Moad Kissai

Xavier Mouton

Bruno Monsuez

Didier Martinez

Adriana Tapus

Complementary Chassis Systems for Ground Vehicles Safety

Keywords: Control Allocation, Fault-Tolerance, Reconfiguration, Chassis Systems, Vehicle Dynamics, Online Optimization

Redundancy of integrated systems has always been used in order to increase vehicle's safety. Some new technologies are however too expensive to be redundant. This paper proposes a new way to preserve the safety by enabling a kind of complementarity between different chassis systems. Optimization-based control allocation redistribution algorithms are used in order to find the best way to combine conflicted systems. Results have shown that one system can take over another one when a failure occurs making the control logic fault-tolerant and reconfigurable. This suits better future cars as additional chassis systems are intended to be integrated.

I. INTRODUCTION

The automotive sector is facing one of its biggest revolutions with the arrival of autonomous vehicles. Several technical challenges and ethical debates are still not completely solved, which delay their commercialization. One of the consequences of making vehicles autonomous is the growing number of smart chassis systems to integrate. For each new problem, car manufacturers and equipment suppliers propose constantly new subsystems with new features to solve the problem. It started by brake-based active systems, e.g. the Anti-lock Braking System (ABS) in 1978 [START_REF] Gerard | Global Chassis Control and Braking Control using Tyre Forces Measurement[END_REF]. Then steeringbased systems got more interest for their bigger influence on car's lateral behavior, e.g. the 4-Wheel Steering (4WS) system in 1987 [START_REF] Gerard | Global Chassis Control and Braking Control using Tyre Forces Measurement[END_REF]. So, at first, systems based on longitudinal tire forces control were used for vehicle's longitudinal control, and systems based on lateral tire forces control were used for vehicle's lateral control. With the appearance of systems such as the Electronic Stability Program (ESP) [START_REF] Liebemann | Safety and performance enhancement: The bosch Electronic Stability Control (ESP)[END_REF], the previous approach was no longer valid. This is also the case for any system that uses different right longitudinal tire forces than the left ones as the Torque Vectoring system [START_REF] Velardocchia | Control systems integration for enhanced vehicle dynamics[END_REF]. When several subsystems control the same physical quantity, the overall system becomes over-actuated. If no coordination is ensured, conflicts may occur causing the vehicle's loss of control. A proper way to prevent this would be to formulate the problem as a constrained optimization problem. The solver can then allocate the control optimally avoiding any conflict and without exceeding any constraint.

{moad.kissai, bruno.monsuez, adriana.tapus}@ensta-paristech.fr This has already been developed in flight control, when conventional ganging methods were no longer able to handle advanced aircraft [START_REF] Bodson | Evaluation of Optimization Methods for Control Allocation[END_REF]. As the overall system is over-actuated, if an optimized coordination is taken into account, multiple solutions can be found. This gives additional features as ensuring multiple objectives at the same time when it is possible [START_REF] Kissai | Review of integrated vehicle dynamics control architectures[END_REF]. One of the main objectives, if it is not the most important one, is the vehicle's safety.

One common industrial practice is redundancy of safety critical systems. In [START_REF] Anwar | An Analytical Redundancy-Based Fault Detection and Isolation Algorithm for a Road-Wheel Control Subsystem in a Steer-By-Wire System[END_REF] a redundancy-based fault detection and isolation regarding the Steer-By-Wire (SBW) has been proposed to reduce the total number of redundant road-wheel angle sensors while maintaining a high level of reliability. Authors of [START_REF] Bishop | Control of redundant manipulators using logic-based switching[END_REF] used a switched control scheme in order to control redundant planar robotic manipulators. An example has also been given in [START_REF] Zhang | Active fault-tolerant control system against partial actuator failures[END_REF] to demonstrate the effectiveness of a fault-tolerant control against partial actuator failures.

However, several expensive systems cannot be redundant in commercial ground vehicles. As different systems can influence the same physical quantity in an over-actuation context, the existing synergies between different chassis systems should be taken benefit from [START_REF] Coelingh | Open-interface definitions for automotive systems -Application to a Brake by Wire System[END_REF]. This can ensure some sort of complementarity between systems with different natures. So if a system fails, another completely different system can take over. Techniques used to solve the redundancy problem can be used to solve over-actuation problems. But attention should be given to the control technique to employ, as in this case, the control should switch from a system with a given behavior to another one with different behavior. For this reason, control allocation methods are more suitable, as in contrast to the existing reconfiguration methods that modify controllers to tolerate faults, control allocation methods only change allocation laws. In one hand, this is advantageous in a way that allocation laws take account of systems with different nature, and in the other hand, this implies that stability of the closed-loop system after reconfiguration can be guaranteed [START_REF] Yang | Fault-tolerant control strategy based on control allocation using smart actuators[END_REF].

This paper outlines the benefits of making complementary non-redundant chassis systems to enhance vehicle's safety. A simple new example of a vehicle equipped by the Active Rear Steering (ARS) system and the brake-based Vehicle Dynamics Control (VDC) system is provided in order to demonstrate the effectiveness of the proposed method. The architecture proposed is extensible to additional subsystems and additional objectives, which makes it a good candidate for future autonomous vehicles [START_REF] Kissai | Review of integrated vehicle dynamics control architectures[END_REF]. Additional objectives could include energy consumption [START_REF] Chen | Energy-efficient control allocation with applications on planar motion control of electric ground vehicles[END_REF] or tire energy dissipation [START_REF] Shyrokau | Vehicle motion control with subsystem prioritization[END_REF]. Good results were obtained using Matlab/Simulink c co-simulated with AMESim c , which contains high-fidelity vehicle models to provide more realistic signals. Results showed that one system can easily complete the maneuver of the other one, proving that there is no need of redundancy of such expensive system such as the ARS system.

The rest of the paper is structured as follows: We start in Section II by providing the dynamics modelings necessary for the high-level control. In Section III, the method used reallocate the control commands in case of failure is detailed. Section IV presents results obtained by co-simulation of Matlab/Simulink c and AMESim c . A discussion about the relevance and implication of this method is provided in Section V. Conclusions and future works are outlined in Section VI.

II. VEHICLE DYNAMICS CONTROL

In order to show the effectiveness and relevance of the method presented in this paper, we choose to give a practical example of one of today's commercial vehicles. This should not be seen as a particular situation. In Section III, a general explanation of the method is provided. This can be adaptable to any situation. The vehicle chosen in this paper is the latest Renault Talisman1 . This vehicle is equipped with the Active Rear Steering (ARS) system, which has a strong influence on the group's brand image, and the brake-based Vehicle Dynamics Control (VDC) system, which functionality is similar to that of the ESP. We chose these two systems because they both influence the vehicle's yaw rate. Moreover, the ARS system produces a rear steering angle generating a lateral tire force, while the VDC system generates a yaw moment by means of differential longitudinal tire forces between right tires and left tires. This makes the two systems having complete different behaviors. In this situation, industries tend to avoid operating both conflicting systems in the same time, making the coordination downstream the systems by enabling one command at a time [START_REF] Kissai | Review of integrated vehicle dynamics control architectures[END_REF]. In this work, an upstream approach is adopted that enables combining both systems and making benefit from the vehicle's whole potential.

A. System Modeling

Unlike most of lateral control papers that use the bicycle model [START_REF] Selby | Intelligent Vehicle Motion Control[END_REF]- [START_REF] Bchle | Slip-Constrained Model Predictive Control Allocation for an All-Wheel Driven Electric Vehicle[END_REF], here a four-wheeled vehicle model is chosen (more details are provided in the following subsections). This choice is motivated by the fact that we want to allocate optimally longitudinal tire forces to each tire by means of the VDC system, and to do so, we need to know the effect of each tire on the overall vehicle dynamics.

1) Vehicle model: Fig. 1 illustrates the model adopted. As only longitudinal and lateral forces are controllable, vertical motions were ignored making the model planar. However, vertical forces variations have significant influence on tire behavior [START_REF] Pacejka | Tyre and Vehicle Dynamics[END_REF], [START_REF] Dugoff | Tire Performance Characteristics Affecting Vehicle Response to Steering and Braking Control Inputs[END_REF]. This should be taken into account in the tire model. Using Newton's laws of motion, we find the following state-space representation:

ẋ (t) = A (t) x (t) + Bu (t) y (t) = Cx (t) (1) (2)
Where:

• x (t) = V x ψ : is the state vector, • y (t) = V x ψ : is the output vector, • u (t) = F xtot M ztot : is the input vector, • A (t) = 0 V y 0 0 : is the state matrix, • B =    1 M 0 0 1 J z   
: is the input matrix,

• C = 1 0 0 1 : is the output matrix.

With:

                 F xtot = F x f l + F x f r cos (δ f ) + F x rl + F xrr M ztot = F x f l + F x f r l f sin (δ f ) + F x f r -F x f l E 2 cos (δ f ) + (F xrr -F x rl ) E 2 -F yr l r (3) (4)
Where:

• V x : longitudinal velocity of the vehicle, • V y : lateral velocity of the vehicle, • ψ : yaw rate of the vehicle, • M : vehicle's mass, • J z : vehicle's yaw moment of inertia, • F x f,r : front-right braking force, • F x f,l : front-left braking force, • F xr,r : rear-right braking force, • F x r,l : rear-left braking force, • F yr = F y rl + F yrr lateral rear force, • δ f : front steering angle, • l f
: distance between the front axle and the vehicle's center of gravity (CoG),

• l r : distance between the rear axle and the vehicle's CoG,

• E : vehicle's track. Note that we have considered only controllable forces to distribute.

2) Tire model: To complete modeling the system, a tire model is required. As long as systems with different behaviors are concerned soliciting tires both longitudinally and laterally, a combined tire model is needed. This model should be precise enough in stable operating points, but also simple enough to be used in real-time control maneuvers.

Therefore, the linear tire model with varying parameters is chosen, which details and validation through AMESim c is provided in [START_REF] Kissai | A New Linear Tire Model With Varying Parameters[END_REF]. We recall here the main results. Tire forces are expressed using varying stiffnesses, taking into account couplings, vertical forces influence, and friction influence.

F x = C * s (α, µ, F z ) κ F y = C * α (κ, µ, F z ) α (5) (6)
where:

• κ : the longitudinal slip, • α : the side-slip, • µ : the friction coefficient, • F z : the vertical load, • C * s (α, µ, F z )
: the tire varying longitudinal stiffness with respect to the side-slip α, µ, and F z , • C * α (κ, µ, F z ) : the tire varying cornering stiffness with respect to the longitudinal slip κ, µ, and F z . Detailed expressions of C * s (α, µ, F z ) and C * α (κ, µ, F z ) can be found in [START_REF] Kissai | A New Linear Tire Model With Varying Parameters[END_REF].

In order to respect the friction ellipse concept described in [START_REF] Pacejka | Tyre and Vehicle Dynamics[END_REF], which describes penalization between tire forces, dynamic constraints are added [START_REF] Kissai | A New Linear Tire Model With Varying Parameters[END_REF]:

     F x ≤ (µF z ) 2 -F 2 y F y ≤ (µF z ) 2 -F 2 x (7) (8)

B. High-Level Control

In order to distribute the forces to each effector, the generalized force F xtot and moment M ztot should be first generated. According to equations (1) and (2), a multivariable high-level controller is needed. Due to expression of the state matrix A (t), couplings between the longitudinal velocity and the yaw rate are related to the lateral velocity value. V y can be considered as a varying parameter. The vehicle model is then linearized with respect to a range of V y values. Moreover, as several parametric uncertainties exist at the vehicle level 2 and the tire level 3 , a robust controller should be designed. For these reasons, a Gain-Scheduled H ∞ controller has been chosen to ensure the high-level control 2 Mass, moment of inertie, and so on. 3 Basically the friction coefficient where V y is the scheduling parameter. As the scope of this paper is not the high-level vehicle dynamics control, the design of this controller is not addressed here.

III. FAULT-TOLERANCE USING CONTROL REALLOCATION

Once the generalized forces required to ensure safe vehicle motions are calculated, they should be optimally distributed to the different systems in order to effectively generate them. This upstream approach has a lot of advantages as extensibility, modularity, and easy design of fault-tolerance control [START_REF] Kissai | Review of integrated vehicle dynamics control architectures[END_REF]. This separation of high-level control and control allocation allows taking into account the actuators constraints and states in an explicit way. So if an actuator fails, only the allocation will be updated. The high-level control remains unchanged, and the stability of the overall system can still be guaranteed.

A. Method Description

The control allocation problem can be defined as follows [START_REF] Johansen | Control allocation ? A survey[END_REF]: find the control vector, u ∈ R n such that

B u = v (9)
subject to

u min ≤ u ≤ u max ˙ u ≤ ˙ u max (10) (11)
where B ∈ R m×n is a control effectiveness matrix, u min ∈ R n and u max ∈ R n are the lower and upper position limits, respectively, ˙ u ∈ R n is the control rate, ˙ u max ∈ R n is the maximum control rate, v ∈ R m are the desired accelerations, n is the number of control effectors, and m is the number of axes to control with n > m.

The allocation is closely related to the effectiveness matrix B. It expresses each control component's effectiveness to modify the overall behavior of the system. The idea is to simply modify this matrix to take account of the actuators states. In this way, if an actuator fails, the value of the effectiveness matrix will change to express the fact that the failed actuator has no longer effect on the overall system. The control will be then reallocated to the healthy actuators continuing the maneuver in a degraded mode.

B. Application

For the ARS-VDC coordination case, the control vector contains controllable tire forces:

u =       F x f l F x f r F x rl F xrr F yr       (12)
u min and u max reflect tire limits with respect to the friction ellipse concept [START_REF] Bishop | Control of redundant manipulators using logic-based switching[END_REF] and [START_REF] Zhang | Active fault-tolerant control system against partial actuator failures[END_REF]. We suppose that the friction coefficient can be estimated [START_REF] Svendenius | Tire Modeling and Friction Estimation Department of Automatic Control[END_REF], and so can be the vertical loads [START_REF] Soltani | Low Cost Integration of Electric Power-Assisted Steering (EPAS) with Enhanced Stability Program (ESP)[END_REF]. The desired acceleration v contains in this case the generalized forces:

v = F xtot M ztot (13)
To complete the problem definition described in (9), B is filled by geometric relations between the vehicle and its tires using equations (3) and (4):

B = cos (δ f ) cos (δ f ) 1 1 0 b 2,1 b 2,2 - E 2 E 2 -l r (14)
where:

• b 2,1 = l f sin (δ f ) - E 2 cos (δ f ) , • b 2,2 = l f sin (δ f ) + E 2 cos (δ f ) .
In this paper, we suppose that we are able to detect and isolate the fault 4 . Moreover, we recall that our objective is to control the vehicle's yaw rate by means of two conflicted chassis systems. We modify then only the second line of the effectiveness matrix to take into account systems' failures. Let us note ϕ i the flag of the i th actuator expressing its status where:

ϕ i = 1 if the actuator is working fine, 0 otherwise. ( 15
)
The effectiveness matrix becomes then:

B = cos (δ f ) cos (δ f ) 1 1 0 b 2,1 ϕ 1 b 2,2 ϕ 2 - E 2 ϕ 3 E 2 ϕ 4 -l r ϕ 5 (16)

C. Optimization Algorithm Choice

Two main criteria should be taken into account. First, the algorithm should provide enough potential to solve the control allocation and reallocation and converge to the optimum in a finite number of iterations. Secondly, the algorithm should be fast enough to be suitable for real-time operations.

Various techniques have been tested. In [START_REF] Soltani | Low Cost Integration of Electric Power-Assisted Steering (EPAS) with Enhanced Stability Program (ESP)[END_REF], the Daisy-Chain method has been combined with the Weighted Pseudo-Inverse (WPI) method to handle coordination of the ESP with the Electric Power-Assisted Steering (EPAS) system. The advantage of this technique is the fact that it is based on an algebraic calculation which makes it faster with respect to online optimization based methods. However, on one hand, the Daisy-Chain method imposes a predefined prioritization of one system over another, which contradicts an upstream approach necessary for future cars [START_REF] Kissai | Review of integrated vehicle dynamics control architectures[END_REF]. And on the other hand, the WPI is more suitable as long as only one objective is pursued. For multi-objectives problems, no algebraic expression exists. This limits the utilization of this method.

In this work, we focus more on online optimization techniques. Active Set Algorithms (ASA) have shown good 4 Renault's smart actuators for both systems contain fault detection modules.

results in this context. Here, the optimal control vector is expressed as [START_REF] Harkegard | Efficient active set algorithms for solving constrained least squares problems in aircraft control allocation[END_REF]:

u opt = arg min umin≤ u≤ umax A u -b (17)
Two different methods based on ASA have been derived. Sequential Least Squares (SLS) uses two stage ASA to separate the global problem into two optimization problems [START_REF] Harkegard | Efficient active set algorithms for solving constrained least squares problems in aircraft control allocation[END_REF]. This leads to the following formulation:

   u opt = arg min u∈Ω W u ( u -u p ) Ω = arg min umin≤ u≤ umax W v (B u -v) (18) (19)
Where:

• u p : preferred control vector, • W u : non-singular weighting matrix affecting control distribution among the actuators, • W v : non-singular weighting matrix affecting the prioritization among the virtual control components when B u = v cannot be attained due to the actuator constraints. In contrast, the Weighted Least Squares (WLS) solves the global problem in one stage ASA by means of different weights to determine the importance of each objective [START_REF] Harkegard | Efficient active set algorithms for solving constrained least squares problems in aircraft control allocation[END_REF]. Generally, the allocation objective is prioritized using a highvalue weight of the order γ 10 6 [START_REF] Harkegard | Efficient active set algorithms for solving constrained least squares problems in aircraft control allocation[END_REF]. This gives the following expression:

u opt = arg min umin≤ u≤ umax W u ( u -u p ) 2 + γ W v (B u -v) 2 (20)
Other techniques non based on ASA exist as the Interior Point (IP) solver [START_REF] Petersen | Constrained quadratic programming techniques for control allocation[END_REF] and Cascading Generalized Inverses (CGI) [START_REF] Bordignon | Constrained Control Allocation for Systems with Redundant Control Effectors[END_REF]. One of the most interesting one is the Fixed-Point Iteration (FXP) [START_REF] Burken | Two Reconfigurable Flight-Control Design Methods: Robust Servomechanism and Control Allocation[END_REF] because of its rapidity with respecting to other optimization techniques. These techniques are compared in Section IV trough co-simulation. The reader can refer to [START_REF] Bodson | Evaluation of Optimization Methods for Control Allocation[END_REF], [START_REF] Harkegard | Efficient active set algorithms for solving constrained least squares problems in aircraft control allocation[END_REF], [START_REF] Johansen | Control allocation ? A survey[END_REF] for further details on solver algorithms and their comparison.

D. Low-Level Control

The allocation algorithm generates tire forces commands. These commands should be transformed before being fed to the different actuators actuators. As the relations between efforts and actuators inputs are dynamic, a proper way to interpret the tire forces commands would be to add additional low-level controllers. However, this will add additional time lags to the global control logic. Moreover, for good precision and robustness, a closed-loop will be needed. Unfortunately, tire forces are not measurable in commercial vehicles. Therefore, here only an algebraic transformation is added:

     T bij = -R i F xij δ r = F yr C * α - J z M l r -l r ψ V x (21) (22)
Where:

• T bi,j : brake torque at the i -j5 wheel,

• R i : wheels' effective radius of axle "i",

• δ r : rear steer angle. The minus sign in equation ( 25) is due to the fact that the brake pressure should be positive, while the brake forces are negative. Equation (26) comes from a combination of (1),( 6) with the following:

α r = δ r - V y -ψl r V x ( 23
)
Note that the new tire model is not only used in control allocation, but also in the rear steering angle computation. The value of this angle will be then adapted to respect the rear tires conditions.

IV. CO-SIMULATION RESULTS

To give reliable results, control algorithms have been written in Matlab c , while a high-fidelity vehicle model 6equipped with an ARS and VDC systems has been developed in AMESim c . Simulink c is used as a bridge to co-simulate Matlab's high performance algorithms and AMESim's high fidelity vehicle model.

A. Maneuver Description

For safety tests, we choose the ISO 3888-1:1999(E) Double Lane-Change, or what is commonly called the VDA test, to validate the control logic. Fig. 2 illustrates this severe double lane-change maneuver which consists on rapidly driving a vehicle from its initial lane to another parallel lane, and returning to the initial lane, without exceeding lane boundaries. Track dimensions are mentioned in Table I. According to the ISO 3888-1:1999(E) standard, the desired speed during all the maneuver should be maintained to 80 km/h. The yaw rate target is generated using the static expression of the bicycle model [START_REF] Selby | Intelligent Vehicle Motion Control[END_REF] for fast computation.

B. Results

In order to test the effectiveness of the method proposed in Section III, three tests are carried out: comparison of the classical control allocation method with the method proposed in this paper when there is no failure, comparison of the two methods when the ARS system fails in the middle of the lane-change maneuver, and comparison of classical control allocation solvers when failure.

1) Comparison of methods when no failure: In order to focus on the method used only, the WLS algorithm is used for both methods at first. A discussion about algorithms is provided at the end of this section. Here, the VDA test is carried out normally without any failure. Fig. 3 shows the yaw rate response following both methods. As expected, both methods exhibit the same performance as the value of the flags, ϕ i remains equal to 1 during all the maneuver. The effectiveness matrix for both methods is the same. This simulation serves actually to evaluate how each system is solicited. Fig. 4 shows the ARS actuation and Fig. 5 shows the VDC one. We can see that the difference between right brakes and left ones can be ignored because of their low values. The ARS system is then automatically prioritized. This could have been predicted as the yaw moment generated by the ARS system is related to the distance between the rear axle and the vehicle's CoG: l r , which is bigger than the half value of the vehicle's track E to what the VDC system is related. The ARS system is more effective than the VDC system. 2) Comparison of methods when failure: As the ARS system is naturally prioritized in this maneuver, making the VDC fail will not give any pertinent result. Therefore, we choose to simulate the ARS failure at time t = 5s as Fig. 6 shows. Both methods are again compared using the WLS algorithm. The yaw rate response is illustrated in Fig. 7. According to Fig. 7, the proposed method gives nearly the exact same result as the previous case when no failure has occurred, making the failure unnoticeable to the driver. In contrast, the classical control allocation method loses its precision after the failure. This is due to the fact that in the proposed method the effectiveness matrix is updated to best represent the new situation, while this is ignored in classical methods. Consequently, in the proposed method, the VDC system is more solicited to complete the maneuver that the ARS system should have ensured. This makes both systems complementary as Fig. 8 shows.

In the classical method, the VDC is poorly utilized only because a large yaw rate error is sensed. SLS, WLS, IP, and FXP algorithms exhibit almost the same response. The CGI seems to be more precise. However, when zooming in Fig. 9, we can notice that the CGI signal is vibrating. This is due to non-continuous activation of the brake as Fig. 10 shows. Redistributing Pseudo-Inverses could lead to tire wear more rapidly with respect to other algorithms. Imposing some rate limits may even give different results. In fact, the CGI requires only a finite number of iterations but does not guarantee that the optimal solution is found [START_REF] Bordignon | Constrained Control Allocation for Systems with Redundant Control Effectors[END_REF].

Regarding other algorithms, simulation time may be used to select the best algorithm for real-time maneuvers. Tic/toc commands have been used for comparison purposes only. The SLS algorithm simulation completed in 175s, WLS in 90s, IP in 243s, FXP in 75s, and CGI in 110s. The WLS and FXP algorithms seems to be the fastest thanks to their nonsequential formulation. The WLS algorithm gives the option of easily taking into account the multi-objectives problems. This makes the WLS algorithm more attractive.

V. CONTROL ARCHITECTURE RELEVANCE

Integrated systems are increasing in number in order to make autonomous driving a reality. For economic competition matters, car manufacturers tend to diversify their suppliers [START_REF] Kissai | Review of integrated vehicle dynamics control architectures[END_REF]. Each system is then developed independently by equipment suppliers without taking into account the interactions with other systems. Coordination strategies should be then designed by car manufacturers to avoid conflicts and take advantage of the whole potential of the vehicle. In [START_REF] Kissai | Review of integrated vehicle dynamics control architectures[END_REF], it was concluded that the multi-layer architecture separating the high-level control from the interactions management layer is more suited for over-actuated systems.

In this way, optimization-based methods can be used giving an optimal coordination strategy. This induces several advantages.

A. Safety Improvement

Making subsystems complementary has the important advantage of improving safety. As it is shown in this paper, fault-tolerance can be ensured by simply modifying the effectiveness matrix in order to take into account the actuators' state. When a fault occurs, the value of the effectiveness matrix is updated by representing the new situation. The control is then redistributed favoring healthy actuators. The simple example provided in this work proves the effectiveness of this method in severe maneuvers as the double lane change.

In this work, actuators' states were limited to faulty or healthy. However, the failure model can be classified into four different types [START_REF] Yang | Fault-tolerant control strategy based on control allocation using smart actuators[END_REF]: Lock-In-Place (LIP), Hard-Over Failure, Float, and Loss Of Effectiveness (LOF). While LIP, HOF, Float failures can be considered as total failures to their independence from input commands, the LOE failure is rather a degradation of performance with respect of nominal input due to for example actuators' aging. These cases can also be taken into account by making the parameters ϕ i variable with respect to the actuator performance. However, aging should be quantified by evaluating the performance degradation. More investigations are needed for addressing this aspect.

B. Economic Advantage

Complementarity of systems could reduce considerably the overall cost. In fact, smart actuators and new technologies are expensive. If autonomous vehicles rely on such systems, and if no complementarity is proposed, these systems should be redundant for safety requirements. Unlike this common practice, making integrated systems act as a backup for different other critical systems could reduce of necessary redundant systems. A deep safety study should however be carried out before taking any decision for commercial cars.

Moreover, information contained in one system can be used to reduce the number of sensors and reduce computational overheads by not duplicating controller computations [START_REF] Selby | Intelligent Vehicle Motion Control[END_REF]. Calculators hosting online optimization algorithms may be more expensive, but the number of Electronic Cuntrol Units (ECU) may be reduced [START_REF] Wallentowitz | Scope for the Integration of Powertrain and Chassis Control Systems: Traction Control -All-Wheel Drive -Active Suspension[END_REF].

C. Potential Expansion

Actuators' faults and constraints are not the only reason for control allocation redistribution. Ground vehicles' performance is closely related to road friction. Coefficient of friction sudden changes are the cause of many accidents [START_REF] Van Zanten | Evolution of electronic control systems for improving the vehicle dynamic behavior[END_REF]. In fact, even if it is said in the police jargon that 90% of accidents are due to driver errors, 50% of these accidents are actually due to the environment [START_REF] Brown | Analysis of 104 Eastern Iowa Motor Vehicle Casualty Accidents[END_REF]. Normal drivers' experience is limited largely to driving well within the physical limit of adhesion, and this should be taken into account. Advanced Driver Assisted Systems should be then effective beyond this limit. Redistribution of control allocation could be used to face this problem. Using the tire model implemented in this work [START_REF] Kissai | Review of integrated vehicle dynamics control architectures[END_REF], loss of potential due to friction change can be estimated. Weights related to the maximum potential of each tire can be added to the parameters ϕ i . In this way, if a tire approaches saturation, weights will be decreased to near zero making the control redistributed to other non-saturated tires. Consequently, the overall potential of the four tires can be used by the different integrated systems expanding the vehicle performance as Fig. 11 shows. One challenge still remains, which is the coefficient friction estimation. An ongoing work is carried out in order to overcome this challenge by means of closedloop observation techniques.

Another reason why autonomous vehicles stakeholders should favor this approach, is the ability of solving multiobjectives problems. As it was shown in [START_REF] Shyrokau | Analysis of subsystems coordination for electric vehicle during straight-line braking and brake-in-turn[END_REF], control allocation is able of not only preserving stability, but also favoring actuators with the least impact on energy consumption, which is very attractive for electric vehicles. This approach can also be used to generate different motion feelings. This is particularly very important for autonomous vehicles, because the challenge is not only following automatically a trajectory, but also how to follow it and which dynamics should the car favor. As motion feelings are related to vehicle's Influence of integrated systems coordination on tyre friction utilization. Regions: I -without control; II -integration of active suspension and Active Front Steering (AFS) and ARS; III -integration of traction control and AFS and ARS; IV -integration of ABS and AFS and ARS [START_REF] Ivanov | Systematization of Integrated Motion Control of Ground Vehicles[END_REF].

accelerations according to ISO 2631-1, control allocation can be executed by combining forces respecting this standards and generating more expected motions to make drivers trust their vehicles. VI. CONCLUSIONS More evidence of the necessity of employing control allocation methods have been provided in this paper. The faulttolerance criterion has been focused on to prove the safety improvement provided by control reallocation algorithms. Co-simulation results showed that by making complementary completely different chassis systems, one system can take over another one even in severe conditions, avoiding redundancy of the same system. This gives the possibility of integrating additional systems without costs concerns and accelerating autonomous vehicles development.

Real experiments should however be conducted in order to validate this approach. Close collaboration of car manufacturers is expected in order to provide a standardization of these solutions. Upcoming future works include experimental studies, multi-objectives problems, and various techniques comparison for both high-level and low-level control.

Fig. 1 .

 1 Fig.1. The four-wheeled planar vehicle model (adapted from[START_REF] Soltani | Low Cost Integration of Electric Power-Assisted Steering (EPAS) with Enhanced Stability Program (ESP)[END_REF]).

Fig. 2 . 3 ×

 23 Fig. 2. Double lane-change track.

Fig. 3 .

 3 Fig. 3. Comparison of the proposed method and the classical one when no failure.

Fig. 4 .

 4 Fig. 4. Rear steer angle when no failure.

Fig. 5 .

 5 Fig. 5. VDC activation when no failure.

Fig. 6 .

 6 Fig. 6. Rear steer angle when ARS fails.

Fig. 7 .

 7 Fig. 7. Comparison of the proposed method and the classical one when ARS fails.

Fig. 8 .

 8 Fig. 8. Comparison of the VDC activation in the proposed method and the classical one when ARS fails.

3 )

 3 Comparison of control allocation solvers: Other algorithms are compared in order to justify the utilization of each one. The Sequential Least Squares (SLS) algorithm, The Weighted Least Squares (WLS) algorithm, the Interior Point (IP) algorithm, the Fixed-Point (FXP) iteration, and the Cascading Generalized Inverses (CGI) are compared using a CORE i7 7 th generation machine in the failure co-simulation case by means of LMS Imagine.Lab 15 c and MATLAB R2015a c . Results in terms of the yaw rate response are shown in Fig. 9.

Fig. 9 .

 9 Fig. 9. Comparison of CA algorithms one when ARS fails.

Fig. 10 .

 10 Fig. 10. VDC activation using CGI algorithm when ARS fails.

Fig. 11 .

 11 Fig. 11.

Moad Kissai, Bruno Monsuez, and Adriana Tapus are with ENSTA ParisTech, Department of Computer and System Engineering, 828 Boulevard des Marchaux, 91762 Palaiseau Cedex, France

We thank the Group Renault for sharing its technical parameters.

i = f for "front" or r for "rear", and j = l for "left" or r for "right".

The model has been provided by the Group Renault. Its details cannot be shared unfortunately.


Rafael Freitas Reale

Joberto Romildo Martins
email: romildo@ifba.edu.br

S B Martins

Da S Bezerra

Dmcc / Insert

Joberto S B Martins
email: joberto.matins@unifacs.br

Applying Autonomy with Bandwidth Allocation Models

Keywords: Bandwidth Allocation Models -BAM, Dynamic Resource Management, G-BAM, BAM Switching

  L'archive ouverte pluridisciplinaire

I.

MOTIVATION Bandwidth Allocation Models (BAMs) are resource allocation methods used for networks in general. The handling of on-demand resource allocation such as bandwidth (LSP -Label Switched Path setup) in MPLS DS-TE networks is the main target of BAMs. From the management point of view, BAMs need high-level administration including manager's specialization and constant monitoring of the network traffic and operational parameters in order to adopt the most suitable among the currently available BAM models: MAM [START_REF] Faucher | Maximum Allocation Bandwidth Constraints for DiffServ-Aware MPLS Traffic Engineering[END_REF], RDM [START_REF] Faucheur | Russian Dolls Bandwidth Constraints Model for DiffServ-aware MPLS Traffic Engineering[END_REF], G-RDM [START_REF] Adami | G-RDM: A New Bandwidth Constraints Model for DS-TE Networks[END_REF] or AllocTC-Sharing [START_REF] Reale | Routing in DS-TE Networks with Opportunistic Bandwidth Allocation Model[END_REF] .

The choice for a model (BAM) and its parameters configuration directly imply in complying with the dynamicity of input traffic, defined SLAs (Service Level Agreement) and other managerial high-level requirements. The decision about the most suitable BAM also depends on the actual state of the network. In brief, managing BAM adequacy for networks implies in deciding on the most suitable BAM to adopt followed by configuring it according with the actual network traffic demand. Typically, a long search time is required for computing the BAM solution for problems and, beyond that, it needs a high-level of specialization for managers and constant network monitoring. [START_REF] Bezerra | Scalable and Autonomic Management to Computer Networks[END_REF]. An autonomic choice for BAM model and related parameters configuration is then the main motivation of the investigation presented in this paper. To the extent of our knowledge, the literature has not yet focused on this kind of approach whether autonomic decisions are proposed to both choose and configure an specific BAM according with the actual network state. The approach adopted is in the direction to allow dynamic BAM switching based on new G-BAM model and consider the dynamic network traffic demand [START_REF] Reale | G BAM: A Generalized Bandwidth Allocation Model for IP/MPLS/DS-TE Networks[END_REF].

In general, Network Management Systems (NMS) need more automated and efficient management solutions for current networks like IP/MPLS, optical networks and Next Generation Network (NGN) [START_REF] Agoulmine | Autonomic Network Management Principles: From Concepts to Applications[END_REF] [START_REF] Bashar | Application of Bayesian Networks for Autonomic Network Management[END_REF]. Figure 1 illustrates the basic autonomic management levels and its evolution. There is an evolutionary process towards a fully autonomic solution motivated mainly by the development of the technology and increasing complexity of actual systems. The fully autonomic management solution represents the final management levels in which some reasoning and learning approaches are included (Fig. 1). Fig. 1. Management evolution levels towards autonomy [START_REF] Bezerra | Network Autonomic Management: A Tutorial with Conceptual, Functional and Practical Issues[END_REF] [START_REF] Samaan | Towards Autonomic Network Management: an Analysis of Current and Future Research Directions[END_REF] This paper aims to investigate the application of autonomic management together with BAMs. The target is to evaluate the applicability and define basic requirements for the steps involved in the autonomic computation, including monitoring, analysis, planning and execution. The expected overall result is to determine the viability to manage with autonomic characteristics the dynamic behavior of BAM-based networks supporting an on-the-fly operation towards network optimization.

In brief, it is investigated the switching among "BAM behaviors" and BAM´s reconfiguration with distinct network traffic scenarios by using G-BAM.

The structure of this paper is as follows: Section II presents a summary with the main characteristics of the most adopted Bandwidth Allocation Models (MAM, RDM, G-RDM and AllocTC-Sharing) according to their allocation characteristics and resources sharing. G-BAM is then presented with emphasis on its capability to generalize all other BAM´s "behaviors". Section III explores the application of autonomy with BAMs. Autonomic management implementation steps (monitoring, analysis, planning and execution) by using a framework are considered together with the inherent "behavior" of BAM models. Finally, section IV presents a case study scenario oriented to the evaluation of BAM with autonomic characteristics.

II.

BANDWIDTH ALLOCATION MODELS -AN OVERVIEW Bandwidth Allocation Models (BAMs) were originally proposed to define rules and limits (Bandwidth Constraints -BCs) for links usage by traffic classes (TCs) in DS-TE (MPLS Traffic Engineering) networks. The BAMs effectively define how resource (bandwidth) is obtained and shared among traffic classes (applications). Operationally, the application of a BAM in MPLS DS/TE networks results in setup, blocking or preemption of LSPs for specific links.

MAM, the most basic model, aims to support network traffic profiles in which a strong isolation between traffic classes (TCs) is required. In MAM, traffic classes use only private resources and there is no resource sharing (bandwidth) between traffic classes. RDM allows non-allocated resources (bandwidth) belonging to high priority TCs to be shared by low priorities TCs. Preemption of less priority LSPs using shared resources is required by high priority LSP setup (priority applications) in order to maintain defined bandwidth constraints (BCs).

AllocTC-Sharing model extends the strategy of nonallocated resources sharing to high priority TCs. As such, high priority TCs (applications) may "loan" (share) unused resources belonging to low priority TCs. A loan corresponds to a temporary use of the bandwidth allocated in low priority TCs by LSPs belonging to a high priority TC. In AllocTC-Sharing, "devolution" is the teardown of an established priority LSP using shared resources by loan. G-RDM is a hybrid model between RDM and MAM. G-RDM uses private and sharable resources. As such, it incorporates both MAM and RDM behaviors.

A. G-BAM -A Generalized Bandwidth Allocation

Model The Generalized Bandwidth Allocation Model (G-BAM) is an innovative bandwidth allocation model that allows the definition of private resources, incorporates all sharing resources alternatives (HTL1 and LTH2 ) and, beyond all this, has the capability to reproduce the "behavior" of other proposed BAMs, such as MAM, RDM, G-RDM and AllocTC-Sharing [START_REF] Reale | G BAM: A Generalized Bandwidth Allocation Model for IP/MPLS/DS-TE Networks[END_REF]. The new G-BAM model reproduces these "BAM behaviors" by reconfiguring its operational parameters.

Among the new possible allocation strategies provided by G-BAM, it is worth to mention:

•

The integration of private resources with AllocTC-Sharing behavior (HTL + LTH); and

•

The integration of private resources with LTH.

An important advantage in adopting G-BAM, instead of a single BAM or multi-BAMs for a network is the possibility to provide to the network administrators a reconfigurable BAM solution. G-BAM allows the possibility to adapt the currently adopted BAM behavior to distinct traffic profiles.

Actually, G-BAM has the full capability to deal with the dynamics of the network traffic profile by making use of its configurable "BAM behavior". Its configurable BAM behavior, beyond the possibility to switch between distinct BAMs, also allows the configuration of intermediary and transitory network states (behaviors). Transitory and intermediary behaviors are not possible to setup when using the strategy of switching between existing BAM models (MAM to RDM or RDM to AllocTC-Sharing, other switching alternatives) [START_REF] Reale | Analysis of Bandwidth Allocation Models Reconfiguration Impacts[END_REF].

Another relevant aspect of BAM switching is the migration strategy adopted [START_REF] Reale | A Preliminary Evaluation of Bandwidth Allocation Model Dynamic Switching[END_REF]. Since G-BAM is a single configurable model, sharing values for HTL, LTH and private resources can be adjusted in order to provide both "SOFT" or "HARD" migration between BAM behaviors. Operationally, G-BAM also supports the reconfiguration of BCs.

The above-mentioned set of G-BAM capabilities provides additional implementation methods that can be used to support new classes and dynamic traffic profile configurations that are not supported with basic BAMs (MAM, RDM and AllocTC-Sharing) in a single, multi-BAM, static and/or dynamic BAM switching implementation.

As such, the following section explores the application of autonomy with BAMs considering G-BAM as the model adopted by the network.

III.

APPLYNG AUTONOMY WITH BAMS -BASIC APPROACHES ADOPTED Applying autonomy with BAMs means, fundamentally, to look for the most suitable BAM and related configuration in order to achieve high-level management rules, like SLAs and other high-level business and management constraints, under the condition of dynamic input traffic.

In brief, this corresponds to a specific case of resource allocation with BAMs being defined as the basic mechanism adopted to control resources. This is similar to the resource allocation problem found in cloud computing [START_REF] Zhao | Resource Management in Utility and Cloud Computing[END_REF], traffic engineering [START_REF] Jiang | Optimal dynamic bandwidth allocation for complex networks[END_REF], datacenters [START_REF] Guo | On Efficient Bandwidth Allocation for Traffic Variability in Datacenters[END_REF] and access and wireless networks [START_REF] Seong | Optimal Resource Allocation for OFDMA Downlink Systems[END_REF], where technologies, algorithms, methods and/or heuristics are used.

Applying autonomy with BAMs will consider three strategies in this paper:

• Dynamic BAM switching;

• BAM´s parameter dynamic reconfiguration; and • BAM optimization.

A. Dynamic BAM switching

In effect, each possible BAM (MAM, RDM, AllocTC-Sharing or other) adopted/ configured in a network has a specific behavioral characteristics (BAM "behavior") that will result indifferent sets of operational parameters (utilization, blocking, preemption, …) for the same input traffic profile. In other words, link utilization, preemptions, blocked LSPs and devolutions will change for the same input traffic for distinct BAMs adopted.

Therefore, BAM dynamic switching (an on-the-fly BAM switching approach) is effectively a method to achieve a defined network state and/or control operational parameters as required by the network administration. As a simple example, the number of preemptions may be kept below a defined limit by switching BAM "behaviors" (MAM to RDM or to AllocTC-Sharing) as a function of the network input traffic.

Autonomy may play a key role in this operational scenario since there is a potential decision whether to change or not among BAM models. Another way to perceive this strategy is to take into account that link utilization, preemptions, blocked LSPs (blocking) and devolutions are some operational parameters that can be autonomously managed/controlled by choosing the BAM to be configured as the resource (bandwidth) controller.

B. Reconfiguration of BAM´s Bandwidth Constraints

(BCs) Obviously, any BAM "behavior" strongly depends on its configuration parameters like, for instance, the BCs (Bandwidth Constraints) defined for each traffic class (TC). As such, another set of possibilities to implement autonomic management with BAM´s support relies on changing their BC configuration.

However, the basic approach frequently used by managers for BAMs is to keep BAM´s BC parameters unchanged (static) independently of input traffic for all traffic classes. This is an "understandable" natural approach adopted by most network managers because the computation of a new network state (represented by a set of operational parameters like utilization, blocking and others) does require a lot of computation time and requires some expertise from previous network states. As such, the "standard" approach is to calculate the best BAM "behavior" for a specific medium or commonly expected traffic profile and adopt this configuration statically.

The computer networks are dynamic, asymmetric, multipath and with limited resources in terms of bandwidth. Given this, an autonomic management approach may explore the reconfiguration of bandwidth constraints (BCs) for any adopted BAM in order to comply with high-level requirements defined for network operation.

In [START_REF] Reale | Analysis of Bandwidth Allocation Models Reconfiguration Impacts[END_REF], two preliminary approaches for BAM´s BC reconfiguration were proposed and evaluated for distinct traffic profiles: (i) the "SOFT" approach; and (ii) the "HARD" approach.

The "HARD" approach premise is to reconfigure BCs immediately whenever BAM reconfiguration is decided to be necessary according to network traffic profile.

The "SOFT" approach premise is to reconfigure BCs slowly and adopts a "transition time" between actual and future network state.

For the three allocation models analyzed in [START_REF] Reale | Analysis of Bandwidth Allocation Models Reconfiguration Impacts[END_REF] (MAM, RDM and AlloctTC-Sharing) the "HARD" approach leads to a new state at the cost of having "forced" preemptions resulting from the fact that the availability of resources has changed. As such, the drawback is that some applications pay the price to get the network to a new and, expectably, more "efficient" state. Anyway, this is an issue to consider with any autonomic solution.

The "SOFT" solution minimizes the operational impact at the cost of requiring a management plan to coordinate the reconfiguration transition time. In this case, the migration between network states is executed gradually. The operational effect of this approach is to better preserve the BAM´s operational characteristics at the cost of a variable convergence time to the new network state.

C. BAM optimization

Another possibility to apply autonomy with BAMs is to consider optimization in general for a specific BAM. In this case, it is a matter of evaluating Bandwidth Constraints (BCs) and priorities among Traffic Classes (TCs) and TC application and services mapping for a single BAM in order to find out the best possible configuration in terms of high-level constraints (SLA, QoS, other). This is a multi-objective optimization problem involving a high number of variables and constraints.

IV.

APPLYING AUTONOMY WITH BAMS -THE FRAMEWORK The implementation of autonomy with BAMs makes use of a framework that follows the basic control loop adopted by most autonomic management systems [START_REF] Samaan | Towards Autonomic Network Management: an Analysis of Current and Future Research Directions[END_REF] [START_REF] Kephart | The Vision of Autonomic Computing[END_REF]. The BAM framework with autonomic characteristics is based on three planes corresponding to the management cycle (Fig. 2):

• Information Plane: that monitors the network in relation to the set of monitoring parameters adopted by the BAM autonomic solution.

• Knowledge Plane: that analyses network monitored data and plans for effective actions.

• Execution Plane: that acts on the BAMs and network configuring or switching them according with the actions defined by the knowledge plan. The challenge involved in implementing the BAM autonomic framework is mostly concentrated on acquiring (onthe-fly computing) the knowledge supporting the decisions to either switch among BAMs or reconfigure them in order to comply with high-level management requirements.

The BAM framework adopts a centralized operation for monitoring data collection, knowledge computation and execution dispatch.

A. Monitoring

The monitoring phase of the BAM autonomic framework aims to collect (gather) data elements that will be filtered and aggregated in order to be used at analysis phase.

The basic parameters (metrics) defined for the monitoring phase in the context of BAM´s autonomic management are:

• Utilization (Utilization) -corresponds to the effective bandwidth used in relation to link capacity for all network links.

• Number of Preemptions (Preemption) -the total number of accumulated "preemptions" in the network (MPLS DS-TE) in a configured period.

The network manager configures the evaluation period.

• Number of blocked LSPs setup (Blocking) -A "blocking" is computed every time an LSP request cannot be granted in the network.

• Number of "Devolutions" (Devolution)corresponds to the premature teardown of a priority LSPs established by "loan".

• Number of "Loans" (Loan) -The "loan" corresponds to the temporary use of bandwidth allocated to less priority TCs (LSPs) with this resource (bandwidth) belonging to higher priority TCs (LSPs).

• Number of LSPs Request (Request) -Number of requests for new LSP´s setup.

These are performance metrics resultant from the utilization of different BAMs collected by link and by TC. Effectively, BAMs act at link level arbitrating the concurrency for resources (bandwidth) between TCs. Metrics are collected and aggregated in periods defined by the network manager (day/night, week/weekend, holidays and others).

B. Knowledge Plane (Analysis and Planning)

The "analysis phase" of the autonomic knowledge management cycle determines the current network state and possible future transitions based on the monitoring metrics gathered. Generally, this represents a complex analysis using various techniques in order to identify the several possible states and determine the next state that complies with the high level management requirements (Fig 3).

The analysis phase of the BAM autonomic framework, as a first implementation approach, determines three possible actions to be planned by the next phase (planning phase):

• BAM Switching action -results from an analysis concluding that BAM switching is the best possible recommended action for the network;

• BAM Reconfiguration action -results from an analysis concluding that BAM reconfiguration is the best possible recommended action for the network.; and

• BAM Optimization action -results from an analysis concluding that actual BAM may be kept, but overall network behavior can be improved by adjusting operational parameters of the BAM in use.

As previously indicated, each bandwidth allocation model has specific characteristics that result on distinct network operational parameters (link utilization, preemption, blocking, devolution and others) as a function of the input traffic. Thus, the "analysis phase" typically may decide on the most suitable bandwidth allocation model or recommend a new BAM configuration.

Obviously, BAM´s behavior (MAM, RDM and AllocTC-Sharing) have already been identified or are deductible from its overall characteristics. The autonomic framework analysis phase is expected to "perceive" the scenarios that can be further verified by simulation. Some more obvious "perceptions" are illustrated next for MAM, RDM and AllocTC-Sharing.

MAM model is indicated when the administrator expects a behavior in which a strong isolation between Traffic Classes (TC) is required. The MAM model typically implies in low utilization of links and a high number of blocking since the available resources of a TC cannot, by definition, be shared with other TCs (total isolation of TCs). On the other hand, by not allowing the sharing of TCs, MAM model does not generate preemptions and devolutions.

RDM model is indicated when the administrator expects that the resources not used by high priority TCs can shared the low priority TCs. With more bandwidth available for low priority TCs the positive impact is higher link utilization and lower probability of blocking. The high priority bandwidth used to benefit low priority TCs can be requested back generating preemptions.

AllocTC-Sharing model supports the sharing of available bandwidth of high priority TCs for low priority TCs and viceversa. This "opportunistic" model maximizes link utilization and minimizes the probability of blocking when allowing the utilization of the available link bandwidth. The monitoring of the levels of preemption and devolution is important for this model since LSPs and TCs owners of the shared bandwidth can request them resulting in preemption and/or devolution.

In general, some behaviors become evident in terms of the analysis when links tend to saturate, such as:

The more sharing, the better link utilization and possibly smaller blocking;

The more utilization of high to low sharing, the higher the probability of preemptions;

The higher utilization of low to high sharing, the higher the probability of devolutions;

In a network frequently experiencing congestion, models with conservative politicies are, in principle, the best solution (e.g. MAM or its equivalent configuration); and

In a network frequently experiencing unsaturated links, models with more flexible politicies can be the adopted (e.g. AllocTC-Sharing or its equivalent configuration).

The "planning phase" of the knowledge plane receives state information and network state transition (decision/action) from the "analysis phase" aiming to accomplish the specified management objective. The computed action can affect only one or several managed elements in the network.

The "planning" defined within the BAM autonomic framework has, as a first implementation approach, three possible actions (Fig 3): BAM switching action; BAM reconfiguration; and BAM optimization action.

"BAM Switching" in terms of the planning phase consists in planning (computing) a soft or hard transition. "BAM Reconfiguration" in terms of the planning phase consists in planning (computing) a new configuration of BCs. The "BAM Optimization" phase corresponds to the computation of a new configuration setup for the current BAM and subsequent application to the network by the execution plane.

The analysis and planning cycle is repeated according the period configured by the administrator or in case a new network state is received by the knowledge plan.

C. Execution Plane

The execution phase controls the set of actions defined and planned in the previous phases. In short, execution phase transforms into practical actions the result obtained from previous phases. This change affects routers that can have different form of access and commands.

SIMULATION SCENARIO

The main purpose of this evaluation is to demonstrate the applicability and need of autonomy with bandwidth allocation models in IP networks.

The BAM used in the evaluation is the G-BAM. In the simulation performed, G-BAM is switched between two "behaviors": MAM and RDM behaviors. The BAM switching simulated adopts the HARD approach and explores the concept of autonomy applied to MAM e RDM "behaviors" as presented in previous sections. G-BAM configuration for MAM and RDM behaviors are the reference for comparison with a new solution with autonomic characteristics. The simulation implemented in this scenario alters dynamically the configuration of G-BAM in order to switch from MAM to RDM and vice-versa. It is based on three intuitive parameters configurable by the network administrator: Observation window; Maximum number of preemptions; and Link utilization.

The specialized bandwidth allocation model simulator BAMSim [START_REF] Reale | Routing in DS-TE Networks with Opportunistic Bandwidth Allocation Model[END_REF] is used for the simulation. BAMSim has a central managing unit that has a full view of network´s topology (Fig. 4). BAMSim receives a routing plan and configuration (routing paths) that is kept during all the simulation scenarios.

The network topology used is the NTT network containing 55 nodes and 144 links of 622Mbps (STM-4 -SDH). For this evaluation scenario, we defined a single traffic source, in the router 0, for each traffic class and destiny (Fig. 4). The principle is that the simulation is evaluating the applicability of BAM with autonomy and, as such, behaviors can be extracted from any set of input traffic. The (randomly) chosen destinations adopted in the simulation were routers 54, 52, 48 and 45 and three traffic classes are configured: TC0 -low priority applications; TC1medium priority applications; and TC2 -high priority applications.

G-BAM was configured reflecting bandwidth constraints (BCs) according to Table I. Routes (LSP paths) are statically defined in order to have competition in a high number of links. Consequently, saturated links are forced during simulation in order to observe the consequences:

• 0->2->5->11->14->19->20->21->22->26->27- >35->42->51->52 • 0->2->5->11->14->19->20->21->22->26->27- >35->42->51->52->54 • 0->2->5->11->14->19->20->21->22->26->27- >35->42->41->45 • 0->2->5->11->14->19->20->21->22->26->27- >35->42->41->45->48
The configuration parameters for LSPs are:

• LSPs length exponentially modeled establishment -average of 200 seconds, leads tolink saturation;

• LSP bandwidth -uniformly distributed between 5 Mbps and 15 Mbps;

• Halting criteria -1 hour (3600s); and

• Interval of LSPs requests arrival modeled exponentially in phases according the table below: Phases 1 to 3 create a traffic profile where there are, initially, only low priority LSPs, then medium priority LSPs come and, finally, they are followed by high priority LSPs in a high flow rate forcing them to be used in the maximum. On phase 4, we reduced the rate of high priority LSP arrivals and, on phase 5, the medium priority ones. On phase 6, we maintained a low arrival rate of medium priority LSPs and we increased the arrival rate of high priority LSP. On phase 7, we generate a high number of LSPs for all classes in order to saturate the link. Finally, on phase 8, we reduced the arrivals of high and medium priority LSPs and we maintain the high arrival flux of low priority LSPs.

VI.

EVALUATION The number of preemptions and link utilization are the first set of parameters considered in the evaluation towards the applicability of autonomy with BAMs.

Figure 05 illustrates the MAM behavior (configured with G-BAM) in which there are no preemptions (inherent behavior of MAM) but implies in links not being fully used for the entire simulation window. In other words, link utilization most of the time is below the 622Mbps TC capability even when TC0, TC1 and TC2 are saturated. In this case, it is observed that link utilization is fully maximized being at the maximum capability of 622 Mbps most of the time. The drawback in keeping a high link utilization with RDM behavior is that it also results in a high and cumulative number of preemptions (Figure 7). As such, the simulation, until this point, indicates that there is a potential decision between the utilization of these two BAM models/"behaviors". As a very simple example, it could be required by the high-level management that link utilization should be maximized but the acceptable number of preemptions should be limited to a certain value/ operational parameter.

In terms of the application of autonomy with BAMs, this effectively means that BAMs should be either switched or reconfigured or optimized, as illustrated in Figure 03 (knowledge planning phase of the management process with autonomic characteristics).

In order to illustrate more clearly the BAM switching alternative (one out of three possible options to autonomic management) and the applicability of autonomy for the resulting possibilities, a specific simulation was realized in which:

• RDM is switched to MAM using the HARD approach when the number of cumulative preemptions reaches a certain level (this prevents further preemption to happen).

• MAM is switched to RDM using the HARD approach when link utilization reaches a certain level (this attempts to improve link utilization).

• Various (arbitrarily defined) high-level management parameters (number of preemptions/ link utilization tuple on Table III Again, in terms of the applicability of autonomy in the BAM switching, configuration or optimization context, it is show in Table III that various "management decisions" are possible and, as such, that could be supported by a framework with autonomic characteristics.

As a simple example of autonomic management decision, the tuple 25/65 (maximum number of 25 preemptions/ link utilization of 65%) simulation is illustrated in Figures 08 and09. In this case, G-BAM switches from RDM to MAM behavior when preemption limit is reached and, as such, keeps preemption stable (fixed). The cost is that link utilization is reduced. In the same way, an autonomic decision to switch from MAM to RDM is executed when link utilization falls below 65%. In this case, preemption might increment again. The point is that these simulations point out to the applicability of BAMs with autonomic characteristics in order to decide and/or follow transitions that are the most adequate according with the defined high level management configuration requirements. As a final remark, the utilization of operational parameters like the adopted for the switching of BAM behaviors (preemption/ utilization) through G-BAM configuration enables a managed BAMs evolution in such a way that it can be adjusted dynamically to fulfill the objective defined by the network administrator.

VII.

FINAL CONSIDERATIONS The applicability of autonomy with Bandwidth Allocation Models (BAMs) was evaluated by considering BAM switching among distinct "behaviors" (RDM -MAM) using a HARD switching approach. The switching is executed in the simulation by configuring "BAM behaviors" (MAM and/or RDM) with the G-BAM model. The simulation over the NTT network demonstrate that, firstly, there are various possible configuration approaches that can be considered by a framework with autonomic characteristics and, secondly, that improvement in network quality parameters like link utilization and preemption are achievable. In general, the results point to the direction where some preemption and link utilization control is effectively achievable by using an autonomic framework approach and considering high-level management parameters.

In general, authors argue that autonomy and BAM-based dynamic resource allocation can coexist and may result in an overall improvement in network operation.

Fig. 2 .

 2 Fig. 2. BAM autonomic framework and the management cycle

Fig. 3 .

 3 Fig. 3. The analysis and planning phase -BAM autonomic framework

Fig. 4 .

 4 Fig. 4. Network topology used in the simulation

Fig. 5 .

 5 Fig. 5. Link utilization with G-BAM´s MAM behavior Figures 06 and 07 illustrate the RDM behavior (configured with G-BAM).In this case, it is observed that link utilization is fully maximized being at the maximum capability of 622 Mbps most of the time. The drawback in keeping a high link utilization with RDM behavior is that it also results in a high and cumulative number of preemptions (Figure7).

Fig. 6 .

 6 Fig. 6. Link 0 "utilization" (router 0 to 2) with G-BAM´s RDM behavior

Fig. 8 .Fig. 9 .

 89 Fig. 8. Preemptions with dynamic switching configured as 25/65

TABLE I .

 I BANDWIDTH CONSTRAINT BY TRAFFIC CLASS (TC)

	BCs	Max	MAX	TC per BC	Max	MAX	TC
		BC	BC		BC	BC	per
		(%)	(Mbps)		(%)	(Mbps)	BC
			G-BAM (RDM)	G-BAM (MAM)
	BC0	100	622	TC0+TC1+TC2	40	248,8	TC0
	BC1	60	373,2	TC1+TC2	30	186,6	TC1
	BC2	30	186,6	TC2	30	186,6	TC2

TABLE II -

 II RATE OF LSP ARRIVALS BY TRAFFIC CLASSES (TCS)

	Phase	1	2	3	4	5	6	7	8
	Time (s)	300	600	900	1500	1800	2100	2500	3600
	TC0	8	8	8	8	8	8	8	8
	TC1	0	8	8	8	100	100	8	50
	TC2	0	0	8	100	100	8	8	50

  top line) are statically defined and the simulated results (means) are summarized in Table III: o Maximum number of preemptions in the defined time window; o Link utilization in the defined time window. • Figures 08 and 09 illustrate the simulation results for a set of high-level configuration parameters as follows: The results are presented in terms of the mean value obtained in Figures 08, 09 and TableIII. The 5 minutes observation window in the simulation is a manager defined configuration parameter. RDM to MAM switching using HARD approach generates additional LSP preemptions in order to liberate shared bandwidth (MAM inherent operation and configuration).

o RDM to MAM switching with 25 cumulative preemptions and MAM to RDM switching with link utilization below 65% (considering the defined window).

Eight simulations were run with 05 random seeds.

TABLE III -

 III SIMULATION RESULTS (MEANS) WITH PREEMPTIONS/ LINK UTILIZATION TUPLE ARBITRARILY DEFINING BAM SWITCHING

Simulation of Autonomic Characteristics MAM 25/65 30/65 25/70 30/7 0 25/75 30/75 25/80 30/80 RDM Number of Preemptions 0 105 122 125 140 154 179 184 209 358 Blocking 1882 1687 1679 1655 1635 1608 1591 1580 1543 1335 Generated LSPs 3269 3269 3269 3269 3269 3269 3269 3269 3269 3269 Established LSPs 1387 1582 1590 1614 1634 1661 1678 1689 1726 1934 LSPs not Preempted 1321 1406 1398 1415 1419 1428 1418 1481 1437 1494 Generated LSP (Bandwidth)

					2620
	26208	26208	26208	26208	8	26208	26208	26208	26208	26208
				Established LSP (Bandwidth)
	8639	9517	9494	9681 9701	9804	9763	9843	9940	10549
					Blocking (CT0)
	1081	905	892	877	857	841	822	819	786	664
					Blocking (CT1)
	485	467	470	461	462	450	453	445	441	355
					Blocking (CT2)
	316	316	316	316	316	316	316	316	316	316
				Number of Preemptions (TC0)
	0	93	104	110	117	130	149	152	170	288
				Number of Preemptions (TC1)
	0	11	14	15	23	24	30	33	39	70
				Number of Preemptions (TC2)
	0	0	0	0	0	0	0	0	0	0

  TableIIIshows that the preemption values in the 05 minutes observation window and the maximum utilization of the bottleneck link have various intermediary behaviors between MAM and RDM.

HTL: high-to-low sharing -non-allocated resources belonging to high priority TCs can be shared by low priority TCs.

LTH: low-to-high sharing: non-allocated resources belonging to low priority TCs can be shared by high priority TCs.

ACKNOWLEDGEMENTS

We gratefully acknowledge the financial support from FAPESB (Fundo de Amparo à Pesquisa do Estado da Bahia) -Brazil.