent framework for smart grids recovery[END_REF]- [START_REF] Grichi | RWiN: new methodology for the development of reconfigurable WSN[END_REF]. In such applications, it is necessary to guarantee the stability of the controlled system. Based on the environment conditions and also the required performance, the system designer imposes that each periodic task must be executed at a constant rate in order to guarantee the stability. For critical applications (where missing a deadline is a total system failure), the schedulability of the system has to be satisfied a priori and no task period modification is allowed at run-time. Such a critical application in which periodic tasks operate is determined by the schedulability analysis that must be done according to the task set to ensure its feasibility under constraints, such that real-time and/or energy. Feasibility analysis can be based on the work reported in [START_REF] Liu | Scheduling algorithms for multiprogramming in a hard-real-time environment[END_REF] on the RM and the EDF policies, a periodic task τ i is characterized by two parameters, its WCET W i and its period T i , which are assumed as constants for all task instances (homogeneous multi-core architecture). This is a fair supposition for hard real-time systems; however it might be too restrictive for other applications.

For instance, timing constraints are more flexible and dynamic in multimedia systems than control applications. Tasks such as voice sampling, image acquisition, data compression, and video playing are executed periodically, but their execution rates are not as strict as in control applications. Thus missing a deadline while displaying an MPEG video may degrade the quality of service (QoS), but this will not engender the systems failure. According to the requested QoS, the tasks may increase or decrease their execution rate to fit the requirements of other concurrent activities. The variation of the tasks rates would increase the flexibility of the system while managing the overload conditions and providing a more general admission control mechanism. When the system cannot guarantee the execution of a new task, it can reduce the rate of the other tasks (by increasing their periods in a controlled fashion) to decrease the processor utilization and accommodate the new request instead of rejecting it. In this context, several research studies reported in [START_REF] Wang | Dynamic multiple-period reconfiguration of real-time scheduling based on timed DES supervisory control[END_REF]- [START_REF] Cecilio | Architecture for uniform (re) configuration and processing over embedded sensor and actuator networks[END_REF]- [START_REF] Li | QoS-aware scheduling of servicesoriented internet of things[END_REF]- [START_REF] Grichi | New Extended Object Constraint Language for Adaptive Discrete Event Systems with Application to Recongurable Wireless Sensor Networks[END_REF]- [START_REF] Zhang | R-TNCES: A novel formalism for reconfigurable discrete event control systems[END_REF]- [START_REF] Ghribi | R-Codesign: Codesign Methodology for Real-time Reconfigurable Embedded Systems Under Energy Constraints[END_REF] have focused on the dynamic reconfiguration of real-time systems. Concerning the dynamic reconfiguration, two policies are defined in the literature: manual, applied by users [START_REF] Martijn | Zero downtime reconfiguration of distributed automation systems: The εcedac approach[END_REF]; and automatic, applied by intelligent control agents [START_REF] Pavel | Capabilities of dynamic reconfiguration of multiagent-based industrial control systems[END_REF]. The most promising approach is the elastic scheduling reported in [START_REF] Wang | Dynamic multiple-period reconfiguration of real-time scheduling based on timed DES supervisory control[END_REF]- [START_REF] Wang | Dynamic low-power reconfiguration of real-time systems with periodic and probabilistic tasks[END_REF]- [START_REF] Marinoni | Elastic DVS management in processors with discrete voltage/frequency modes[END_REF]- [START_REF] Buttazzo | Elastic task model for adaptive rate control[END_REF].

A system, denoted RT Sys, can be implemented by N 1 dependent and periodic tasks to be assigned to p cores linked by a network-on-chip (NoC) [START_REF] Hu | Energy-and performance-aware mapping for regular NoC architectures[END_REF] in order to ensure the communication between dependent tasks. Reducing the cost of communications between cores becomes a major concern to ensure high-performance and reliability of such systems. Several academic studies reported in [START_REF] Bhardwaj | An Effective Load Balancing Task Allocation Algorithm using Task Clustering[END_REF] and [START_REF] Govil | A smart algorithm for dynamic task allocation for distributed processing environment[END_REF] propose mapping algorithms using task clustering while considering both inter-task communication and execution costs. The basic idea of the clustering based algorithm reported in [START_REF] Bhardwaj | An Effective Load Balancing Task Allocation Algorithm using Task Clustering[END_REF] and [START_REF] Govil | A smart algorithm for dynamic task allocation for distributed processing environment[END_REF] is to group heavily communicating tasks into the same cluster. The tasks that are grouped into the same cluster are assigned to the same processor to avoid communication costs. These algorithms are interesting since the communication cost is reduced. Nevertheless, the authors are not interested in the verification of the processor utilization after assigning the tasks, i.e. the processor utilization exceeds 100% in certain cases. In addition, they do not check the overflow on the communication medium. To solve these two problems, effective solutions based on the modification of WCETs, deadlines, and periods of tasks to manage the processor utilization after any assignment of tasks are reported in [START_REF] Gammoudi | New Pack Oriented Solutions for Energy-Aware Feasible Adaptive Real-Time Systems[END_REF], [START_REF] Wang | Dynamic multiple-period reconfiguration of real-time scheduling based on timed DES supervisory control[END_REF], [START_REF] Wang | Dynamic low-power reconfiguration of real-time systems with periodic and probabilistic tasks[END_REF], [START_REF] Marinoni | Elastic DVS management in processors with discrete voltage/frequency modes[END_REF]. Similarily to the research works reported in [START_REF] Wang | Dynamic multiple-period reconfiguration of real-time scheduling based on timed DES supervisory control[END_REF]- [START_REF] Marinoni | Elastic DVS management in processors with discrete voltage/frequency modes[END_REF]- [START_REF] Buttazzo | Elastic task model for adaptive rate control[END_REF], we consider a more flexible task model, in which the tasks can operate within a given range of periods with different performances. We consider that the system RT Sys is running on a reconfigurable platform which is powered by a battery and is recharged periodically with a well-known recharging period. A reconfiguration scenario is defined, in this paper, as any internal or external event that leads to the addition and/or removal of dependent periodic tasks as well as their exchanged messages to adapt the system's behavior to its environment [START_REF] Quadri | Expressing embedded systems configurations at high abstraction levels with UML MARTE profile: Advantages, limitations and alternatives[END_REF].

After any reconfiguration scenario, the real-time constraints can become no more satisfied i.e. a task misses its deadline and a message takes a long time to arrive to its destination. Moreover, a reconfiguration scenario may increase the energy consumption and the system RT Sys can deplete the available energy before the next recharge. Therefore, the system RT Sys will be unfeasible and should provide optimal real-time solutions with a controlled power consumption to maintain the system up until the next planned recharge of the battery. An RT Sys is feasible if and only if it satisfies under different constraints: (i) the deadlines of the tasks are ensured/respected (real-time constraints), (ii) the messages deadlines on the communication medium are ensured (communication constraints), and (iii) the energy constraint is sufficient to ensure the execution until the next periodic recharge (energy constraints).

In real-time scheduling, effective solutions based on the modification of WCETs, deadlines, and periods of tasks in order to re-obtain the system feasibility after any reconfiguration scenario are reported in [START_REF] Gammoudi | New Pack Oriented Solutions for Energy-Aware Feasible Adaptive Real-Time Systems[END_REF]- [START_REF] Wang | Dynamic multiple-period reconfiguration of real-time scheduling based on timed DES supervisory control[END_REF]- [START_REF] Wang | Dynamic low-power reconfiguration of real-time systems with periodic and probabilistic tasks[END_REF]- [START_REF] Gharsellaoui | Reconfiguration of Synchronous Real-Time Operating System[END_REF]- [START_REF] Marinoni | Elastic DVS management in processors with discrete voltage/frequency modes[END_REF]. The work presented in [START_REF] Wang | Dynamic low-power reconfiguration of real-time systems with periodic and probabilistic tasks[END_REF] proposes a feasible low-power dynamic reconfiguration of real-time systems where addition and removal of tasks are applied at run-time. Three solutions are presented to cut-down the energy consumption after any reconfiguration scenario. The authors propose to extend the periods (or reduce the WCETs) of tasks by assigning a single value to all the tasks in order to re-obtain the system feasibility. Recently, the work reported in [START_REF] Gammoudi | New Pack Oriented Solutions for Energy-Aware Feasible Adaptive Real-Time Systems[END_REF] improves these solutions by proposing a new approach based on grouping tasks in packs and modifying task parameters by assigning a unique period (or WCET) to all the tasks of the same pack. Each pack is a group of tasks having "similar" periods (or WCETs). In order to satisfy the real-time and the energy constraints after any reconfiguration scenario, specific modifications are to be undergone on the parameters of the packs and their related tasks. Each modification of periods (or WCETs) of the tasks has a cost in terms of delay. The cost of each modification on a task is the difference between the parameter's value before and after the reconfiguration. The total cost of the modification on the system is the sum of all these costs. In the research work reported in [START_REF] Gammoudi | Reconf-Pack: A Simulator for Reconfigurable Battery-Powered Real-Time Systems[END_REF], the authors develop the Reconf -P ack simulator to evaluate and compare these two approaches ( [START_REF] Gammoudi | New Pack Oriented Solutions for Energy-Aware Feasible Adaptive Real-Time Systems[END_REF] and [START_REF] Wang | Dynamic low-power reconfiguration of real-time systems with periodic and probabilistic tasks[END_REF]) by generating a large number of random systems and random reconfiguration scenarios for each one. The authors show that the total cost delay introduced by applying the solution presented in [START_REF] Wang | Dynamic low-power reconfiguration of real-time systems with periodic and probabilistic tasks[END_REF] in 88% of the randomly generated cases is drastically higher than that introduced by the method reported in [START_REF] Gammoudi | New Pack Oriented Solutions for Energy-Aware Feasible Adaptive Real-Time Systems[END_REF]. To show that the pack-based solution, proposed in [START_REF] Gammoudi | New Pack Oriented Solutions for Energy-Aware Feasible Adaptive Real-Time Systems[END_REF], can be implemented in a real application, the work reported in [START_REF] Gammoudi | New Reconfigurable Middleware for Adaptive RTOS in Ubiquitous Devices[END_REF] proposes a new reconfigurable middleware, named Reconf -M iddleware, that presents a plugin implemented in RTLinux and describes the transition from the pack theory to the implementation. An extension of the technique reported in [START_REF] Gammoudi | New Pack Oriented Solutions for Energy-Aware Feasible Adaptive Real-Time Systems[END_REF] to homogeneous multi-core platforms is described in [START_REF] Gammoudi | Real-Time Scheduling of Reconfigurable Battery-Powered Multi-Core Platforms[END_REF]. The authors propose four solutions to schedule a real-time application composed of independent periodic tasks under energy constraints. The authors develop a new strategy for allocating N tasks to p cores of a given distributed system using task clustering by considering the load balancing over the different cores. The proposed strategy guarantees that, when a task is mapped into the system and accepted, then it is correctly executed prior to its deadline. Nevertheless, they do not consider the case of dependent periodic software tasks and they do not treat the influence of communication on the energy consumption.

The general goal of this paper is to propose a comprehensive strategy based on the pack-based solutions reported in [START_REF] Gammoudi | New Pack Oriented Solutions for Energy-Aware Feasible Adaptive Real-Time Systems[END_REF]- [START_REF] Gammoudi | Real-Time Scheduling of Reconfigurable Battery-Powered Multi-Core Platforms[END_REF]. It is applied in order to re-obtain the RT Sys feasibility after any reconfiguration scenario. The proposed strategy offers five solutions (A, B, C, D and E) based on the modification of temporal parameters of the processed tasks to meet the real-time, communication and energy constraints. If some constraints are violated after any reconfiguration scenario, then the proposed strategy starts first by modifying the periods of tasks and also the periods of the exchanged messages until reaching their specific maximal periods (Solution A or C). If RT Sys is still unfeasible, then it applies another solution to decrease the WCETs of tasks (Solution B). In the worst case, the strategy applies the last solution that removes some tasks according to a functional importance factor I i defined for each task (Solution E). The proposed strategy applies these solutions in this order since the modification of periods (Solution A or C) does not have a significant influence on the consumed energy. Nevertheless, the application of Solution B or D increases implicitly the energy consumption.

To evaluate the performance of the proposed strategy, we perform different simulations scenario. We then compare these solutions with the research work reported in [START_REF] Wang | Dynamic low-power reconfiguration of real-time systems with periodic and probabilistic tasks[END_REF] and show that the cost in terms of delaying tasks is significantly reduced. We formalize this strategy as an optimization problem by using integer linear programming (ILP) and we compare the proposed solutions with the optimal results provided by the CPLEX solver [START_REF] Cplex | IBM ILOG CPLEX Optimize[END_REF]. The originality of this paper is twofold, the first one is to propose a new tool named OptimalM appingT asks to look for the optimal placement of tasks on cores after any reconfiguration scenario in order to minimize the traffic on the NoC by trying to place the dependent tasks as close as possible to each other. The second is to propose a new scheduling strategy to meet the related constraints after any reconfiguration in order to re-obtain the RT Sys feasibility by modifying the parameters of tasks and the exchanged messages or by removing some of them. Even if the three constraints are simultaneously violated, the proposed strategy is deterministic since it is able to re-obtain the feasibility of the system by reducing less delay than that introduced by the method reported in [START_REF] Wang | Dynamic low-power reconfiguration of real-time systems with periodic and probabilistic tasks[END_REF]. The proposed algorithm is compared with two others EDF-based algorithms reported in [START_REF] Bhardwaj | An Effective Load Balancing Task Allocation Algorithm using Task Clustering[END_REF] and [START_REF] Govil | A smart algorithm for dynamic task allocation for distributed processing environment[END_REF] and we show that the traffic on the NoC is minimized.

The rest of this paper is organized as follows. Section II presents the system model and the used terminologies. We formalize the considered problem in Section III. The proposed strategy is presented in Section IV. This section deals also with the modification of temporal parameters of the processed tasks to guarantee the related real-time and energy constraints after any run-time event-based reconfiguration scenario. The strategy is implemented and simulated in Section IV-F. The performance evaluation of the proposed contribution is reported in Section IV-F. Some interesting results are discussed in Section VII. Finally, Section VIII concludes this work.

II. SYSTEM MODEL AND ASSUMPTIONS

In this section, we present the task model and the platform architecture that consists of a reconfigurable real-time system RT Sys composed of periodic tasks. RT Sys is powered by a battery to be recharged periodically, and running on an architecture composed of p homogeneous cores. We also present, in this section, the models of hardware devices, including the processor architecture, battery and the communication between cores.

A. Task Model

The feasibility analysis of periodic tasks under earliest deadline first (EDF) scheduling was proposed by Liu and Layland [START_REF] Liu | Scheduling algorithms for multiprogramming in a hard-real-time environment[END_REF]. EDF is a dynamic scheduling policy used in real-time operating systems to allocate tasks in a priority queue. Whenever a scheduling event occurs, the next task is extracted from the queue by considering the timing to the deadline. The task with the closest deadline will be extracted first, i.e., the task is the next to be scheduled for execution. With a preemptive scheme, among all scheduling policies, EDF is optimal [START_REF] Liu | Scheduling algorithms for multiprogramming in a hard-real-time environment[END_REF]. Assuming that the period is equal to the deadline for each task, the necessary and sufficient condition for schedulability is to verify that the processor utilization rate is less than 1 [START_REF] Liu | Scheduling algorithms for multiprogramming in a hard-real-time environment[END_REF]. Hence, in this paper, we apply EDF to schedule the tasks. We suppose that RT Sys processes a task set Π containing N 1 periodic tasks, i.e., Π = {τ 1 , τ 2 , ..., τ N1 }. Some tasks are considered as flexible, whose utilization can be modified by changing their periods within a specified range. The elastic model introduced by [START_REF] Marinoni | Elastic DVS management in processors with discrete voltage/frequency modes[END_REF]- [START_REF] Buttazzo | Elastic task model for adaptive rate control[END_REF] considers task parameters as flexible as a spring with a given rigidity coefficient. In particular, we consider in this paper the task's period T i as an elastic parameter whose value can be changed within a specified range. According to [START_REF] Wang | Dynamic multiple-period reconfiguration of real-time scheduling based on timed DES supervisory control[END_REF]- [START_REF] Marinoni | Elastic DVS management in processors with discrete voltage/frequency modes[END_REF]- [START_REF] Buttazzo | Elastic task model for adaptive rate control[END_REF], a periodic task τ i , i ∈ {1, 2, ..., N 1 }, is characterized by: (i) a release time A i , (ii) a worst-case execution time (WCET) W i that represents the time elapsed from the time task acquires the processor to the end of the task without being interrupted. The WCETs are considered in this paper as inputs, (iii) a relative deadline D i , (iv) a period T i , (v) a maximum tolerable period T max i , and (vi) a functional importance factor I i to be fixed manually by users. Such that more I i is bigger, less τ i is important. If RT Sys is not feasible or consumes too much energy than the available, then the tasks with the highest value of I i should be removed to keep as many tasks as possible running on the system. The relative deadline of a periodic task is considered as a hard deadline if its missing is unacceptable [START_REF] Baruah | Scheduling real-time tasks: Algorithms and complexity[END_REF].

B. Multi-Core Processor Model

We suppose that a homogeneous multi-core platform contains a set Γ of p cores Γ={C 1 , C 2 , ..., C p }. We assume that, each core C j (j ∈ [1..p]) executes its local tasks by using the EDF algorithm. We assume that the cores can be reconfigured dynamically by authorizing the addition and/or removal of periodic tasks. We also assume that the frequency of each core can be changed in order to modify the execution time of tasks. To ensure that all the tasks can be executed on the cores, we define the mapping matrix H where

H i,j = 1 if task τ i is running on core C j . 0 otherwise.
Furthermore, to guarantee that each task is executed at most by one core, it is necessary to verify that

p j=1 H i,j = 1; ∀i ∈ [1..N 1 ] (1)

C. Communication Model

Several distinguished studies deal with network-on-chip (NoC) and its different typologies [START_REF] Khemaissia | New Methodology for Feasible Reconfigurable Real-Time Network-on-Chip NoC[END_REF]- [START_REF] Hu | Energy-and performance-aware mapping for regular NoC architectures[END_REF]. In this paper, we do not consider a specific NoC architecture, but we present a general formalization which is adaptable to different architectures. As defined in subsection II-A, we consider a set Π of dependent periodic tasks, each one is affected to a particular core. We denote in the following by M i,j , the message to be exchanged between a pair of tasks τ i and τ j . According to [START_REF] Bui | Real-time scheduling of concurrent transactions in multidomain ring buses[END_REF] the communication model is based on: (i) the regular inter-arrival time T M i,j , (ii) the spent time to transmit a message W M i,j , (iii) the absolute deadline DM i,j , and (iv) the amount of exchanged data SM i,j . We note that period T M i,j of message M i,j is equal to period T i of sending task τ i (T M i,j =T i ). If the task's period is changed, then the message's period will be changed implicitly. The NoC architecture implies a communication cost between each pair of cores depending on the distance between them. We model each NoC architecture by a specific cost matrix Cost such as

Cost C k ,C l = X C k ,C l if k = l, ∀ k, l ∈ [1..p]. 0 otherwise.
where X C k ,C l is a constant giving the cost of transferring one bit from core C k to core C l .

To calculate the cost of communication between each pair of cores C k and C l , it is necessary to multiply the volume of exchanged data by Cost C k ,C l . Then, the total cost of communications is given by

CommCost = p k=1 p l=1 N1 i=1 N1 j=1 SM i,j * Cost C k ,C l * H i,k * H j,l (2)
We suppose that the energy consumed by the communication is proportional to the distance between cores.

D. Processor Utilization Model

According to [START_REF] Liu | Scheduling algorithms for multiprogramming in a hard-real-time environment[END_REF] the processor utilization U Cj of core C j is given by

U Cj = N1 i=1 W i T i * H i,j ; ∀j ∈ [1..p] (3)
The core C j is feasible under the EDF policy, if and only if

U Cj ≤ 1; ∀j ∈ [1..p] (4)
Eq. 4 is the real-time constraint, denoted RTConst.

According to the works reported in [START_REF] Bui | Real-time scheduling of concurrent transactions in multidomain ring buses[END_REF]- [START_REF] Khemaissia | Reconfigurable CAN in real-time embedded platforms[END_REF]- [START_REF] Khemaissia | New Methodology for Feasible Reconfigurable Real-Time Network-on-Chip NoC[END_REF], to evaluate the communication feasibility between two cores, the related medium is considered as a virtual processor. Based on this hypothesis, the utilization of the communication medium between two cores C k and C l , denoted U Com (C k , C l ), is given by

U Com (C k , C l ) = N1 i=1 N1 j=1 W M i,j T M i,j * H i,k * H j,l ; ∀k, l ∈ [1..p]
(5) According to the work reported in [START_REF] Khemaissia | New Methodology for Feasible Reconfigurable Real-Time Network-on-Chip NoC[END_REF], to ensure that the communication between cores that are physically close is feasible, it is necessary to check

U Com (C k , C l ) ≤ 1; ∀k, l ∈ [1..p] | Cost C k ,C l = 1 (6)
Eq. 6 is the communication constraint, denoted CommConst.

E. Power Consumption Model

In the works reported in [START_REF] Wang | Dynamic low-power reconfiguration of real-time systems with periodic and probabilistic tasks[END_REF] and [START_REF] Quan | Minimal energy fixed-priority scheduling for variable voltage processors[END_REF], the authors show that the power consumed by a DVS processor is directly proportional with at least the squared value of its utilization, i.e., P α U 2 . We consider that RT Ssys is periodically fully recharged. Thus, the power consumption of core C j is given by

P Cj = k * U 2 Cj ; ∀j ∈ [1..p] (7)
Hence, the power consumption of all the tasks running in the p cores is given by

P P roc = p j=1 P Cj (8)
Similarly, we define the power consumption due to the communication on the NoC by

P Com = k p k=1 p l=1 U 2 Com (C k , C l ) (9)
Therefore, the total power consumption of RT Sys is P T otal = P P roc + P Com [START_REF] Lin | Energy-efficient task scheduling for multi-core platforms with per-core DVFS[END_REF] Since, we consider periodic tasks, it is possible to compute the energy needed to support their until the next battery recharge. We suppose that E(t) is the available energy in the battery at time t and t recharge is the time remaining until the next recharge. We note that these two parameters are supposed known at any time t. Therefore, to ensure that RT Sys runs correctly until the next recharge, assuming that the configuration will remain the same, it is necessary that at time t, i.e.,

P T otal (t).t recharge ≤ E(t) (11)
We define the variable P Limit by the quantity E(t) t recharge . It is the maximum power consumption tolerable at time t otherwise RT sys will be off due to energy shortage before the next recharge. Thus, after each reconfiguration scenario, we have to satisfy the following power consumption constraint, i.e.,

P T otal ≤ P Limit (12)
Eq. 12 is the energy constraint, denoted EnergyConst.

III. PROBLEM POSITION

We present in this section the problem of reconfiguration and we describe and formalize each constraint as an optimization problem by using ILP. This section presents first the general ILP formulation of the problem, and continues with the ILP formulations of the proposed heuristics.

A. Reconfiguration Problem

We suppose that at time t 0 RT Sys is initially composed of Γ(t 0 ) = {C 1 , C 2 , ..., C p } and Π(t 0 ) = {τ 1 , τ 2 , ..., τ N1 }. Assuming that RT Sys at t 0 is feasible implies that all three constraints of real-time, energy and communication must be satisfied. In the following, we assume that RT Sys is dynamically reconfigured at time t 1 by adding N 2 tasks. Therefore, the new implementation of tasks is

Π(t 1 ) = {τ 1 , τ 2 , ..., τ N1 , τ N1+1 , ..., τ M }, with M = N 1 + N 2 .
This reconfiguration scenario is appointed in the following by RE-CON F . To ensure that the system runs correctly after RE-CON F , it is necessary to guarantee that the new configuration satisfies the constraints of the following model

RE                                            M inimize CommCost (Eq.2) s.t. p j=1 H i,j = 1, ∀ i ∈ [1.
.M ] (Eq.1)

U Cj ≤ 1, ∀ j ∈ [1..p] (Eq.4) U Com (C k , C l ) ≤ 1 | Cost C k ,C l = 1 (Eq.6) ∀ k, l ∈ [1..p] P T otal ≤ P Limit (Eq.12)
where Eq.2 calculates the total cost of the communications, Eq.1 guarantees that each task can be executed at most by one core, Eq.4 satisfies the real-time scheduling under the EDF policy for each core, Eq.6 ensures that the communication between the cores C k and C l is feasible and Eq.12 ensures a rational use of the remaining energy until the next recharge.

The RE problem can be solved by integer programming solvers such as CPLEX [START_REF] Cplex | IBM ILOG CPLEX Optimize[END_REF], which is hard to be implemented in an embedded platform since it is too complex to be executed on-line. We note that this solver does not produce any solution if one or more constraints are not satisfied. To solve the problem RE, it is necessary that all the constraints are satisfied. Nevertheless, after each RE-CON F scenario, one or more of these constraints can be violated. We formalize first of all each constraint as an optimization problem by using the ILP formulation. Then, we present a heuristic to solve them in an efficient way.

B. Real-Time Problem

After the RE-CON F scenario, if core C j is not feasible (U Cj > 1) and since

U Cj = M i=1 Wi Ti * H i,j ; ∀j ∈ [1..p],
we propose first of all to modify the periods of the local realtime tasks in order to decrease the processor utilization. The principle is to extend the periods of tasks until they reach T max i . If U Cj is still greater than 1, then we have to reduce the WCETs in order to satisfy U Cj ≤ 1. In the worst case, we apply another alternative that removes some tasks according to their importance factor I i . Using the ILP model, we formalize this problem by

∀ j ∈ [1..p] | U Cj > 1 P b1 =                                M inimize M i=1 ∆W i * H i,j s.t. M i=1 W i -∆W i T i + ∆T i * H i,j ≤ 1 W i -∆W i > 0, ∀ i ∈ [1..M ] T i + ∆T i ≤ T max i , ∀ i ∈ [1..M ]
where ∆T i is an integer that extends the period of the real-time tasks and ∆W i is an integer that reduces their WCETs. This formalization permits to minimize the WCETs modification and exploits the possible flexibility of the periods.

C. Energy Problem

After the reconfiguration scenario RE-CON F , the processor utilization of certain cores will be increased due to the added tasks. According to the work reported in [START_REF] Wang | Dynamic low-power reconfiguration of real-time systems with periodic and probabilistic tasks[END_REF], the power consumption P is quadratically dependent on the processor utilization. The new power consumption, in the worst case, may surpass the available energy budget. Therefore, RT Sys can violate the energy constraint. In this context, we suggest to decrease the processor utilization of core C high (high ∈ [1..p]) that has the highest processor utilization until the energy constraint is satisfied. To decrease the processor utilization, we propose to adapt the periods of real-time tasks, running on C high , until they reach T max i in order to ensure that the system RT Sys will run correctly until the next battery recharge. This idea is formalized by

P b2                                M inimize M i=1 ∆T i * H i,high s.t. M i=1 W i T i + ∆T i * H i,high ≤ 1 T i + ∆T i ≤ T max i , ∀ i ∈ [1..M ]
P T otal ≤ P Limit (Eq.12)

After adapting the task parameters, running on C high , the processor utilization U C high is decreased and the energy constraint (Eq. 12) can be satisfied. If it is still violated, then we propose to remove some tasks according to their importance factor I i .

D. Communication Problem

After the addition of a pair of dependent tasks on two cores that can be caused by RE-CON F , a periodic message will be added to the NoC and should respect a corresponding deadline related to these tasks. Then, it is necessary to verify the feasibility of the communication between each pair of cores

C k and C l (k, l ∈ [1..p]). According to Eq. 6, if U Com (C k , C l )
is greater than 1, then the communication between these two cores is not feasible. In order to solve this problem, we propose to modify the period of messages exchanged between the tasks running on cores C k and C l . We can formalize this problem by

∀ k, l ∈ [1..p] | U Com (C k , C l ) > 1 P b3 =                        M inimize M i=1 M j=1 ∆T M i,j * H i,k * H i,l s.t. M i=1 M j=1 W M i,j T M i,j + ∆T M i,j * H i,k * H i,l ≤ 1 T M i,j + ∆T M i,j ≤ T max i , ∀ i, j ∈ [1..M ]
where ∆T M i,j is an integer value that extends the period of message M i,j . P b1, P b2 and P b3 can be solved by CPLEX [START_REF] Cplex | IBM ILOG CPLEX Optimize[END_REF] that provides an optimal solution since it seeks for each task and message the suitable and exact modification with a minimal cost. Nevertheless, it is not reasonable to implement an ILP solver in an embedded system. In other words and since we propose a new strategy to schedule real-time tasks in an operating system, it is too complex to execute on-line an ILP solver, but it is useful to calculate the optimal solution that will be considered as a reference target for any implementable heuristic. Therefore, we present in the next Section some efficient and implementable heuristics compared with the optimal solutions provided by the CPLEX solver to solve these problems.

IV. CONTRIBUTION

When the RE-CON F scenario is applied at run-time, the processor utilization of certain cores will be certainly increased. If the new utilization is greater than 1, then the real-time constraint is violated as reported in [START_REF] Wang | Dynamic low-power reconfiguration of real-time systems with periodic and probabilistic tasks[END_REF]- [START_REF] Liu | Scheduling algorithms for multiprogramming in a hard-real-time environment[END_REF]. In addition, the energy and/or communication constraints can be violated after the addition of tasks and consequently RT Sys will be unfeasible. In this section, we present in Fig. 1 a new scheduling strategy based on adapting task parameters T i and/or W i to fulfill the feasibility condition. If some tasks of the new execution model violate the related deadlines, or if the power consumption is increased, or the charge of the communications between two cores is greater than 1, then this strategy proposes new solutions in order to re-obtain the RT Sys feasibility with a low power consumption. It proposes also to remove some tasks according to their importance factor I i . Each modification of periods or WCETs of tasks has a cost in terms of delay. The cost of each modification on a task is the difference between the parameter's value before and after this reconfiguration scenario. Therefore, the objective is to re-obtain the system feasibility while minimizing the modification cost. We present in the remainder of this section some new solutions with various costs and with different implementation complexities.

A. Technical Overview

In order to re-obtain the system feasibility, we propose a heuristic based on grouping the tasks that have "similar" periods (or WCETs) in several packs, denoted P ack. As described in the second part of Section I, after a reconfiguration, we do not calculate a new period for each task, but we assign a unique new period (or new WCET) to all tasks of the first pack P ack 1,j (j ∈ [1..p]). Moreover, all the new periods (or WCETs) affected to the tasks of pack P ack x,j are multiple of the one affected to the tasks of P ack 1,j . Hence, we have only to compute the suitable value P k 1,j . In order to satisfy the real-time and the energy constraints after any reconfiguration scenario, specific modifications are to be undergone on the parameters of the packs and their related tasks. Each modification of periods (or WCETs) of tasks has a cost in terms of delay. The cost of each modification on a task is the difference between the parameter's value before and after a reconfiguration. Full details can be found in [START_REF] Gammoudi | New Pack Oriented Solutions for Energy-Aware Feasible Adaptive Real-Time Systems[END_REF].

B. Solution A: Periods' Modification under Real-Time Constraint

If C j (j ∈ [1..p]) is not feasible after the RE-CON F scenario, then we propose to extend the periods of tasks that run on C j . In order to satisfy the real-time constraints, we assign each task to the pack P ack T x,j according to its period. To construct the packs, we need to seek the suitable new period P k T 1,j that minimizes the cost of the new solution for the whole system. We formalize this problem by

               M in M i=1 (P k T 1,j -(T i mod P k T 1,j )) mod P k T 1,j * H i,j s.t. P k T 1,j ≥ M in(T i ), ∀ i ∈ [1..M ] | H i,j = 1
Once P k T 1,j is calculated, we construct the packs of the system tasks as follows: P ack T x,j , x ≥ 1, includes the tasks that have a period in the range [(x -1) * P k T 1,j + 1 ; x * P k T 1,j ], x ∈ N + . The first value of x is 1 and when all tasks are affected, x is no more incremented. Example: P ack T 1,j includes the tasks that have a period in the range [1 ; P k T 1,j ], P ack T 2,j includes the tasks that have a period in the range [P k T 1,j + 1 ; 2 * P k T 1,j ], etc. To satisfy the real-time constraints under the EDF policy, it is necessary that

M i=1 W i T i * H i,j ≤ 1.
Since the periods are now multiple of the same value P k T 1,j , we get

τi∈P ack T 1,j W i P k T 1,j + ... + τi∈P ack T x,j W i x.P k T 1,j ≤ 1 thus, 1 P k T 1,j *   τi∈P ack T 1,j W i + ... + τi∈P ack T x,j W i x   ≤ 1 then, P k T 1,j ≥ τi∈P ack T 1,j W i + ... + τi∈P ack T x,j W i x
Since the periods are integer values, then,

P k T 1,j =     τi∈P ack T 1,j W i + ... + τi∈P ack T x,j W i x     (13)
where P k T 1,j is the new period affected to tasks of the first pack P ack T 1,j , x * P k T 1,j to the tasks of x th pack P ack T x,j . After adapting the tasks' parameters running on C j , all the tasks are executed without missing their deadlines. Therefore, the real-time constraint can be satisfied. As described in subsection II-C, if the task's period is changed implicitly, then the message's period will be changed since T M i,j =T i . For that, the periods of messages that are associated to the adapted tasks will be changed.

C. Solution B: WCETs' Modification under Real-Time Constraint

In this part, as an alternative solution, we adjust the WCETs of tasks to re-obtain the feasibility of C j . We use the same technique presented in Solution A to calculate the new WCETs of tasks that run on core C j (j ∈ [1..p]). First of all, we seek the value P k W 1,j in order to group the tasks according to their WCETs. We formalize it by

               M in M i=1 (P k W 1,j -(W i mod P k W 1,j )) mod P k W 1,j * H i,j s.t. P k W 1,j ≥ M in(W i ), ∀ i ∈ [1..M ] | H i,j = 1
We construct the packs of tasks as follows: P ack W x,j includes the tasks having a WCET in the range [(x -1)

* P k W 1,j + 1 ; x * P k W 1,j ].
The objective is the same to satisfy the real time constraint

M i=1 W i T i * H i,j ≤ 1.
Since the WCETs W i are multiple of the same value P k W 1,j , we get

τi∈P ack W 1,j P k W 1,j T i + ... + τi∈P ack W x,j x.P k W 1,j T i ≤ 1 thus, P k W 1,j *   τi∈P ack W 1,j 1 T i + ... + τi∈P ack W x,j x T i   ≤ 1 therefore, P k W 1,j = 1 τi∈P ack W 1,j 1 Ti + ... + τi∈P ack W x,j
x Ti [START_REF] Cecilio | Architecture for uniform (re) configuration and processing over embedded sensor and actuator networks[END_REF] where P k W 1,j is the new WCET affected to the tasks of the first pack P ack W 1,j . τ i ∈ P ack W x,j if and only if

(x -1) * P k W 1,j + 1 ≤ W i ≤ x * P k W 1,j
After the modification of the WCETs, the processor utilization of C j is reduced and can satisfy the real-time scheduling.

D. Solution C: Periods' Modification under Energy Constraint

Let us assume that the core C high violates the energy constraint after the RE-CON F scenario. This solution proposes to extend the periods of tasks running on C high (high ∈ [1..p]) in order to ensure that the current power should be less than the critical one. The energy constraint is P T otal ≤ P Limit and Eq. 10 is [START_REF] Li | QoS-aware scheduling of servicesoriented internet of things[END_REF] where P k T 1,high is the new period affected to the tasks of P ack T 1,high and the other packs are multiple. After adapting the task' parameters, the processor utilization of C high is decreased. Therefore, the system can run correctly until the next recharge. We note that the period T M i,j of message M i,j is equal to the period T i of sending task τ i . Since this solution proposes to adapt the tasks' periods, thus the periods of messages associated to the modified tasks are changed implicitly.

P P roc + P Com ≤ P Limit i.e
W i P k T 1,high + ... + τi∈P ack T x,high W i x.P k T 1,high ≤ α thus, 1 P k T 1,high *   τi∈P ack T 1,high W i + ... + τi∈P ack T x,high W i x   ≤ α finally, P k T 1,high =     τi∈P ack T 1,high W i + ... + τi∈P ack T x,high Wi x α     (

E. Solution D: Modification of Message's Period under Communication Constraint

We are interested in this part in the communication feasibility. After the RE-CON F scenario, a message are added to the NoC whenever two related added dependent tasks are assigned to different cores.

If U Com (C k , C l ) (∀ k, l ∈ [1.
.p]) is greater than 1, then the communication between the cores is not feasible. We propose to extend the periods of messages exchanged between the tasks running on cores C k and C l . In order to satisfy the communication constraint, we assign each message to P ack T M x,k,l according to its period. We formalize

this problem by ∀ k, l ∈ [1..p] | U Com (C k , C l ) > 1                        M in M i=1 M j=1 (P k T M 1,k,l -(T M i,j mod P k T M 1,k,l )) mod P k T M 1,k,l * H i,k * H i,l s.t. P k T M 1,k,l ≥ M in(T M i,j ), ∀ i, j ∈ [1..M ]
Once P k T M 1,k,l is calculated, the packs of messages are processed such that P ack T M

x,k,l includes the messages that have a period in the range

[(x -1) * P k T M x,k,l + 1 ; x * P k T M 1,k,l ], x ∈ N + .
To satisfy the communication constraint, it is necessary that

M i=1 M j=1 W M i,j T M i,j * H i,k * H j,l ≤ 1.
Since the periods T M i,j are now multiple of the same value

P k T M 1,k,l , we get Mi,j ∈P ack T M 1,k,l W M i,j P k T M 1,k,l + ... + Mi,j ∈P ack T M x,k,l W M i,j x.P k T M 1,k,l ≤ 1
Since the periods are integer, then,

P k T M 1,k,l =     Mi,j ∈P ack T M 1,k,l W M i,j + ... + Mi,j ∈P ack T M x,k,l W M i,j x     (16)
where P k T M 1,k,l is the new period affected to the messages of the first pack P ack T M 1,k,l , x * P k T M x,k,l to the messages of x th pack P ack T M

x,k,l . After adapting the parameters of messages running on the communication bus between cores C k and C l , U Com (C k , C l ) will be smaller than 1. Therefore, the communication constraint can be satisfied. Since the periods of messages are modified, it is necessary to adapt the periods of their sending tasks.

F. Solution E: Removal of Tasks

This is the last chance solution proposed by the strategy described in Fig. 1. It allows the removal of tasks in order to cut-down the processor utilization after the RE-CON F scenario. By defining for each task τ i an importance factor I i , the strategy suggests removing tasks that have the higher I i because their removal can be useful for a low power reconfiguration of the system.

G. Deterministic Strategy of Reconfigurable Platforms

In this section, we present the operating mode to allow a feasible multi-core system RT Sys. We therefore need to develop a tool to find the optimal mapping of the tasks on cores in order to optimize the energy consumption while meeting temporal and communication constraints. Communicating tasks are placed as close as possible. This tool, named OptimalM appingT asks (Fig. 2), solves the problem formalized by RE in sub-section III-A. It provides a graph that presents the energy cost for each possible placement and it chooses just the possibilities that have a minimal cost of energy consumption and that occupy a minimum number of cores.

After any reconfiguration scenario, OptimalM appingT asks places all the tasks on cores. After this step, the real-time, communication and/or energy constraints can be violated. In this section, the defined strategy proposes a deterministic choice between the different solutions (A, B, C, D or E). It starts first by modifying the periods of tasks and the exchanged messages until reaching their specific allowed maximal periods (Solution A or C). If RT Sys is still unfeasible, then it decreases the WCETs of tasks (Solution B). In the worst case, the strategy applies the last solution that removes some tasks according to an importance functional factor that we name I i (Solution E). Algorithm 1 explains these steps and uses three functions: (i) Feasible(RTSys) that returns true if the system RT Sys is feasible, (ii) Max(Solution X, Solution Y) selects the solution that has the highest value P k T 1,j from solutions X and Y , and (iii) Apply(Solution X) which applies the solution X.

all the tasks, we suppose that we have 5 cores (p = 5) and the cost matrix is

Cost = C 1 C 2 C 3 C 4 C 5 ↓ ↓ ↓ ↓ ↓       0 1 2 3 4 1 0 1 2 3 2 1 0 1 2 3 2 1 0 1 4 3 2 1 0       ← C 1 ← C 2 ← C 3 ← C 4 ← C 5
The objective is to minimize the traffic cost on the NoC under real-time, energy and communication constraints. We suppose that the energy available in the battery is 450 EU (Energy Units). Fig. 2 presents the optimal cost of tasks' placement and shows the corresponding mapping. 1 Fig. 3 represents the different possibilities to map all the tasks. Each blue circle indicates a possible mapping of tasks and has a corresponding value of energy consumption. We have in this case 78125 possibilities for mapping the given tasks to cores. We notice that OptimalM appingT asks provides many possibilities which consume energy less than 450 EU . According to the result produced by this tool, 220 EU is the minimal energy consumption which respects the energy constraint (Fig. 3). We note that there is 93 mapping possibilities that lead to this minimal energy consumption. Therefore, the chosen mapping is one of the possibilities that has the minimal energy consumption (220 EU in Fig. 3).

Once all the tasks are placed on cores, Algorithm. 1 that represents the proposed strategy must check the rest of constraints. If one or more of them are violated, then it must apply the suitable solutions for each core. It proposes to increase the periods or to modify the execution time of tasks or to remove some of them.

Since the proposed solutions can be applied core per core and in order to compare the current paper's contribution to Wang's approach [START_REF] Wang | Dynamic low-power reconfiguration of real-time systems with periodic and probabilistic tasks[END_REF], we suppose that the tasks in Figs. 7 and 8 in [START_REF] Wang | Dynamic low-power reconfiguration of real-time systems with periodic and probabilistic tasks[END_REF] are executed by the five considered cores. The objective is to apply the proposed solutions and the solutions reported in [START_REF] Wang | Dynamic low-power reconfiguration of real-time systems with periodic and probabilistic tasks[END_REF] to the same case study.

After the implementation of these tasks on C 1 , the real-time constraint is not satisfied because the processor utilization is greater than 1 (U C1 = 1.02). To re-obtain the core feasibility, we explore (i) the heuristic proposed in solution A, (ii) the optimal solution formalized by P b1, and (iii) the solution presented in [START_REF] Wang | Dynamic low-power reconfiguration of real-time systems with periodic and probabilistic tasks[END_REF]. These solutions deal with the modification of temporal parameters of the processed tasks where each modification has a cost in terms of delay. The cost of each modification on a task is the difference between the parameter's value before and after a reconfiguration. After the modification of the periods (Solution A), the processor utilization is decreased and can satisfy the real-time scheduling. After the execution of these three solutions, the processor utilization is reduced to 0.997 and satisfies the real-time scheduling. Fig. 4 compares the performance of the proposed solution A (bars in orange) with the approach reported in [START_REF] Wang | Dynamic low-power reconfiguration of real-time systems with periodic and probabilistic tasks[END_REF] (bars in grey) and the optimal solution generated by CPLEX (bars in blue). Using the same colors, Fig. 5 compares the performance of the proposed solution B with the approach reported in [START_REF] Wang | Dynamic low-power reconfiguration of real-time systems with periodic and probabilistic tasks[END_REF]. We note that the total cost (Fig. 6) of the proposed strategy is equal to 3275 ms, the total cost by using the approach proposed by Wang et al. in [START_REF] Wang | Dynamic low-power reconfiguration of real-time systems with periodic and probabilistic tasks[END_REF] is equal to 24550 ms and the total cost by applying the optimal solution is 2491 ms. In other words, the proposed heuristic introduces a delay of 1.3 times ( 3275 2491 ) the delay introduced by the optimal solution whereas Wang's method introduces 9.8 times ( 24550 2491 ) the delay of the optimal solution.

In order to evaluate the performance of the proposed strategy, a second tool has been developed and published in [START_REF] Gammoudi | Reconf-Pack: A Simulator for Reconfigurable Battery-Powered Real-Time Systems[END_REF] to generate random systems and reconfiguration scenarios. We compare the proposed solution with the approach proposed in Wang et al. [START_REF] Wang | Dynamic low-power reconfiguration of real-time systems with periodic and probabilistic tasks[END_REF] using 50 randomly generated systems. After observing the results, it is noticed that the delay in 88% of randomly generated tests is reduced thanks to the proposed solution. Moreover, the proposed strategy lowers the average delay to keep the system feasible and up until next recharge. This delay is only 55% of that resulting from Wang's strategy [START_REF] Wang | Dynamic low-power reconfiguration of real-time systems with periodic and probabilistic tasks[END_REF].

VI. PERFORMANCE EVALUATION

To show the effectiveness of the proposed strategy, we propose to compare it with two EDF-based algorithms: Bhardwaj et al. [START_REF] Bhardwaj | An Effective Load Balancing Task Allocation Algorithm using Task Clustering[END_REF] and Govil et al. [START_REF] Govil | A smart algorithm for dynamic task allocation for distributed processing environment[END_REF]. In order to provide a more convincing evaluation, we apply the three approaches to the same case study presented in [START_REF] Bhardwaj | An Effective Load Balancing Task Allocation Algorithm using Task Clustering[END_REF]. The objective is to map all the tasks to the different cores and calculate the total communication cost of each algorithm. Let us indicate that the cost of the cores connections matrix is shown as follows:

Cost = C 1 C 2 • • • C p ↓ ↓ • • • ↓      0 1 • • • p -1 1 0 • • • p -2 . . . . . . . . . . . . p -1 • • • 1 0      ← C 1 ← C 2 . . . ← C p
For several sets of input data (N , p), the comparison is shown in a tabular form as well as in a graphical form.

A. Comparison of algorithms by increasing the number of tasks

The comparison is performed using a constant number of cores (4 cores) and an increasing number of tasks (Tab. II). In Fig. 7, the orange curve represents the communication cost by applying the algorithm proposed by Govil et al. [START_REF] Govil | A smart algorithm for dynamic task allocation for distributed processing environment[END_REF] and and the blue curve indicates the communication cost after applying the algorithm proposed by Bhardwaj et al. [START_REF] Bhardwaj | An Effective Load Balancing Task Allocation Algorithm using Task Clustering[END_REF]. The cost of communication, when we apply the proposed strategy, is represented by the grey curve. The experimental results show that the proposed algorithm offers a gain estimated in average to 10.5% ( 6035-5409 6035 * 100) of communication cost compared with [START_REF] Govil | A smart algorithm for dynamic task allocation for distributed processing environment[END_REF] and 6.5% of communication cost compared with [START_REF] Bhardwaj | An Effective Load Balancing Task Allocation Algorithm using Task Clustering[END_REF].

B. Comparison of algorithms by increasing the number of cores

In this subsection, the comparison is done with a constant number of tasks (50 tasks) and with an increasing number of cores (Tab. III). By measuring the gain obtained in terms of communication costs, we note that the proposed algorithm offers a little more than 5% ( 8104-7685 8104 * 100) of gain compared with the algorithm reported in [START_REF] Govil | A smart algorithm for dynamic task allocation for distributed processing environment[END_REF] and 2% ( 7805-7685 7805 * 100) of gain compared with the second one reported in [START_REF] Bhardwaj | An Effective Load Balancing Task Allocation Algorithm using Task Clustering[END_REF]. Fig. 8 shows the different communication costs illustrated by Tab. III.

C. Comparison of algorithms in terms of task rejection rate

The application of the three algorithms of task mapping may drive to the rejection of some of them for particular reasons such as the violation of i) real-time constraints, ii) communication constraint, and/or (iii) energy constraints. The objective of this subsection is to calculate the task rejection rate of each algorithm. In order to generalize the performance evaluation of these algorithms, we propose to randomly generate 1000 tasks by using the developed simulator T ask -Generator presented in a previous work reported in [START_REF] Gammoudi | Reconf-Pack: A Simulator for Reconfigurable Battery-Powered Real-Time Systems[END_REF] and calculate the task rejection rate when the number of cores is taken in an increasing order. Let us indicate that we configure initially the simulator as follows (Tab. IV): Fig. 9 shows the task rejection rate with the number of cores. After observing the results, it is noticed that the proposed algorithm offers a gain estimated in average to 62% of task rejection rate compared with [START_REF] Govil | A smart algorithm for dynamic task allocation for distributed processing environment[END_REF] and 59% compared with [START_REF] Bhardwaj | An Effective Load Balancing Task Allocation Algorithm using Task Clustering[END_REF].

To further evaluate the proposed algorithm, we use the T ask -Generator simulator and calculate the task rejection rate by increasing the number of tasks and fixing the number of cores equal to four. The idea is to evaluate the proposed algorithm with different loads. Fig. 10 shows that if the number of tasks is less than or equal to 402, then no task will be rejected. Nevertheless, beyond 402 tasks the task rejection rate will be increased. From 1500 tasks, the system rejects almost 48% of tasks. Since the rejection rate is dependent on the tasks' parameters, then it is varied for each set of tasks which are randomly generated. That's why Fig. 10 presents for each task's number, an interval of rejection rate. Concerning the evaluation of the elapsed execution time of the proposed solution, we estimate it when i) the number of tasks is increased from 50 to 500, and ii) the number of cores is fixed to four. Fig. 11 presents the elapsed time to map and construct the packs of tasks. The used processor is an Intel Core 2 Duo (1.3GHz) with 4Go of RAM. Thanks to the grouping of tasks in packs, the placement becomes easier since the tasks of the pack can be mapped to the same core. Consequently, the mapping time of tasks is minimized and acceptable.

VII. DISCUSSION Low-power scheduling of RT Sys after reconfiguration scenarios is the most significant contribution of this study. By dynamically adjusting the tasks parameters, the published research strategies [START_REF] Gammoudi | Real-Time Scheduling of Reconfigurable Battery-Powered Multi-Core Platforms[END_REF], [START_REF] Wang | Dynamic low-power reconfiguration of real-time systems with periodic and probabilistic tasks[END_REF], [START_REF] Yokoyama | Static task scheduling algorithms based on greedy heuristics for battery-powered DVS systems[END_REF] can reduce the power consumption of RT Sys to keep the energy until the next recharge. However, they fail to reduce the power consumption and satisfy the feasibility of an RT Sys with a highpower caused by task addition scenarios. The contributions of this research are summarized as follows: 1) Proposition of the OptimalM appingT asks tool which seeks the optimal placement of tasks on cores after any reconfiguration scenario in order to minimize the traffic on the NoC by trying to place the dependent tasks as close as possible, 2) Proposition of scheduling solutions grouped in a strategy to re-obtain the feasibility of RT Sys after the tasks' mapping by satisfying the real-time, communication and energy constraints.

VIII. CONCLUSION

In this paper, we first presented a general methodology for modelling the power consumption of periodic tasks on rechargeable homogeneous multi-core architectures. Being reconfigurable, they can violate some constraints such as realtime and/or energy and/or communication. To guarantee that between two recharges the energy is sufficient to execute all the tasks without missing their deadlines, we propose four solutions to modify some parameters of tasks and messages in order to decrease the processor utilization and to re-obtain the system feasibility. If the system is still unfeasible, then we propose a fifth solution that removes some tasks according to their importance factor I i . All these heuristics are manipulated by a new deterministic strategy. This strategy is based on a pack classification such that after each reconfiguration scenario, suitable and acceptable modifications are performed on the parameters of the packs and their related tasks. We plan in the future work to implement the proposed strategy in an RTOS that will be assessed by considering real case studies. In this paper, the platform is considered homogeneous. Nevertheless the consideration of an extended strategy for battery-powered heterogeneous platforms is necessary since these are found in diverse applications, such that distributed wireless sensor nodes, telecommunications, etc.

Fig. 1 .

 1 Fig. 1. Steps of strategy.

Fig. 3 .

 3 Fig. 3. Energy consumption of all mapping possibilities.

Fig. 4 .

 4 Fig. 4. Modification's cost of periods T i (Solution A).

Fig. 5 .

 5 Fig. 5. Modification's cost of WCETs W i (Solution B).

Fig. 6 .

 6 Fig. 6. Cost of parameters' modification.

Fig. 7 .

 7 Fig. 7. Communication cost of our strategy when the tasks are in an increasing order and the number of cores is four.

Fig. 8 .

 8 Fig. 8. Communication cost of our strategy when the cores are in an increasing order and the number of tasks is 50.

Fig. 9 .

 9 Fig. 9. Evolution of the task rejection rate when the number of cores increases.

Fig. 10 .

 10 Fig. 10. Task rejection rate when the tasks are in an increasing order and the number of cores is fixed to four.

Fig. 11 .

 11 Fig. 11. Elapsed time to map and group the tasks on packs.

  ., C high ≤ P Limit -P Com -

	According to Eq. 7
			p-1
	k * U 2			P Cj
			j=1
	then,
	U C high ≤	P Limit -P Com -k	p-1 j=1 P Cj
	We suppose that α =	P Limit -P Com -p-1 j=1 P C j k
	then,
	M i=1	W i T i	* H i,high ≤ α
	P ack T x,high is constructed to include the tasks that have a
	period in the range [(x -1) * P k T 1,high + 1 ; x * P k T 1,high ],
	i.e.,
	τi∈P ack T 1,high
	p
	P Cj ≤ P Limit -P Com
	j=1
	p-1
	P C high +
	p-1
	P Cj
	j=1

j=1

P Cj ≤ P Limit -P Com thus,

P C high ≤ P Limit -P Com -

TABLE II COMMUNICATION

 II 'S COST OF THE THREE ALGORITHMS WHEN THE TASKS ARE IN AN INCREASING ORDER AND THE NUMBER OF CORES IS FOUR.

	Tasks N	Cores p	Algo. [33] Algo. [34]	Our Algo.
	6	4	101	106	90
	7	4	135	140	112
	8	4	169	188	135
	9	4	224	243	201
	10	4	251	259	222
	11	4	319	333	290
	12	4	365	378	345
	13	4	401	435	375
	14	4	465	480	450
	15	4	502	518	472
	16	4	522	533	500
	17	4	545	565	523
	18	4	576	588	552
	19	4	591	617	550
	20	4	620	652	592
	Total		5786	6035	5409

TABLE III COMMUNICATION

 III COST OF THE THREE ALGORITHMS WHEN THE CORES ARE IN AN INCREASING ORDER AND THE NUMBER OF TASKS IS 50.

	Cores p	Tasks N	Algo. [33] Algo. [34]	Our Algo.
	4	50	620	645	608
	5	50	640	672	630
	6	50	640	669	625
	7	50	650	678	638
	8	50	649	675	636
	9	50	647	672	635
	10	50	655	682	646
	11	50	666	688	658
	12	50	665	685	659
	13	50	660	685	655
	14	50	658	678	650
	15	50	655	675	645
	Total		7805	8104	7685

TABLE IV UNIFORM

 IV DISTRIBUTION OF TASK'S PARAMETERS.

	Task's parameter	Min	Max
	WCET W	1	10
	Period T	200	1000
	Period max Tmax	T	2*T

V. IMPLEMENTATION AND EXPERIMENTAL STUDY

The goal of this section is to simulate the proposed solutions by following the presented Algorithm. 1.

We suppose that we have a set Π of periodic tasks that will be placed on a set of different cores. We use the same case study Figs. 7 and8 reported in [START_REF] Wang | Dynamic low-power reconfiguration of real-time systems with periodic and probabilistic tasks[END_REF] as a subset in Π where all the tasks are considered independent. In order to evaluate the proposed mapping tool OptimalM appingT asks, we add some dependency constraints between these tasks (Tab. I). We suppose that the multi-core platform uses the one-dimensional network to exchange all messages between the p cores where the total length of the bus is split into p -1 segments. To map


Karim Hammou

Rap en français et racialisation

P. Simon : La question de la racialisation dans le rap peut être abordée de deux points de vue complémentaire : celui des identités et propriétés ethno-raciales des rappeurs (revendiquées ou attribuées), celui du contenu des paroles et des prises de position ou attitudes des artistes et de leur entourage. Est-ce que tu constates une évolution vers une plus grande prégnance des motifs racialisés sur ces deux dimensions dans le rap français depuis les années 1990 ? K. Hammou : Si, par racialisation, on renvoie à des pratiques et représentations qui manifestent la prégnance de catégories raciales d'interprétation, les premiers paramètres à intégrer à l'analyse renvoient à la société française dans son ensemble. Deux processus de racialisation ont un rôle fondateur dans l'histoire du rap en France. Le premier est celui des industries musicales et du divertissement. Lorsque le rap apparaît en France comme forme musicale et chorégraphique identifiée, à partir du début des années 1980, il s'inscrit dans le prolongement de circulations culturelles atlantiques dans lesquelles la ligne de couleur distinguant du « noir » et du « blanc » (parmi les artistes, les genres musicaux, les danses…) a un rôle central. Le rap naît comme un développement des musiques funk, et à ce titre est l'héritier de l'imaginaire mais aussi des réseaux de diffusion associés aux musiques africaines-américaines en France. Il est en particulier tributaire de la racialisation des lieux de danse qui prévaut dans les années 1970-1980, et qui se répercute aussi bien dans la sélection musicale des DJs que dans la ségrégation raciste des publics -les non blancs se voyant régulièrement refoulé de la majorité des boîtes de nuit, des lieux de danse pour les « réfusés » se multiplient. Il est aussi dépendant des logiques de racialisation qui dominent la critique musicale, répétant des clichés sur la musique « noire » (et ses musiciens) 1 , ainsi que le secteur de la production discographique, qui n'exploite les musiques associées aux minorités raciales que dans une logique de niche ou d'exotisme. Le deuxième niveau auquel la racialisation de la société française joue, c'est dans la définition publique du rap en français comme genre musical au début des années 1990. A cette période, le rap est défini à la lumière du paquet interprétatif du « problème des banlieues », un cadrage médiatique qui en fait une musique des Autres, dont l'altérité est indissociablement sociale et raciale. Les artistes de rap héritent de ce cadre racialisé et doivent composer avec lui dans de multiples interactions professionnelles. La première tactique dont ils usent, et la principale encore à ce jour, consiste à contester explicitement le racisme à différentes époques et dans différents contextes. Dès 1989, le rappeur EJM thématise une violence policière en ce qu'elle peut être négrophobe dans « Nous vivons tous ». Peu après, le groupe IAM, avec « Tam-tam de l'Afrique » ou la rappeuse Saliha avec « Enfants du ghetto » dénoncent respectivement l'esclavage transatlantique et l'apartheid en Afrique du sud. La seconde tactique, qui intervient dès le milieu des années 1990, vise à opposer des autodéfinitions raciales aux assignations racialisantes majoritaires puis, de façon croissante, à jouer avec ces autodéfinitions et ces assignations, à les troubler, à des fins aussi bien politiques qu'esthétiques et marchandes. Ce processus est d'abord le fait d'artistes noirs comme les

membres des groupes de rap Ministère AMER ou Tout Simplement Noir, puis un peu plus tard de la part d'artistes d'origine maghrébine comme les rappeurs Yazid ou Hamé. La posture dominante, pourrait-on dire, passe d'un multiculturalisme abstrait à l'affirmation d'un point de vue situé dans les rapports sociaux de race. Le morceau « Blanc et noir » de NTM est emblématique de la première posture, associant des énumérations de couleurs de peau abstraites (« noir et blanc, blanc et jaune, jaune et rouge, rouge ou beur ») à des gages donnés à « l'autre côté », renvoyant dos à dos « les » racismes (« Farakhan ou Le Pen / Même combat pour la haine »). Du côté du point de vue situé, on peut mentionner « Damnés » de Ministère AMER, qui associe jeux sur les sonorités d'épithètes raciaux (« nègre aigre de la pègre »), critique du racisme systémique, de l'héritage colonial (« pas de cadeaux la ville de Bordeaux grosso modo enrichit sur notre dos ») et imaginaire ludique du bandit qui préfigure le « marketing de la marge » qui s'épanouira quelques années plus tard2 . Mais c'est surtout au tournant des années 2000 que ces modes d'autodéfinition racialisés se banalisent dans le rap français, notamment dans le sillage de labels comme Din Record ou Neochrome. Une autre évolution, que j'ai plus particulièrement étudiée, est la façon dont les rappeurs mettent en scène la mémoire de l'esclavage et de la colonisation3 . On observe au milieu des années 1990 une évolution qui fait véritablement entrer la majeure partie de la scène rap, lorsqu'elle traite de ces questions, dans une approche que l'on peut qualifier de « postcoloniale » en ce qu'elle suggère la continuité entre les rapports de pouvoir coloniaux et les rapports de pouvoir contemporains4 . Or ces legs historiques sont éminemment racialisésils sont solidaires d'une conception raciste situant les blancs au sommet d'une hiérarchie des êtres humains.

Que ce soit aux US ou en France, la crédibilité des artistes repose sur leur profil social personnel, en particulier le fait qu'ils viennent de milieu populaire/banlieue/grands ensembles et éventuellement un passage par la délinquance (street credibility) : dans quelle mesure leur origine ou couleur de peau participe de cette crédibilité ? Pour le dire plus directement, les blancs partent-ils avec un handicap pour faire du rap ? Leur position située construit-elle ce qu'ils peuvent dire ou chanter ? Reproche-t-on aux blancs qui font du rap de se livrer à de l'appropriation culturelle, c'est-à-dire de développer un style musical lié aux minorités ethno-raciales sans en être issus ?

La construction de l'authenticité, qu'elle serve de capital dans le monde social du rap français ou de signal marchand auprès des intermédiaires du marché musical et des publics, n'opère pas d'abord sur un critère racial en France. Elle renvoie effectivement à cette assignation du rap à la banlieue, et à ses reformulations au sein même du monde du rap dans les années 1990 et 2000, qui ont érigé « la rue » en symbolique honorifique de la profession de rappeur. Certes, l'imaginaire de la banlieue et de la rue n'est pas neutre sur le plan de la race (pas plus qu'il ne l'est d'ailleurs du point de vue du sexe). La figure de référence est celle de l'homme racisé, et sous ce rapport, être blanc a pu entraîner des a priori défavorables à certains artistes -lorsqu'il était question d'imposer leur nom dans le milieu underground du rap, ou lorsqu'il s'agissait de convaincre une major du disque qu'ils étaient les artistes les mieux placés pour être la prochaine star du rap.

Néanmoins, on ne peut pas parler de ces a priori comme d'un handicap. D'abord, ils n'opèrent que de façon circonscrite et ponctuelle -avant, notamment, la manifestation dans le milieu underground de performances rappées de qualité, ou avant la démonstration auprès des majors de la capacité d'un artiste à rencontrer un large succès commercial. En l'occurrence, la politique des majors lorsqu'elles avaient encore un rôle de sélection, a plus souvent dévalorisé les artistes non blancs, y compris dans le rap, que l'inverse. Enfin, il faut remettre ces a priori en perspective, en les resituant dans un système raciste qui opère à tous les niveaux pour dévaloriser les artistes non-blancs -ne serait-ce, en premier lieu, qu'en déniant le statut d'oeuvre artistique à leurs morceaux. Autrement dit, s'ils affrontent des préjugés occasionnels, ceux-ci pèsent peu face au poids du privilège blanc, lié à un racisme systémique qui joue dans les carrières de rappeurs (dans le rapport aux médias généralistes notamment, mais aussi aux tourneurs et programmateurs de festivals) aussi bien qu'en amont (dans la formation scolaire, dans les opportunités professionnelles extra artistique, etc.) et qu'en aval (dans les reconversions professionnelles, la patrimonialisation, etc.). Pour ce qui est de la thématique de « l'appropriation culturelle », débattue depuis les années 1980 en Amérique du Nord, elle n'émerge que timidement dans le débat public français autour du rap depuis la fin des années 2000. Il y a tout d'abord, en 2006, le début de mobilisation d'un collectif intitulé « Les Motowniens » critiquant le rachat par Universal de la marque Motown, et sa déclinaison en France sous la forme d'un label dirigé par la rappeuse Diam's, jugée trop inexpérimentée pour gérer un fleuron du « patrimoine de la culture noire ». Le collectif lance une pétition signée par plusieurs personnalités des arts et du spectacle. Le rappeur Booba, à l'époque, fait écho à cette mobilisation. Dans les débats, la blanchité de Diam's est aussi en question. Mais le collectif est rapidement caricaturé et discrédité, notamment par la presse spécialisée et généraliste. Le second débat public sur la question se joue dix ans plus tard, autour des artistes nominés dans la catégorie « musiques urbaines » aux Victoires de la musique 2018. La journaliste Rokhaya Diallo, notamment, cadre le débat en termes de discriminations raciales. La couverture médiatique accordée à cette question par la suite est directement informée par un débat croissant, dans le rap états-uniens, sur les performances d'artistes blancs formulé en termes d'« appropriation culturelle 5 », mais aussi par la logique de réseaux sociaux comme twitter, qui rend accessible un plus grand nombre de points de vue, et accorde un privilège à ceux qui suscitent le plus de réactions, qu'elles soient de soutien ou d'hostilité. L'argument de l'appropriation culturelle s'appuie sur une analogie entre culture collective et propriété privée. De la même façon que des personnes possèdent des biens, des groupes possèderaient une culture. Et si s'approprier les biens privés d'autrui est un vol, alors s'approprier « la » culture d'un autre groupe serait également condamnable. L'idée d'appropriation culturelle contribue ainsi à une politisation de la culture. Elle rejoint les critiques de l'exotisation des pratiques minoritaires, elle met en lumière les profits symboliques et matériels inégaux que différents groupes sociaux sont en mesure de tirer d'activités similaires, et interpelle sur les biais de sélection qu'un système de domination impose. Mais l'analogie qui fait la force de l'argument de l'appropriation culturelle, nourrit aussi ses limites. Elle repose sur une conception de la propriété privée et de l'individu qui se sont imposés avec le capitalisme moderne, et les étend à des être collectifs -des groupes pensés sur le modèle du « nationalisme culturel ». Or les groupes sociaux et leurs traits culturels ne sont pas des ensemble stables, homogènes, et clos sur eux-mêmes 6 . La critique de l'appropriation culturelle court ainsi le risque d'essentialiser les cultures qu'elle prétend défendre. A l'inverse, l'argument d'ordinaire opposé à l'idée d'appropriation culturelle revendique le principe d'une libre disponibilité des symboles et répertoires culturels qui est en réalité illusoire pour la plupart des gens car les rapports de pouvoir restreignent juridiquement et pratiquement les circulations culturelles. Pour sortir de cette double impasse intellectuelle, on peut penser les usages et emprunts culturels en les examinant dans des situations concrètes et les rapports de pouvoir effectifs qui y pèsent. Derrière la nouvelle question de « l'appropriation culturelle » du rap, il y a une histoire bien plus ancienne de contestations des formes de marchandisation et de visibilité du genre par des acteurs étiquetés comme « étrangers au rap », avec toutes les luttes de définition qu'une telle étiquette suppose. Ces débats commencent dès les années 1980, avec la réception mitigée de l'émission « H.I.P. H.O.P. », dont l'effet de mode, aux yeux de certains, associe une « image clownesque 7 » à la culture hip-hop naissante en France. Et il est logique qu'ils se prolongent aujourd'hui -en se transformant avec les enjeux économiques et sociaux nouveaux dans lesquels le rap comme genre musical est pris.

Les groupes de rap français sont souvent multi-ethniques, que ce soit mis en scène ou une simple donnée de leur composition. Est-ce qu'il existe malgré tout des styles différents entre origines, et des rivalités jouant sur le registre ethno-racial comme entre afro-américains et hispanics aux Etats-Unis ? coupé-décalé, genre musical ivoirien populaire dans l'ensemble de l'Afrique de l'ouest depuis les années 2000, et initie ce que l'on appelle depuis l'afrotrap.

Les rappels à l'ordre de rappeurs sont fréquents, mais plusieurs affaires ont défrayé la chronique récemment. On pense à l'annulation de la programmation de Black M à Verdun en mai 2016, la campagne sur les réseaux sociaux en juin 2018 pour l'annulation du concert de Medine au Bataclan ou auparavant la plainte de l'AGRIF contre Saïdou et Said Bouamama auteurs du livre-disque "Nique la France". Que penser de ces actions de censure, de plaintes en diffamation (essentiellement venant de la police contre Ministère Amer, NTM, La Rumeur) ou "d'atteinte à l'Etat et aux valeurs républicaines" dans le cas de Sniper ? S'inscrivent-elles dans l'ordinaire des réactions d'un ordre établi face à la licence artistique et à son potentiel de critique et de transformation sociale, ou ces réactions relèvent d'une autre dynamique plus strictement liées à un nativisme racialisé ?

Cette question nous ramène aux processus de racialisation transversaux à la société française, et à la façon dont le rap en général et certains artistes de rap en particulier, volontairement ou non, interrogent les rapports sociaux de race. Cependant, toutes ces affaires ne sont pas similaires. Du côté de Ministère AMER (1995), de NTM (1996), de La Rumeur (2002-2010), c'est d'abord une question d'autorité de la police et, au-delà parfois, de l'Etat qui est en jeu. Dans le cas des affaires Saïdou et Saïd Bouamma (depuis 2012), Black M, Médine, c'est bien au contraire l'extrême droite qui initie les affaires, avec des motifs et un imaginaire différents. Dans le cas de Saïdou et de la chanson « Nique la France », la dénonciation porte sur le « racisme antiblanc ». Dans le cas de Black M, contesté pour sa participation aux événements culturels en marge de la commémoration de la bataille de Verdun, l'extrême droite pointe une trahison de l'histoire de France. Dans le troisième cas, Médine est décrit en apologue du terrorisme, sur fond d'amalgames islamophobes. L'agenda politique derrière ces mobilisations est cependant convergent : traiter ces rappeurs en étranger à la communauté civique, voire en ennemi intérieur, et proscrire autant que possible leur participation aux espaces publics médiatiques. L'effet direct de cet agenda, c'est de renforcer et de légitimer une citoyenneté de seconde zone pour ces artistes et, au-delà, ceux dont ils sont devenus l'emblème, la jeunesse non blanche des quartiers populaires. L'affaire Sniper (2002Sniper ( -2007) ) se trouve à l'intersection de ces deux logiques. Elle commence, comme pour Black M et Médine, par un travail de lobbying de l'extrême droite dont le premier objectif est de faire interdire des concerts du groupes. Ce travail de lobbying intervient à une époque où les réseaux sociaux n'existent pas, et restent donc relativement confidentiel -bien que non dénuée d'effets. C'est la médiation politique, réalisée par Nadine Morano et Nicolas Sarkozy, qui donne à ce travail une visibilité médiatique et entraîne un débat public d'ampleur nationale. Elle se prolonge par des attaques en justice, qui abandonnent le motif du racisme et de l'antisémitisme (qui avaient été mobilisés par Sarkozy) pour se concentrer sur l'accusation d'« incitation à blesser et tuer les fonctionnaires de police et représentants de l'Etat » -délit dont le groupe sera finalement relaxé. Depuis l'affaire Sniper, l'articulation entre les arguments de défense de l'Etat ou de ses institutions (police en tête) et la dénonciation d'un ennemi intérieur racialisé est devenue routinière. Elle s'appuie sur un syllogisme opérant une assignation racialisante : critiquer la France ou les institutions françaises, ce serait critiquer le peuple français. Critiquer le peuple français, ce serait être raciste. Or la prémisse majeure de ce syllogisme, le plus souvent passée sous silence, est raciste : le peuple français serait un groupe ethnique homogène défini par sa blanchité. Cette définition raciste de l'identité nationale, au coeur de l'agenda politique de l'extrême droite, est depuis le milieu des années 2000 présente bien plus largement dans l'imaginaire politique et les débats publics. Elle explique une large part de la forme que prennent les dénonciations publiques de rappeurs et de chansons de rap.

Bonzom Marie-Christine, 1991, « Le Noir, la Femme et le Sudiste. Une mythologie du rock sous presse ». Vibrations.Musiques, médias, société, vol. 1 n°1,

Hammou Karim, 2016, « Mainstreaming French rap music. Commodification and artistic legitimation of othered cultural goods ». Poetics vol.59, p.67-81.

Karim Hammou, 2018, « Les traumatismes (post)coloniaux dans le rap en français : mises en musique d'une citoyenneté critique » in S. Segler-Meßner et I. von Treskow (éd.), Traumatisme et mémoire culturelle. De Gruyter (à paraître).

Sonnette Marie, 2014, « Des mises en scène du "nous" contre le "eux" dans le rap français. De la critique de la domination postcoloniale à une possible critique de la domination de classe ». Sociologie de l'art vol. 23-24, p.153-177.

Djavadzadeh Keivan, 2016, « Les masques noirs des pop stars blanches. Miley Cyrus et les politiques de l'appropriation culturelle », Raisons politiques, n°62, p. 21-33.

Je ne sais pas ce qu'il en est réellement aux Etats-Unis, au-delà du débat académique sur la contribution souvent sous-estimée des Portoricains et autres latino-américains au développement du hip-hop 8 . En français, et pour la période contemporaine, on peut lire les travaux du géographe Séverin Guillard 9 . Mais à ma connaissance, il n'existe pas de rivalités de cet ordre significatives dans le rap français à l'heure actuelle. J'ai réalisé une analyse systématique des featurings entre rappeurs de 1990 à 2004, mais la question de l'ethnicité ou de la racialisation n'étaient pas des éléments que j'ai inclus dans l'analyse. Néanmoins, que l'on regarde les labels discographiques ou les collaborations, il n'y a pas de motifs racialisés clairs qui se dégagent, à l'exception de collaborations autour de chansons prenant explicitement l'origine géographique ou l'expérience du racisme comme thème. De fait, sur le plan esthétique, il y a des sources d'inspiration culturelles privilégiées que l'on peut associer à la trajectoire biographique de certains artistes. Ce sont des artistes congolais ou franco-congolais qui forment, à partir de la fin des années 1990, le collectif Bisso Na Bisso -littéralement « entre nous » -pour travailler la rencontre musicale entre rap et rumba congolaise. Les membres de ce collectif poursuivent par ailleurs leur collaborations musicales dans d'autres cadres avec des artistes aux origines variées. Ce sont des artistes d'origine maghrébine qui poussent le plus loin le rapprochement musical entre raï et rap (les artistes Freeman, Rim'K, DJ Kore, etc.) au tournant des années 2000. C'est un rappeur français d'origine guinéenne et sénégalaise, MHD, qui intègre à la drill états-unienne des éléments de 6 Coombe Rosemary J., 1993, « The Properties of Culture and the Politics of Possessing Identity: Native Claims in the Cultural Appropriation Controversy ». Canadian Journal of Law & Jurisprudence vol. 6 n°2, p.249-285. Voir page 264. 7 Sear, créateur du fanzine Get Busy, propos tenus dans l'émission "Ciel ! Mon mardi", 1991. 8 Harrison Anthony Kwame, 2008, « Racial Authenticity in Rap Music and Hip Hop », Sociology Compass vol. 2 n°6, p. 1783-1800. 9 Séverin Guillard, « Le rap, miroir déformant des relations raciales dans les villes des Etats-Unis », Géoconfluences, janvier 2016.