Anne Bouillard
email: anne.bouillard@bretagne.ens-cachan.frphanthix

Linh T X Phan

Samarjit Chakraborty
email: samarjit@comp.nus.edu.sg

Lightweight Modeling of Complex State Dependencies in Stream Processing Systems

Over the last few years, Real-Time Calculus has been used extensively to model and analyze embedded systems processing continuous data/event streams. Towards this, bounds on the arrival process of streams and bounds on the processing capacity of resources serve as inputs to the model, which are used to calculate end-to-end delays suffered by streams, maximum backlog, utilization of resources, etc. This "functional" model, although amenable to computationally inexpensive analysis methods, has limited modeling capability. In particular, "state-based" processing, e.g. blocking write -where the processing depends on the "state" or fill-level of the buffer -cannot be modeled in a straightforward manner. This has led to a number of recent proposals on using automata-theoretic models for stream processing systems (e.g. Event Count Automata [RTSS 2005]). Although such models offer better modeling flexibility, they suffer from the usual state-space explosion problem. In this paper we show that a number of complex state-dependencies can be modeled in a lightweight manner, using a feedback control technique. This avoids explicit state modeling, and hence the state-space explosion problem. Our proposed modeling and analysis therefore extend the original Real-Time Calculus-based functional modeling in a very useful way, and cover much larger problem domain compared to what was previously possible without explicit state-modeling. We illustrate its utility through two case studies and also compare our analysis results with those obtained from detailed system simulations (which are significantly more time consuming).

Introduction

The escalating complexity of stream processing systems has prompted the need for modeling and analysis techniques that go beyond those traditionally studied in the literature. Many of these systems process irregular data/event streams and rely on highly dynamic resource management policies that cannot be modeled using standard periodic/sporadic event models and fixed-priority or deadline-based scheduling policies.

In this context, the Network Calculus framework [START_REF] Boudec | Network Calculus: A Theory of Deterministic Queuing Systems for the Internet[END_REF][START_REF] Chang | Performance Guarantees in Communication Networks[END_REF] -which was originally proposed for modeling communication networks -has been extensively adapted in recent years for the modeling and analysis of embedded systems processing continuous data and event streams (e.g., see [START_REF] Chakraborty | A general framework for analysing system properties in platform-based embedded system designs[END_REF][START_REF] Thiele | A framework for evaluating design tradeoffs in packet processing architectures[END_REF][START_REF] Wandeler | Quantitative characterization of event streams in analysis of hard realtime applications[END_REF][START_REF] Wandeler | Workload correlations in multiprocessor hard real-time systems[END_REF]). The resulting framework (often referred as Real-Time Calculus or RTC in the literature) is designed to model and analyze heterogeneous real-time systems in a compositional manner. The key feature of this framework is its use of count-based abstraction to model the timing properties of the input streams, as well as the availability of the resources. In particular, the timing properties of a data stream are specified as a constraint on the maximum and minimum number of data items that may arrive over every time interval of length Δ. A collection of such constraints for different values of Δ are captured as functions α l (Δ) and α u (Δ) that denote the lower-and upper-bound on the data arrival process. In other words, α l (Δ) and α u (Δ) specify the minimum and maximum number of items that may arrive within any time interval of length Δ. Clearly, these functions will admit a rich collection of arrival sequences. Standard event models such as periodic, sporadic and periodic with jitter turn out to be special cases of such a specification. Resource availability can also be specified in a similar fashion. Here, β l (Δ) and β u (Δ) shall specify the minimum and maximum number of items that can be processed by a resource within any time interval of length Δ. Given the functions α, denoting (α l , α u ), and β denoting (β l , β u ), it is possible to compute using purely algebraic techniques, the bounds on system properties such as the maximum delay suffered by the stream and the maximum backlog of data items in front of the resource. Further, it is also possible to compute α = (α l , α u ) which denotes bounds on the timing properties of the processed stream. α may now serve as the input to the next resource which further processes this stream, and the output from which may be denoted as α . This is repeated for all resources until the timing properties of the output stream α out are computed (see Figure 1).

Figure 1 shows an architecture consisting of n resources PE 1 ,... ,PE n , which process an input stream sequentially. Each PE i has an input buffer to store incoming data items waiting to be processed. The service rendered by each PE i is constrained by β i . Similar to α , the service function β i that bounds the remaining resource which can be used to process other data streams. Besides buffer requirements and the delay incurred by the input stream at each resource PE i , various other performance characteristics such as the utilization of each resource, output jitter, the maximum endto-end delay and the total buffer requirement in the system can also be obtained from the bounds α and α out .

Our contributions

Owing to the functional nature of RTC, analysis in this framework involves algebraic manipulations which allows for highly efficient computation of system properties in a fully compositional manner. However, modeling of complex state dependencies is awkward; common scenarios such as the one where the service offered by a resource depends on the fill-level of a buffer cannot be modeled easily. In constrast, fine-grained modeling of state information, e.g. using timed automata [START_REF] Abdeddaïm | Scheduling with timed automata[END_REF][START_REF] Fersman | Schedulability analysis of fixed-priority systems using timed automata[END_REF] or event count automata [START_REF] Chakraborty | Event count automata: A state-based model for stream processing systems[END_REF] often leads to state space explosion when applied to realistic problems.

In this paper, we present a technique to model a variety of complex state dependencies in the existing RTC framework with a feedback control mechanism without resorting to explicit state-space modeling. Firstly, this technique significantly enhances the modeling power of the framework but without having the problems associated with state-space modeling. Secondly, our model of a system is a composition of multiple abstract components with each component capturing all the relevant state-dependencies as well as processing semantics. The properties of these components can be computed functionally using our results and thereby attain a high efficiency. Thirdly, our technique enables state-based scheduling policies to be modeled and efficiently analyzed in a modular manner.

Through case studies, we illustrate how our method can be seamlessly integrated into the current RTC framework, and at the same time we show the effects of capturing state-dependencies on the accuracy of the analysis. We also provide experimental validation of our analysis method against simulation. The analysis results obtained from both methods match well with each other, however our analysis is significantly faster than simulation.

Related work

The first line of related work is concerned with developing task and event models that generalize classical periodic or sporadic event models, which assume fixed execution times for tasks. Towards this, timed automata and related automata-theoretic formalisms have been recently used in various setups to model and analyze task scheduling problems (e.g., see [START_REF] Abdeddaïm | Scheduling with timed automata[END_REF][START_REF] Fersman | Task automata: Schedulability, decidability and undecidability[END_REF][START_REF] Fersman | Schedulability analysis of fixed-priority systems using timed automata[END_REF]). To overcome the lack of state-based modeling in the RTC framework, we had proposed event count automata (ECAs) [START_REF] Chakraborty | Event count automata: A state-based model for stream processing systems[END_REF] that retain the count-based abstraction used in RTC. Although automata-based models are much more expressive and capable of representing a wide variety of state-dependencies, they suffer from the state explosion problem and can become inefficient when analyzing large system architectures.

The next line of work focuses on extending RTC to model complex event patterns and task activation schemes. For example, [START_REF] Haid | Complex task activation schemes in system level performance analysis[END_REF] presented a method to model conditional blocking-read on an input buffer. In particular, it modeled tasks that are triggered by events on multiple input streams using AND/OR-activation, where an OR-task is triggered whenever an event is available on either of the input streams and an AND-task is only activated when there is at least one event from each stream. [START_REF] Huang | Performance analysis of multimedia applications using correlated streams[END_REF] proposed a way to compute delay and output arrival functions of data streams that are split and joined during the system execution following the OR-activation and in-order activation semantics, while taking into account correlations in data streams and data distribution based on different types of delay. Correlation between jitter and response time of individual events were also considered in [START_REF] Henia | Improved output jitter calculation for compositional performance analysis of distributed systems[END_REF]. Analysis methods of more complex scheduling policies such as non-preemptive and scenarioaware scheduling of tasks were studied in [START_REF] Haid | Complex task activation schemes in system level performance analysis[END_REF] and [START_REF] Henia | Scenario aware analysis for complex event models and distributed systems[END_REF] respectively. Timing properties of hierarchical event streams that are generated by the communication stack are modeled in [START_REF] Rox | Modeling event stream hierarchies with hierarchical event models[END_REF]. Although extensive in variety, these proposed techniques do not handle state-modeling and control-feedback dependencies.

The back-pressure effect with finite buffer capacities has been studied in the context of data flow graphs [START_REF] Lee | Synchronous data flow[END_REF]. For instance, in [START_REF] Wiggers | Efficient computation of buffer capacities for multi-rate real-time systems with back-pressure[END_REF], an algorithm for computing the buffer capacities that satisfy throughput constraints was presented. Analysis of self-time scheduling for multirate data flow with finite buffer capacities was considered in [START_REF] Moreira | Self-timed scheduling analysis for real-time applications[END_REF]. Also, back-pressure was used in [START_REF] Tripakis | Implementing synchronous models on loosely time triggered architectures[END_REF] as a mechanism to allow a semantics preserving implementation of synchronous models on Loosely Time Triggered Architectures. The methods used in this context however are not applicable into our setting.

There have also been hybrid frameworks that combine various analysis methodologies. For example, [START_REF] Schliecker | Performance analysis of complex systems by integration of dataflow graphs and compositional performance analysis[END_REF] unified the SDF [START_REF] Lee | Synchronous data flow[END_REF] and SymTA/S [START_REF] Henia | System level performance analysis -the symta/s approach[END_REF] into a single framework that is able to model data-dependencies using SDF and to abstract event streams using SymTA/S. SymTA/S and RTC have been merged in [START_REF] Künzli | Combined approach to system level performance analysis of embedded systems[END_REF] to capture more complex interactions with high accuracy. RTC and ECA can also be integrated using the interfacing technique provided in [START_REF] Phan | Composing functional and state-based performance models for analyzing heterogeneous real-time systems[END_REF] to achieve higher accuracy than using RTC alone while being more efficient than using ECA alone. The method we propose here can be plugged into the integrated RTC-ECA framework to further increase the efficiency of the analysis, since we can now use RTC to analyze a number of statedependent components in the system instead of using ECAs, which will in turn reduce the total analysis time.

Organization of the paper

In the next section we describe the basic concepts of the RTC framework. In Section 3 we present our analysis method. We begin with an example that will be used to illustrate our method, followed by an overview of our analysis technique in Section 3.2. Sections 3.3 and 3.4 establish the theoretical results that enable the analysis of a statedependent component, which will be applied to model statebased scheduling in Section 3.5. In Section 4 we present experimental results using two case studies derived from an MPEG-2 decoder to illustrate the benefits of our analysis methods. Finally, we conclude with a discussion on the prospects for extending our study initiated in this paper.

The Real-Time Calculus Background

RTC is based on the (min,+) algebra [START_REF] Boudec | Network Calculus: A Theory of Deterministic Queuing Systems for the Internet[END_REF][START_REF] Chang | Performance Guarantees in Communication Networks[END_REF] and models data streams and services in a network with non-decreasing non-negative functions taking their values in the (min,+) semiring. More formally, (R min + , min, +), with R min + = R + ∪ {∞}, is a commutative semi-ring, its zero element is ∞ and its unitary element is 0.

Consider the set

F = { f : R + → R min + | ∀s < t, 0 ≤ f (s) ≤ f (t)}.
One can define as follows two operators on F : the minimum, denoted by ⊕ and the (min,+) convolution, denoted by ⊗:

for all f , g in F , ∀t ∈ R + , • f ⊕ g(t) = min( f (t), g(t)) and • f ⊗ g(t) = inf 0≤s≤t ( f (s) + g(t -s)).
The triple (F , ⊕, ⊗) is also a commutative semiring and the convolution can be seen as an analogue to the classical (+,×) convolution of filtering theory, transposed in the (min,+) algebra. Its zero element is the function ε : t → ∞ and its unitary element is e : 0 → 0;t → ∞.

Two other important operators for RTC are the subadditive colsure and the (min,+) deconvolution, denoted by : let f , g ∈ F ,

• f * = ∞ n=0 f n , where f 0 = e and f n+1 = f n ⊗ f . • f g(t) = sup u≥0 ( f (t + u) -g(t)).
The following lemma holds for the sub-additive closure operator.

Lemma 1. ( [7, theorem 2.1.6]) Let f , g, h ∈ F , and con- sider the inequation f ≤ f ⊗ g ⊕ h. Then we have f ≤ h ⊗ g * .

Arrival and service curves

Given a data stream traversing a system that contains a single processing element (PE), let A be its cumulative arrival function (i.e. A(t) is the number of data items that have arrived until time t). Here a data item can be a network packet or a video/audio macroblock. We say that α is an (upper) arrival curve for A (or that A is upper-constrained by α) if ∀s,t ∈ R + , A(t + s) -A(s) ≤ α(t). This means that the number of items arriving between time s and t + s is never larger than α(t). An important particular case of arrival curve is the affine functions: α(t) = σ + ρt. Then σ represents the maximal number of items that can arrive simultaneously (the maximal burst) and ρ the maximal longterm rate of arrivals.

Consider D the cumulative departure function of the stream, defined similarly by the number D(t) of items that have left the system until time t. The system provides a (minimum) service curve β , D(t) ≥ A ⊗ β . Particular cases of service curves are the peak rate functions with rate r (the system can process r items per unit of time and β (t) = rt) and the pure delay service curves with delay d: β (t) = 0 if t < d and β (t) = +∞ otherwise. The combination of those two service curves gives a rate-latency function β : t → R(t -T ) + where a + denotes max(a, 0).

A strict service curve β is a service curve such that for all t ∈ R + , let u be the last instant before t when there is no packet in the system, then

D(t) ≥ A(u) + β (t -u).

Performance characteristics and bounds

The worst-case backlog and the delay can be easily characterized in the RTC framework as below.

Definition 1. Let A be the arrival function of a data stream through a system and D be its corresponding departure function. Then the backlog of the stream at time t is b(t) = A(t) -D(t)

and the delay (assuming FIFO order for processing items of the stream) at time t is

d(t) = inf{s ≥ 0 | A(t) ≤ D(t + s)}.
Given an arrival curve and a service curve, it is possible to compute with the RTC operations the maximal backlog and delay.

Theorem 1 ( [4, 7]). Let A be the arrival function with an arrival curve α for a stream entering a system with service curve β . Let D be the departure function. Then,

1. b(t) ≤ B max = sup{α(t) -β (t) | t ≥ 0}, 2. d(t) ≤ D max = inf{d ≥ 0 | ∀t ≥ 0, α(t) ≤ β (t + d)}.
The maximal backlog is the maximal vertical distance between α and β while the maximal delay is given by the maximal horizontal distance between those two functions. Figure 2 illustrates this fact. Further, bounds on the output stream and the remaining resource of the system can be determined using Theorem 2.

Theorem 2 ( [4]

). Assume a stream constrained by an arrival curve α entering a system with service curve β .

The output stream is upper-constrained by an arrival

curve α = α β . 2.
If β is a strict service curve, the remaining resource after processing the stream is bounded by a service curve

β = (β -α) + .
In this paper, we assume that service curves are strict to ensure for the positiveness of remaining service; however, our method is not restricted to this assumption.

From the results concerning systems with a single PE, one can obtain more general results for systems with multiple PEs, using the composition of the RTC operators. For example, if there are two PEs in sequence, for respective service curves β 1 and β 2 , the overall service curve is β 1 ⊗ β 2 (see [START_REF] Boudec | Network Calculus: A Theory of Deterministic Queuing Systems for the Internet[END_REF][START_REF] Chang | Performance Guarantees in Communication Networks[END_REF] for details). Such results have been based on the properties of the (min,plus) algebra.

Modeling complex state-dependencies

Modern stream-processing systems are usually heterogeneous networks of resources processing multiple data streams using complex scheduling policies. Often, the processing of a stream depends not only on the available service but also the internal state of the system. One typical example is when the amount of on-chip memory is limited and hence the internal buffers that hold the processed items can only accommodate up to a certain capacity. To avoid loss of data, the processor may implement blocking-write for its output buffers, i.e it stalls whenever the buffers are full. Otherwise, to save resource, it may proceed to process the next data streams based on some sharing policy, in case the output buffer that stores the currently processed stream is filled up.

Modeling and analysis of systems described above require us to take into consideration the state-dependencies that are imposed among the different elements of a system. The original RTC framework presented in Section 2 (i) does not express state-information and furthermore (ii) assumes that all buffers have infinite capacities. As a result, it is not able to represent and correctly analyze such systems. Automata-based approaches developed recently for stream processing systems [START_REF] Chakraborty | Event count automata: A state-based model for stream processing systems[END_REF][START_REF] Norström | Timed automata as task models for event-driven systems[END_REF] can encapsulate state information; however, their analyses become inefficient for large systems due to the state-space explosion. In this section, we present a functional analysis technique, developed on top of the original RTC framework, which is capable of capturing the complex state-dependencies while achieving high efficiency. We shall illustrate our method with an example of stream-processing systems that is described below. More general systems can be easily modeled and analyzed using the same approach.

An illustrative example

Figure 3 sketches the system architecture of a picture-inpicture (PiP) application where two video streams are decoded. The first stream represents a set of regular video clips with high motion contents and the latter represents a set of still images. After fully decoded by the PEs, they will be displayed at the output device. PE 3 schedules the two streams s 1 and s 2 using a fixedpriority scheduling policy, with s 1 having higher priority than s 2 . Further, PE 3 implements blocking-write on the playout buffer B 1 ; when B 1 is full, the processor will process s 2 if there are some items in b 2 . This is done regardless of whether there are items in b 1 .

Given the above system architecture, we are interested in answering questions concerning the behavior of the system such as [START_REF] Abdeddaïm | Scheduling with timed automata[END_REF] what is the maximum backlog of a buffer? [START_REF] Henia | System level performance analysis -the symta/s approach[END_REF] what is the maximum delay experienced by a stream? (3) is the system schedulable while guaranteeing none the buffers overflows? A correct evaluation of such properties are essential for designers to optimize the design of the system. As mentioned earlier, we cannot use the standard RTC framework to analyze the system since PE 3 implements state-based scheduling scheme.

A functional analysis approach

In constructing the model for the system, we describe each input stream to the system as an arrival curve and each processing resource of the system as a service curve. The processing of a stream by a resource is represented by an abstract component whose inputs are the arrival curve of the input stream and the service curve of the resource. The outputs of an abstract component are an arrival curve that bounds the output stream and a service curve that bounds the resource left after processing the input stream. By connecting the abstract components following the flow of the stream (from left to right) and the order at which the different streams are processed by a shared resource (from top to bottom), we obtain the complete abstract model of the system. Figure 4 depicts the abstract model of the system architecture in Figure 3.

In this figure, α 1 and α 2 denote the arrival curves of the two input video streams; β 1 , β 2 and β 3 denote the service curves of PE 1 , PE 2 and PE 3 respectively. Similarly, β 4 and β 5 are the service curves that bound the consumptions of the two fully processed streams. The processing of the streams by PE 1 and PE 2 are represented by the abstract components C 1 and C 2 , whose output arrival curves are denoted by α 1 and α 2 . The processing of PE 3 on the output streams s 1 and

PE PE PE 1 2 3 C 1 C 2 C 3 C′ 3 C 4 C 5 α 1 α 2 α′ 1 α′ 2 α″ 1 α″ 2 β 1 β 2 β 5 β 4 OD 1 OD 2 β 3 3 β′ Figure 4
. The abstract model of the system in Figure 3.

s 2 comprises two abstract components C 3 and C 3 . Since PE 3 processes s 1 before s 2 , the remaining service of C 3 is connected as input to C 3 . Finally, the consumption of the items from B 1 and B 2 are modeled by C 4 and C 5 . The connection of the arrival curves to the abstract components follows the sequence at which the corresponding streams are processed.

Our analysis proceeds component-wise where we evaluate each abstract component and thereafter combine the evaluated results. To analyze a component, we first determine the input arrival curve and effective service curve of the component if they are not yet known. An effective service curve is a service curve that bounds the actual resource used to process a stream taking into account the state dependencies in the system. Based on the obtained input arrival curve and effective service curve, we can compute the different performance characteristics and bounds of the component using Theorem 1 and 2.

In Figure 4, since C 1 and C 2 have no state dependency with the succeeding components, their effective curves are equal to β 1 and β 2 , respectively. By the same reason, the output arrival curve α 1 from C 1 can be computed from α 1 and β 1 using Theorem 2. Similarly, the arrival curve α 2 can be derived from α 2 and β 2 .

On the other hand, since the processing at PE 3 is contingent on the state of the playout buffer B 1 , the actual resource that is used to process s 1 depends not only on the total available resource of PE 3 but also the readout rate of the output device and the capacity of B 1 . Hence the effective service curve β eff 3 of C 3 is dependent on β 3 , β 4 and the capacity of B 1 . This effective service curve will in turn affect the remaining service curve β 3 . The computation of β eff 3 and β 3 will be described in the coming sections. With the obtained β eff 3 and β 3 , we can apply Theorem 2 to compute the output arrival curves α 1 and α 2 that are inputs to C 4 and C 5 . The effective service curves of C 4 and C 5 are exactly β 4 and β 5 since there is no state-dependency in these two components.

In the next three sections, we present our technique for computing the effective service curve of a component taking into account the state-dependency of the subsequent compo-nents in the system. Section 3.3 looks into the case where the processing of the stream in the component is dependent on only one buffer of the next component. Section 3.4 moves one step further to solve for the general case when the processing within the component is dependent on the buffer state of many components in tandem. The computation of the effective service curves of components that are scheduled using fixed-priority policy while being subjected to the state of the buffers in the system is described in Section 3.5. Before going into the details, we first prove the following lemma, which will be used in our formulation. Lemma 2. Let f and g be two functions and c be a constant. Then,

1. ( f ⊗ g) + c = ( f + c) ⊗ g = f ⊗ (g + c) 2. ( f ⊗ g * ) * = e + f + ⊗ g * and ( f ⊗ g * ) + = f + ⊗ g * , where f + = n>0 f n . Proof. 1. Let h c ∈ F , such that h c (0) = c and h c (t) = ∞, ∀t > 0. Then, for every function f ∈ F , f ⊗ h c = f + c.
The formula follows from the associativity and the commutativity of the ⊗ operator.

( f ⊗ g

* ) * = n≥0 ( f ⊗ g * ) n = e ⊕ n>0 ( f ⊗ g * ) n . As (g * ) n = g * , then ( f ⊗ g * ) * = e ⊕ g * n>0 f n , hence the result.

Simple blocking-write at a single buffer

In this section, we model a setup where the processing of a stream is interrupted when an output buffer is full (i.e. blocking-write). This is done by extending the existing RTC framework using a feedback control mechanism. The system, shown in Figure 5 consists in two PEs in tandem, where the second one has a finite capacity B 2 . The PEs have respective service curves β 1 and β 2 , and when the backlog in PE 2 exceeds B 2 , then the service at PE 1 is interrupted. The functions A 1 , A 2 and A 3 are the respective arrival processes at the entrance of the system, after serviced by the first PE and at the output of the system. As the backlog on the second PE cannot exceed B 2 , one must have A 2 -A 3 ≤ B 2 and then A 2 ≤ A 3 + B 2 . A simple solution to ensure this is to put a feedback control before PE 1 , admitting only the amount of data that ensures that the backlog constraint in PE 2 is satisfied. In entrance of PE 1 , the arrival process then becomes A 1 = min(A 1 , A 3 + B 2 ). Figure 6 represents the system that can be translated into the following equations:

B 2 A 1 A 2 A 3 β 2 β 1
A 2 β 1 β 2 A 3 A 3 + B 2 A 1
A 2 ≥ min(A 1 , A 3 + B 2 ) ⊗ β 1 A 3 ≥ A 2 ⊗ β 2 ,
which leads to the following inequation:

A 2 ≥ min(A 1 , A 2 ⊗ β 2 + B 2 ) ⊗ β 1 = min(A 1 ⊗ β 1 , A 2 ⊗ (β 2 + B 2 ) ⊗ β 1 ).
From Lemma 1, the solution if this inequality is:

A 2 ≥ A 1 ⊗ β 1 ⊗ [(β 2 + B 2 ) ⊗ β 1 ] * ,
which proves the following lemma:

Lemma 3. The effective service curve for PE 1 taking into account the interruption of service when B 2 is full is:

β eff 1 = β 1 ⊗ [(β 2 + B 2 ) ⊗ β 1 ]
* . Suppose α is the arrival curve of the input stream. The maximal backlog and delay of the PE as well as the arrival curve of the output stream can be easily deduced from α and β eff 1 following Theorem 1 and 2.

Blocking-write at multiple buffers in sequence

Now suppose that there are several PEs in sequence, each of which has a buffer with finite capacity. Then, the effective service curve of the first PE (the one which has an infinite capacity) will depend on the capacities of all the buffers and on the other service curves: the feedback controls induce some cycles in the network, as shown in Figure 7.

β 1 A 3 + B 2 A 2 A 1 β 2 β 3 A 3 A 4 A 4 + B 3 βn A n+1 An A n+1 + Bn
β eff 1 = β 1 ⊗ n min i=0 i j=1 [β j-1 ⊗ (B j + β j )] + .
Proof. The result is proved by induction. The initialization step exactly corresponds to Lemma 3. Suppose that the result holds for n PEs, and let us show it for n + 1 PEs. The system obeys to the following equations:

⎧ ⎨ ⎩ A i ≥ min(A i-1 , A i+1 + B i ) ⊗ β i-1 ∀i ∈ {2,...n + 1}, A n+2 ≥ A n+1 ⊗ β n+1 .
In particular, the equations concerning PE n+1 are:

A n+1 ≥ min(A n , A n+2 + B n+1 ) ⊗ β n A n+2 ≥ A n+1 ⊗ β n+1 , which is equivalent to A n+1 ≥ A n ⊗ β n ⊗ [(β n+1 + B n+1 ) ⊗
β n ] * . Now, one can replace the system with n + 1 PEs in tandem with an equivalent system with n PEs, the n -1 first PEs having the same service curve, and the last PE having service curve

β n = β n ⊗ [(β n+1 + B n+1 ) ⊗ β n ] * .
The capacities of buffers 2 to n remain the same. Consequently, on can apply the induction hypothesis to that system and obtain a service curve for the first PE (denoting β i ⊗ (B i+1 + β i+1 ) by f i and β n-1 ⊗ (B n + β n ) by f n-1 ):

β eff 1 = β 1 ⊗[e⊕ f + 1 ⊕ f + 1 ⊗ f + 2 ⊕•••⊕ f + 1 ⊗•••⊗ f + n-2 ⊗ f + n-1 ].

Consider only the last factor f +

n-1 and replace β n by its expression:

f + n-1 = [β n-1 ⊗ (B n + β n ⊗ [(β n+1 + B n+1 ) ⊗ β n ] * )] + = [β n-1 ⊗ (β n + B n ) ⊗ [(β n+1 + B n+1 ) ⊗ β n ] * )] + = [f n-1 ⊗ f * n ] + = f + n-1 (e ⊕ f + n )
, which leads the desired formula and finishes the proof.

Remark that this formula takes into account the fact that if PE i on the line has no backlog constraint (the buffer has an infinite capacity and B i = ∞), then the service curve does not depend on the service curves β j , j ≥ i. Indeed, in that case

f i = ∞ and f + i ⊗ ••• ⊗ f + j = ∞.
Analysis bounds on the system can be easily computed in the same fashion as done in the simple case when blocking-write is imposed at a single buffer.

Similar networks have been studied (see [START_REF] Chang | Performance Guarantees in Communication Networks[END_REF]), but the goal in this reference is to compute the overall service curve. Here, we are only interested in findig the real service curve of the first server, in order to dimension the size of the buffer, taking into account the block-writing phenomenon.

State-based scheduling policies

Recall that in the illustrative example in Figure 3 (Section 3.1), the resource of PE 3 is shared between two streams s 1 and s 2 . The processing policy used by PE 3 is dependent on the state of the playout buffer B 1 as well as the priorities of the streams. Specifically, PE 3 will first process s 1 and only process s 2 when b 1 is empty or B 1 is full.

The analysis for such a state-based scheduling policy is divided into two phases. First, we determine the effective service curve that is used to process each stream taking into consideration the state dependency. With the obtained effective service curves, we compute the various performance characteristics using the results presented in Section 2.

The effective service curve β eff 3 that is used to process s 1 taking into account the state dependency is computed using Lemma 3 and Theorem 3 described above. The effective service curve that is used to process s 2 is also the one that bounds the remaining resource after processing s 1 , which can be computed using Corollary 1 below.

Corollary 1. Given a PE with service curve β processing a higher priority stream s with arrival curve α. Assume β eff is the effective service curve used to process the stream taking into account the state-dependency. The remaining resource of the PE given to the lower priority streams is bounded by the service curve

β = β -α β eff .
Proof. For any given Δ > 0, the maximum number of items that are processed in any interval of length Δ is (α β eff )(Δ) (Theorem 2.1). Since the PE starts processing the lower priority streams as soon as there is no more items from s to be processed or when the output buffer is full, the amount of service given to the lower priority streams in any interval of length Δ is at least β (Δ) -(α β eff )(Δ). This proves the corollary.

Using the computed effective service curve, the maximum backlog, maximum delay the output arrival curve can be easily computed using Theorem 1 and 2.1.

Experimental Case Studies

We employed two case studies to evaluate our theoretical results and to illustrate the effect of state-dependency on the behavior of a system. The first case study aims to show the immediate ramification of processor stalling on the filllevels of the buffers in a system. The second case study illustrates the intermediate effect of blocking of one stream on another, at the same time demonstrates how our technique can be used to evaluate systems with multiple input streams that are scheduled using fixed-priority scheduling policy with state-dependency.

Case study 1: Blocking-write of a stream

Figure 8 shows the architecture of an MPEG-2 decoder which consists of two PEs decoding an input video stream in sequence. The MPEG-2 application is partitioned and mapped onto these PEs where the VLD and IQ tasks run on PE 1 while the IDCT and MC tasks run on PE 2 . The coded input stream arrives at the system at a constant rate and it is initially processed by PE 1 . The partially decoded macroblocks of the stream are subsequently stored in the buffer b before being processed by PE 2 . The resulting fully decoded macroblocks are written to the playout buffer B and finally transmitted to the output video device. We are particularly interested in the behavior of the components shown in the rectangle box. Although the input bit stream enters the system at a constant bit-rate, the execution times of the VLD + IQ tasks may vary. The number of bits constituting each partially decoded macroblock is also not constant. Consequently, the stream that is written to b is highly bursty. We assume that (a) the bursty behavior of this stream is specified by an arrival curve α(Δ); (b) the variability in the execution requirements of the IDCT + MC tasks running on the PE 2 is captured by a service curve β f (Δ) where f represents the clock frequency of PE 2 ; (c) PE 2 implements blocking-write for B where it stalls when B is full; (d) the output device reads the macroblocks from B at a constant rate r.

In order to understand the effect of blocking-write on the behavior of the system, we permuted different capacities of B and frequencies f of PE 2 to observe the resulting changes on the maximum backlog of b. The maximum backlog of b is computed following Lemma 3 and compared with our simulated results. The theoretical technique is implemented using the Java API provided by the Real-Time Calculus Toolbox [START_REF] Wandeler | Real-Time Calculus (RTC) Toolbox[END_REF].

Obtaining arrival and service curves

To obtain the arrival curve that characterizes the partially decoded stream, we collected execution traces of the different tasks by simulating their executions on a customized version of the SimpleScalar instruction set simulator [START_REF] Austin | SimpleScalar: An infrastructure for computer system modeling[END_REF]. From these traces, we measured the execution demands of the VLD and IQ tasks for each macroblock and derived a function x(t), where x(t) denotes the number of macroblocks arriving at b during the time interval [0,t]. The function x(t) was used to compute the arrival curve α(Δ) of the partially processed stream.

Similarly, based on the execution demands of the IDCT and MC tasks, we computed the workload function γ(k) which gives the maximum number of cycles required by any k consecutive macroblocks at PE 2 . By combining γ and the frequency f of PE 2 , we derive the service curve β f (Δ). The service curve that represents the consumption at the output device is given by C(Δ) = rΔ. As f increases, more macroblocks are processed thus leading to declining backlog for all the different capacities of B. However, beyond a certain threshold frequency, the value of the maximum backlog of b stabilizes for a fixed capacity of B. This happens at the point where B is full and no other macroblocks in b can be processed until there is available space in B. Therefore, as we increase the capacity of B, the maximum backlog of b decreases, which is also illustrated in the figure .  Thus, running a processor beyond a threshold frequency reduces its utilization rate. With a fixed memory size, a designer can therefore determine the processor frequency and the corresponding capacities of the buffers in the system which maximize the utilization rate of the processor.

Analysis results

To compare our method against simulation-based approaches, we implemented a SystemC simulator and used it in conjunction with the SimpleScalar instruction set simulator in [START_REF] Austin | SimpleScalar: An infrastructure for computer system modeling[END_REF] to run a detailed SimpleScalar+SystemC simulation. Our simulated results match well with the ones computed using our analytical method described above. In particular, the analytical bounds are always less than 5% more than those obtained from simulation. On the other hand, performing the analysis using the RTC toolbox incorporated with our method is significantly faster than pursuing the pure simulation approach (less than a minute vs. several hours). Note also that results from simulation are unable to provide a formal guarantee on the maximum backlog that may incur in the system.

Case study 2: State-based scheduling of multiple input streams

In this case study, we analyze the example system described in Section 3.1. We assume the two input video streams arrive at a constant bitrate of 8 Mbps and their fully decoded macroblocks are read by the output device at a rate of 40,000 macroblocks per second. The frequencies of PE 1 and PE 2 are set to be f 1 = 1.3GHz and f 2 = 1.25GHz, respectively. Given these values fixed, we are interested in the backlog of b 2 with respect to different values of the frequency of PE 3 and capacity of B 1 .

First, we obtain the arrival curves α 1 and α 2 of the two input streams and the service curves β 1 , β 2 and β 3 of the three PEs (see Section 4.1.1). From α 1 and β 1 , we compute the arrival curve α 1 that characterizes the output stream from PE 1 . Similarly, the arrival curve α 2 that represents the output stream from PE 2 is derived from α 2 and β 2 . Based on α 1 , β 3 and the capacity of B 1 , we follow Lemma 3 to compute the effective service curve β eff 3 that processes the output stream from PE 1 considering blocking-write at B 1 . The remaining service curve β 3 that is used to process the second stream is deducted from β eff 3 and α 1 using Corollary 1. The maximum backlog of b 2 is then calculated from α 2 and β 3 using Theorem 1. Thus the maximum backlog of the input buffer corresponding to the lower priority stream exhibits the same pattern as that the higher priority stream (as seen in case study 1). This demonstrates the effect of feedback control at one stream on the other streams that share the same resource. 1 reports the total maximum backlogs of the two buffers b 1 and b 2 in reference to the capacity of B 1 and the frequency of PE 3 . The last column of the table gives the values for the case when there is no state dependency. It is observed consistently for all frequencies that when the capacity of B 1 is finite and blocking-write is imposed on the system, the total backlog at PE 3 is much larger than the computed backlog in the case of no state-dependency. Thus, assuming the buffers having infinite capacity may potentially lead to inaccurate results, as shown in this case study. It is therefore important for us to capture the state-dependency in the model and analysis of such systems.

For simplicity, we assume in both case studies that blocking-write is implemented only at a single buffer in the system. The analysis for the case when blocking-write is imposed on multiple buffers can be done similarly, except that one may additionally need to use Theorem 3 to compute the effective service curve offered by a processor to a stream. The same technique presented here can also be employed to analyze systems with more than two streams.

Additionally, we have also modeled the given case studies using the ECA and carried out the analysis using the SAL (Symbolic Analysis Laboratory) model checker [START_REF]Symbolic Analysis Laboratory[END_REF]. It is observed from our experiments that the analysis time when using ECA is much slower than when using RTC. For example, in case study 1, using ECA takes in average more than 10 times as compared to using RTC. As the system becomes more complex, the speed up is near exponential on the number of PEs in the system. This shows that analyzing blocking-write using our method is considerably more efficient than using an explicit state-based model.

Concluding Remarks

We have formulated a method that enhances the original RTC framework by modeling and analyzing a variety of state-dependencies using a feedback control technique. Our analysis is purely functional and thereby avoids the statespace explosion problem faced by explicit state-modeling in automata-based approaches. Since a number of state-based components that were originally modeled by ECA can now be analyzed functionally, it will be meaningful to integrate our proposed method into the hybrid framework of RTC and ECA [START_REF] Phan | Composing functional and state-based performance models for analyzing heterogeneous real-time systems[END_REF]. It will also be interesting to extend our technique to capture more complex state-dependencies, for instance synchronization between streams.

Figure 1 .

 1 Figure 1. An example system model.

Figure 2 .

 2 Figure 2. Guarantee bounds on backlog and delay.

Figure 3 .

 3 Figure 3. A PiP application. The system consists of three PEs on which the tasks of an

Figure 5 .

 5 Figure 5. System with two PEs in tandem, the second PE has a finite capacity buffer B 2 .

Figure 6 .

 6 Figure 6. Feedback control to ensure nonoverflow for the second buffer.

Figure 7 .Theorem 3 .

 73 Figure 7. Line of PEs with backlog constraints. Consider a system with n PEs processing sequentially, where PE 2 , ••• , PE n have respective buffer capacities B 2 ,...,B n . Theorem 3 gives the formula for computing

Figure 8 .

 8 Figure 8. An MPEG-2 decoder application.

Figure 9

 9 Figure 9 reports the estimated values of the maximum backlog of b against the different frequencies f of PE 2 for the varying capacities of buffer B.

Figure 9 .

 9 Figure 9. Maximum backlog analysis of b.

Ca pa cit y of th e pl ay ou t bu ffe r B [n um be r of m ac ro bl oc ks ] 1 BacklogFigure 10 .

 110 Figure 10. Case study 2: Maximum backlog of the lower priority stream.

Figure 10 plots

 10 Figure 10 plots the maximum backlog of b 2 in relation to the capacity of B 1 and the frequency of PE 3 . Observe from the figure that the maximum backlog of b 2 is smallest around the region with highest frequencies of PE 3 and largest capacities of B 2 . Reversely, b 2 has smallest backlogs in the area where PE 3 has lowest frequencies and B 2 has smallest capacities. In fact, the result shown in the figure demonstrates that the maximum backlog of b 2 is always proportional to the frequency of PE 3 and the capacity of B 1 .Thus the maximum backlog of the input buffer corresponding to the lower priority stream exhibits the same pattern as that the higher priority stream (as seen in case study 1). This demonstrates the effect of feedback control at one stream on the other streams that share the same resource.

Table 1 .

 1 Total buffer space required for PE 3 . Total backlog of b 1 and b 2 (macroblocks) PE 3 Freq. B 1 = 1000 B 1 = 2000 B 1 = 3000 No feedback

	2.8 GHz	31170	29498	28043	14382
	2.9 GHz	30490	28624	27169	12430
	3.0 GHz	29619	28332	26347	10868
	3.1 GHz	29359	27478	25825	9104
	3.2 GHz	28603	26885	25439	7396
	Table


ECONOMIX Marie Salognon

Reorienting companies' hiring behaviour: an innovative 'back-to-work' method in France

Keywords: back-to-work policies, employability, employers' evaluation methods, interventionist approach, long-term unemployment, labour quality, recruitment

Current 'back-to-work' programmes, particularly in France, tend to be built on a concept of personal responsibility for (long-term) unemployment and follow an 'adaptive' approach: improving the 'employability' of the unemployed, which is seen as an individual capacity, independent of the work and evaluation context. Our contribution justifies an alternative approach to back-to-work initiatives, so that society's share of responsibilities for long-term unemployment and social exclusion is taken into account within a collective, emergent and context-related conception of employability. Our study is based on observation of an innovative back-to-work programme in France (IOD) which seeks to change employers' assessment and recruitment practices to help vulnerable candidates who are generally discriminated against when seeking work. This interventionist approach aims to alter the demand side of the labour market and bring about changes in companies' practices to encourage more stable jobs and reduce selectivity in hiring.

Introduction/issues

The issue of getting people into or back to work, known in French as 'insertion', came to prominence in France in the mid-1980s in response to the structural nature of the unemployment problem and its corollary, high growth in long-term unemployment, which is now over 40% of total unemployment (source: INSEE, French National Statistics Office, Attal-Toubert and Lavergne, 2006: 2). Specific measures were introduced, then gradually reinforced and extended to tackle longterm unemployment which, like a kind of 'scrapheap', appears to offer no hope of reemployment unless an extremely large-scale economic recovery occurs.

Although it may not be possible to derive a general explanatory theory from recent arguments in economic literature concerning long-term unemployment [START_REF] Fougère | La durée du chômage en France[END_REF], the research stresses individual determinants perceived as the cause of personal unemployability [START_REF] Salognon | Évaluation de la qualité du travail et chômage de longue durée[END_REF]: the strategic behaviour of the unemployed in the theory of job prospecting [START_REF] Mortensen | Unemployment insurance and job search decisions[END_REF][START_REF] Devine | Empirical Labor Economics, The Search Approach[END_REF], deterioration of human capital as the period of unemployment increases [START_REF] Pissarides | Loss of skill during unemployment and the persistence of employment shocks[END_REF][START_REF] Coles | Retraining and long-term unemployment in a model of unlerning by not doing[END_REF], duration of unemployment itself [START_REF] Jackman | Does long-term unemployment reduce a person's chance of a job ? A time-series test[END_REF][START_REF] Machin | The causes and consequences of long-term unemployment in Europe[END_REF], or ex ante heterogeneity [START_REF] Lockwood | Information Externalities in the Labour Market and the Duration of Unemployment[END_REF][START_REF] Decreuse | L'employabilité des chômeurs de longue durée : mise en perspective des littératures théoriques et empiriques[END_REF]. All in all, economic analysis of long-term unemployment has been restricted to the division between employable people and the rest, with companies having no role to play in the construction or destruction of employability but simply selecting already employable candidates. Quite logically, the recommendations derived from these theories solely concern adjusting jobseekers' employability -understood in its broad sense as the aptitude to find and keep a normal job -to 'format' and fit it to employers' requirements. These latter are considered as data to which the jobseekers must adapt themselves [START_REF] Gazier | L'employabilité[END_REF].

The current systems are broadly based on a conception of individual responsibility for unemployment, in which the unemployed person's individual characteristics -demographic (sex, age, nationality, family status), socio-economic (training and qualifications, duration of unemployment) and/or behavioural (discouragement, passive nature) -are considered to underlie their current situation. They take an 'adaptive' approach which involves adapting offer to demand in the labour market and mainly targets the unemployed person: in France [START_REF] Salognon | Évaluation de la qualité du travail et chômage de longue durée[END_REF], getting long-term unemployed back to work is achieved by improving their 'employability ' (training, from 'qualifications' to 'rebuilding motivation'), or through hiring incentives designed to compensate for their 'unemployability' (subsidised contracts in the commercial sector, creation of jobs in the non-commercial sector). These measures are based on two common principles [START_REF] Simonin | Indemnisation, placement, activation : la politique de l'emploi tiraillée entre plusieurs modèles de responsabilité[END_REF]: long-term person-centred intervention; and individually-tailored contract-based relations between the public authorities and the beneficiary. Since the late 1990s, under the influence of international institutions such as the OECD, reference to 'job activation' has become increasingly widespread, inciting jobseekers to accept any job that comes along [START_REF] Simonin | Indemnisation, placement, activation : la politique de l'emploi tiraillée entre plusieurs modèles de responsabilité[END_REF]. Meanwhile, as illustrated by the 'Back to Work' Plan ('Plan d'Aide au Retour à l'Emploi, PARE'), treatment becomes part of a 'general context of increasingly individualised measures' (Castra and Valls, 1997, p. 99, my translation): designed coaching and boosting jobseekers to make them 'competitive' on the labour market. However, too much focus on individuals and their drawbacks may generate even more stigma.

It is very difficult to assess the efficiency of these measures and their impact on the structure of unemployment [START_REF] Salognon | Évaluation de la qualité du travail et chômage de longue durée[END_REF], but it would appear that, as opposed to courses focusing essentially on training, the closer they come to a real job situation, like subsidised contracts in the commercial sector, the more they create an employment relationship between the company and the jobseeker that fosters a permanent return to work [START_REF] Reynaud | Le chômage de longue durée : la théorie et l'action[END_REF]. We can therefore think that acting on worker's employability is not the most efficient approach and that financial incentives appear to cause employers to look beyond their prejudices against the long-term unemployed. However, candidate selection inevitably works to the detriment of the most disadvantaged jobseekers [START_REF] Join-Lambert | Politiques sociales[END_REF]. 'Cherry picking' takes place in a contradiction whereby equal allocation of resources within the target population does not prevent the 'most employable' unemployed from being the primary beneficiaries of the systems (Gazier, 1999). Moreover, the end of a subsidised contract is a highly difficult time, as there is frequently no recognition of the experience acquired and stigma may be attached to having worked under such a contract [START_REF] Simonin | Indemnisation, placement, activation : la politique de l'emploi tiraillée entre plusieurs modèles de responsabilité[END_REF].

In accordance with traditional analyses of long-term unemployment which do not examine the question of the evaluation of skills -assimilated to data -, this adaptive logic implicitly assumes that employers are perfectly capable of evaluating job candidates and immediately adopting rational recruitment methods that lead them to reject the applicants who are indeed the least useful for the company. Society's responsibilities, particularly the role of employers and their selection processes, are ignored. Nevertheless, if we think about theoretical researches integrating qualitative uncertainty, then we understand that labour quality is not a pre-established natural datum. Considering incomplete and asymmetric information about quality (of goods and labour), [START_REF] Akerlof | The Market for 'Lemons': Quality Uncertainty and the Market Mechanism[END_REF] and in his continuation [START_REF] Stiglitz | The Causes and Consequences of the Dependence of Quality on Price[END_REF] show that the heterogeneity of goods prevents the market behaviour (until disappearance), as soon as the variation of quality is not always observable by the agents. The quality is then dependent on the agents' action; it is no more a natural datum but becomes a socially constructed variable [START_REF] Orlean | Logique walrassienne et incertitude qualitative : des travaux d'Akerlof et Stiglitz aux conventions de qualité[END_REF]. Thus, there are different ways of assessing labour quality. This context of qualitative uncertainty challenges the evaluator's rationality. In this respect, the results obtained by Simonin (2000, p. 11), which showed that 40% of individuals had no interviews during their unemployment period, can be interpreted in two ways: i) the intensity of their jobhunting efforts is too low (and the system may keep it this way); ii) certain jobseeker profiles never progress beyond the CV-sending stage and are always eliminated before getting the opportunity of being assessed in an interactive situation. This second interpretation reflects the 'unemployability scrapheap' concept [START_REF] Benarrosh | Tri des chômeurs : le nécessaire consensus des acteurs de l'emploi[END_REF] that means there are several ways of evaluating labour quality and some act primarily as barriers to employment access.

According to the French 'Economie des conventions' school, recruitment in the labour market involves an intertwined dual-level choice (Larquier and Salognon, 2006): on the first level, it is the choice of the selection criteria for certain candidates rather than others; and this choice implies a value judgement of what makes a 'good candidate' on the second level. The term 'labour quality convention' is used for one of many possible ways of evaluating and classifying the worker. Although on the first level, any evaluation criterion can serve equally well for selection, measuring labour productivity based on qualifications or the results of psycho-technical tests or interviews do not all give the same outcomes. These measurement tools relate to different quality conventions, involving different consensual mental images associated with the notion of a 'skilled' labourer and giving rise to use of certain criteria to select 'good' workers. This selection takes place in a 'situated rationality' context: the labour quality evaluation devices belonging to the evaluator's environment (CV, application letter, psycho-technical tests…) focus his/her attention on a few features deemed as discriminant.

Evaluation processes vary depending on the quality convention adopted (between companies and countries, over time), and work as principles of inclusion/exclusion. Based on a typological construction of quality conventions (inspired by empirical works of Eymard-Duvernay and [START_REF] Eymard-Duvernay | Façons de recruter. Le jugement des compétences sur le marché du travail[END_REF], Larquier and Salognon (2006) show that putting the emphasis on personal skills rooted in the individual (as measured by psycho-technical tests), or work skills (as shown in the CV) examined away from direct contact with candidates, contributes to a longer period of unemployment. These quality conventions contain a conception of universal employability and its corollary, permanent unemployability, which is a source of social exclusion: if all recruitment processes begin by selection of CVs, it is always the same people who are denied the chance of assessment. In return, the local nature of any local judgement emphasising emergent skills in an interview or distributed skills in a network gives the worker a chance, by negotiation, of being assessed differently in each 'test'. Negotiating skills locally can prevent long-term exclusion: candidates' employability is neither inherent to the individual, nor permanently fixed; it encompasses a local, interactive and emergent nature.

In this respect, the comparative analysis by [START_REF] Marchal | Les a priori de la sélection professionnelle en France : une approche comparative[END_REF] of the assumptions underlying candidate selection, based on advertised job vacancies, shows that since 1980 French job advertisements have been shifting towards an evermore detailed description of the required criteria (rather like profiling), particularly personal qualities. This reflects higher demands plus systematic distancing of candidates (selected via examination of CVs and application letters), to the detriment of face-to-face encounters. Such pre-selection appears particularly common in France, and it is the least qualified, or those whose skills are not immediately apparent from a CV, who are the primary 'rejects'. The severe imbalance in the relationship between the recruiter and the applicant works in the recruiter's favour, depriving the candidate of any negotiating power in the recruitment process. British job advertisements, in contrast, do not give a detailed profile of the candidate and leave room for face-to-face meetings, attributing less importance to preconceptions.

The actions of company managers and labour market intermediaries require attention, with critical examination of their assessment of job applicants. On the one hand, looking beyond the mutual obligations of the public authorities and the unemployed, the factor of employers' responsibilities should be introduced, as the evaluation conventions adopted in assessing job applicants contribute to social exclusion. If this responsibility is acknowledged, it follows that back-to-work policies must be redirected towards employers. On the other hand, the conception of the role of the back-to-work mediator depends on identification of responsibilities for certain dysfunctions in the labour market. If it is accepted that qualifications and employability are not universalisable but emerge in work situation -once unemployed, a person cannot display the skills used in a real working situation (know-how, capacity to work and integrate into a team, autonomy, etc) as there is no formalisation and therefore no recognition of these valuable 'qualifications' -preselection by distancing the candidate and emphasising their personality traits becomes irrational. This claim runs counter the occupational psychology research which points to the predictive validity of pre-selection by tests but joins another research by psycho-sociologists which has established that the 'employability scores' of low-qualified jobseekers (based on a conception of individual and universal employability) are not predictive of subsequent chances of employment; however, 'their commitment to concrete labour market-oriented behaviour appears to be the best predictor of entry into work' (Castra and Valls, 1997, p.100, my translation). The possible rationality of pre-selection in terms of direct search costs is counterbalanced by its irrationality in terms of indirect matching costs. Successful matching cannot be through measures designed to make hiring unemployed candidates more competitive, but implies collective coordination towards changes in employers' evaluation and recruitment methods: so that a candidate deemed 'unemployable' can, under a different evaluation method, becomes the right candidate to fill the vacancy. Questioning the rationality of companies' evaluation modes suggests that the logic of public intervention, presently centred on the supply-side, should be in fact based on the firms' practises. This type of interventionist approach is applied by an innovative 'insertion' method (IOD: Intervention on Offer and Demand) which is developed locally in France by a non-profit association called Transfer. This method is based on two assumptions, which are congruent with our theoretical approach:

-An emerging and collective conception of the notion of employability, as a social construct that is dependent on both theoretical context (the product of beliefs and representations) and practical context (employability is constructed and reflected in a real-life work situation).

-The exclusion of vulnerable people does not result from rational behaviour by employers, but 'over-selection' processes built on social stereotypes.

The IOD method turns the reasoning on its head. It no longer develops back-towork aid campaigns clearly-defined and structured around the difficulties -not to say handicaps -suffered by the unemployed in order to have them fit to the requirements of the labour market. Instead, it considers employers' recruitment practices as determinant in the success or failure of the process for getting people into jobs. The last idea should be in keeping with the literature about the negotiation of 'psychological contracts', which represent the mutual beliefs, perceptions and informal obligations between an employer and an employee; and which could have major influence on employee attitudes and consequently on the success of the job relation [START_REF] Rousseau | Psychological Contracts in Organisations: Understanding Written and Unwritten Agreements[END_REF]. The crucial IOD issue is to implement levers -for instance a quick access to work and a major role attributed to the mediator -to limit over-selection by companies (which is irrational) and to bring about changes in employers' assessment methods and practices. The aim is to make work more accessible to the least qualified and most vulnerable groups (those on RMI income support, the under-25s, and the long-term unemployed), avoiding 'cherry picking'.

The objective of this paper is to show and analyse the proximity (of hypothesis and insights) of our theoretical approach to long-term unemployment, focusing on labour demand and challenging employers' practices, with this practical back-to-work experience. The main research question is to determine the extent and how it is possible to reorient companies' hiring and integration behaviour for the efficient return to work of long-term unemployed. This comprises three concerns: i) clarifying alternative principles which underpin the IOD method; (ii) how to actually negotiate the workers' employability (tactics used); (iii) what is the impact of this negotiation on getting a vulnerable population back to work?

To answer these questions, we will use files produced by the association Transfer, to explain and analyse the intervention principles behind the IOD method, and the empirical data described below.

Research methodology and presentation of the fieldwork

The exercise here involves supporting and extending our theoretical idea with case studies. At a methodological level, we are considering two types of empirical data:

i. Data collected by the concerned organisation and used by psycho-sociologists.

These quantitative data allow us to appraise the effects produced by the IOD method on getting unemployed people back to work.

ii. New data collected by us during a qualitative survey within the Evry IOD team: our study is a complementary survey which aims to observe and analyse the interaction processes more precisely, especially the variations in the assessment from employers. In a concrete way, over a short observation period (February -July 2002), we have collected qualitative information from candidates and their courses by semi-directive interviews with the IOD social workers and observing interactions between candidates and team members. These cases illustrate our purposes and are a convenient way of gaining a good understanding of the firms' evaluation and selection modes, in order to find out how to bring about changes in employer recruitment and assessment practices.

The Bordeaux-based association Transfer has been responsible for the creation of about one hundred IOD teams in France covering approximately 10,000 unemployed people considered particularly disadvantaged. Our study is based on analysis of how the Evry team (in Essonne) operates. This team of one leader and three employment mediators was set up in February 2002 and works with a specific population: people who have been beneficiaries of the RMI (Revenu minimum d'insertion), the minimum income benefit, for three years on average, and are registered as unemployed. Note that IOD teams target different types of vulnerable groups (Transfer, 2002): young persons with no qualifications (14%), long-term unemployed (25%), RMI beneficiaries (54%) or other (the disabled, prison-leavers for 7%). To provide a few figures, during the observation period, 44 jobseekers received the services of the Evry team: 13 permanent employment contracts were 'confirmed' (meaning the trial period was completed and the contract became permanent), 4 people began work on fixed-term contracts that were to lead to permanent contracts, 2 were in their trial period, 14 were still looking for a job and 11 were in a different situation (1 person did not want the team's services, 6 did not keep up contact, for 3 services were suspended pending a change in circumstances and 1 left the programme at their own initiative).

In real terms, the IOD teams' intervention operates on three levels: on the labour market to change job creation, on 'hiring habits' to reduce selectivity and negotiate workers' employability and in the firm for high-quality recruitment and permanent change in employers' practices. At each level, the teams seek to redress the balance of competition and do away with possible irrational selection by companies. Their intervention attempts to change the pecking order, giving more priority to the more vulnerable and eliciting creation of new jobs by revealing employers' unexpressed needs. Action levers rely on direct contacts between employers and jobseekers, and monitoring and follow-up of the employment relationship. Employment mediators act as contacts and guarantors to reduce uncertainty and remove opportunities for selectivity. The aim is to transform the labour demand, inducing a shift in companies' practices towards stable, long-term hiring, and less selectivity based on personal qualities unrelated to the work itself. This study observes, at each level, how these action principles are implemented and what tactics are employed.

Results: experience of back-to-work interventionist approach

Intervention on the labour market to stimulate job creation

The first intervention concerns job prospecting and business networks. This takes the form of developing closer relationships between businesses and the bodies that have contacts with the unemployed. The Transfer team is active on the local labour market via intense job search, the aim being to seize employment opportunities and tap them for people without access to those opportunities. This repeated contact should make it possible to build up a network of local businesses that are regularly called on.

While prospecting, the employment mediator speaks to the head of recruitment in the companies contacted, introducing itself as a representative of an association that is 'developing a new recruitment assistance service for businesses, subsidised by the Essonne County Council'. To avoid employers' prejudgements, the term 'back to work' is replaced by 'recruitment assistance' which is a commerce and business term rather than social work; similarly, the team is careful to avoid using the terms 'long-term unemployed' and 'RMI beneficiary', talking instead about 'workers'. The employment mediator asks the employer about their labour requirements and elicits stable job offers (fulltime, permanent posts) during a meeting.

In parallel, the team maintains a partnership with the business by keeping up regular contact, and developing cooperation. In Evry, a round table discussion was organised in May 2002 for the network of local businesses, to receive the first employers' commitments in favour of a group that tends to suffer discrimination in the labour market, and strengthen collaboration within the network. Five of the ten companies invited agreed to debate the theme of 'integration of employees into the company through the collaboration begun with the IOD team'. This was quite an encouraging result for a new team, as the internal report for 2002 states the average as 3.5 companies per team.

To influence the hiring volume, the IOD teams generate as many decisions or plans to hire more staff as possible, by thorough questioning companies about their personnel requirements, and proposing candidates even if no vacancy has been formally identified. In practice, the employment mediators face two types of employer reaction:

either they are always in need of unskilled labour, because they have staff turnover problems and are unsatisfied with the service of the ANPE (French national job centre);

or they initially respond negatively, and the employment mediator has to prolong the discussion to achieve an offer: 'are you sure you don't need anyone for maintenance work or odd jobs?': the frequent backtracking by recruiters shows that businesses have low awareness of their own requirements.

One illustration of this is the case of Mr X. Before he entered the IOD programme, Mr X had sent his CV to a bakery company three times, but to no avail. The employment mediator contacted the company to find out about its needs and propose him as a worker. In the end, the employer offered an accounting job and agreed to meet Mr X.

To influence the hiring structure, the employment mediators negotiate the status of the jobs offered, i.e. they transform the offers made spontaneously by employers, bringing the latter to define these offers as full-time permanent posts.

This happened in the case of Mrs H (a 32-year-old who had been living on the RMI for 12 months): the employment mediator's intervention turned the proposed 30-hour-week contract into a full-time contract.

In practice, if the company offers a fixed-term contract (or permanent but part-time contract) that could lead to a full-time, permanent contract, the team accepts the offer. The same applies for a part-time post chosen willingly by the worker. In all events, strict monitoring of the employment relationship by the employment mediator, until the contract is confirmed as initially envisaged, prompts the employer to respect their commitments.

Reducing selectivity and negotiating workers' employability

Intervention on employers' expectations aims to go beyond over-qualification of positions, and in general the escalating use of selection criteria (education level, experience, age) in the formulation of offers and the recruitment process. The objective is to hand back unskilled posts to unskilled candidates, by refocusing the employers on their real requirements rather than an ideal profile. It has been observed that the way employers describe their requirements is not always governed by the true needs of the job [START_REF] Reynaud | Le chômage de longue durée : la théorie et l'action[END_REF]: employers tend to display excessive demands and artificially raise the level of qualification required, either because they overestimate the complexity of the tasks to be carried out, or because they implicitly believe that better-qualified workers will offer more of the personal qualities useful for the job.

Out 'in the field', this intervention is observed when job offers are elicited: the employment mediators meet with employers in order to check the job content (features, precise tasks and place of work). The primary value of this process lies in the accurate description of the vacancy for workers, but it also calls into question the qualifications demanded, which are generally excessive for the reality of the job. This is the first chance to 'downsize' the employers' requirements, through asking them to list the tasks involved, and getting them to acknowledge that 'you don't need any qualifications to be a cleaner, do you?'

These observations show that the labour demand does not have a pre-determined character: the decision to make a position available and the qualifications necessary are determined by interaction between the employer and the intermediary. This result concurs with the economic approach to distributed cognition [START_REF] Hutchins | Cognition in the wild[END_REF][START_REF] Laville | La cognition située : une nouvelle approche de la rationalité limitée[END_REF], according to which players' rationality and behaviour derive from interactions with other players.

To avoid placing candidates in a situation of mutual competition, which can be assumed to be damaging for the least qualified, the balance has to be redressed between the choice capacities of each player in the recruitment, by transferring some of the negotiating power away from employers towards jobseekers. Three principles are applied to achieve this:

(1) Candidates never compete for a job: instead, the worker who appears to suit the best to the job requirements is proposed for each vacancy. The number of negotiated vacancies is indeed higher than the number of workers addressed to the team. This method modifies an important parameter of the recruitment situation: it avoids the choice generally made by the employer, who compares several candidates in order to take the best even if they are overqualified for the job, and thus eliminates an opportunity for selectivity.

(2) Coherently, proposing several fixed and clearly described vacancies to each worker (according to their experience and wishes), who can freely respond.

Good balance in recruitment relies on the quality of information available to the candidate [START_REF] Marchal | Les a priori de la sélection professionnelle en France : une approche comparative[END_REF]. In addition, a capacity for choice and control over the situation can reinforce the jobseeker's commitment, which is a necessary factor in a successful reintegration. Moreover, an evaluation of Transfer's action by [START_REF] Castra | L'insertion professionnelle des publics précaires: une alternative au recrutement concurrentiel[END_REF] shows that proposing three vacancies to the candidate is positively correlated with the subsequent confirmation of trial period.

(3) Eliminating the usual distancing of the candidate, which deprives them of any negotiation power; above all, a successful return to work requires contact with the employer. The work of the IOD teams is to bring about and continue direct meetings between employers and jobseekers, by bringing them into face-to-face contact, and arranging an interview after which both the employer and the worker can decide whether or not to continue the process. The employment mediator's attendance at these interviews is one of the method's basic principles, and plays a crucial role.

An efficient way of negotiating skills is to alter the recruitment channel by eliminating the use of the CVs and application letter, an approach systematically taken by French employers. The employment mediator justifies the absence of these traditional documents by the fact that he has personally met the workers face to face, and can vouch for their qualifications and experience. This practice removes the opportunity for selectivity provided by a pile of CVs, and employers' requirements can be made to evolve by focusing the employer/assessor's attention on points other than criteria generally used in the recruitment process. This practice is accepted by firms in 60 % of cases [START_REF] Castra | L'insertion professionnelle des publics précaires: une alternative au recrutement concurrentiel[END_REF]. This is relatively well received by small and medium businesses, but is more difficult to take on board for large businesses, which have fixed recruitment procedures and do not welcome deviation from them. However, the head of recruitment at one large insurance company did agree to meet a worker without presentation of a CV or letter, for a claims clerk post. Also, for highly-qualified posts, the no-CV application is difficult to accept and in such cases the team may help the candidate prepare a CV and letter. This was the situation for Mr M (29, on RMI for 51 months). He was looking for a job that would use his computing skills, and prospecting without a CV was difficult.

The second stage in eliminating opportunities for selectivity is to avoid the standard deskbound job interview by organising, instead, a broader encounter including a tour of the workplace. Once again, the employment mediator brings about a change in practice, proposing an interview in their presence, at the actual workstation concerned if possible. [START_REF] Castra | L'insertion professionnelle des publics précaires: une alternative au recrutement concurrentiel[END_REF] show that: this practice is accepted by firms for 75 % of cases; labour contracts start up more frequently after an interview between the employer, the candidate and the employment mediator, instead of a standard deskbound job interview; and possible contract breaches correspond more frequently to early resignations than early terminations (contrary to breaches occurred after a standard deskbound job interview). These results confirm that tripartite interviews reduce the hiring selectivity induced by standard interviews and redress the balance in the assessor/assessed relationship. The presence of the intermediary can however be perceived negatively for skilled positions: this was the case for Mr X, who went unaccompanied to his interview for the accounting job. Sometimes, too, an employer wishes to have a second interview with the worker alone. If the terms of employment are good and the candidate has no objection, the mediators will occasionally agree to this.

The employment mediators make several attempts to neutralise the selective effect of this meeting:

before the interview, they talk positively about the candidate to the employer, stressing their strong points (to induce positive assumptions). Meanwhile, they briefs the worker to provide reassurance and as far as possible eliminate the sense of failure experienced by most RMI beneficiaries, which makes them vulnerable to employers' questions. Among other advice, they recommend 'above all, don't say you're living on the RMI!', to avoid giving out any information that might be interpreted negatively and bias the judgement.

at the interview, the mediators intervene if the employer tries a 'trick question' or if the candidate is uncertain what to say, to avoid comments such as 'What have you been doing all this time? How come you haven't done anything in so long?' They reframe the meeting by suggesting the employer talks about the post on offer, its features and the required skills, and by showing that they correspond to the worker's know-how. The employment mediator explained to us that the workers should 'say as little as possible about themselves, otherwise the recruiters immediately realise they have been out of work for a while'; an implicit sign that a period spent away from work is a variable that carries particular stigma.

after the interview, they talk with the employer about their impressions and any reservations about the candidate, so as to influence their decision by refocusing on solely work-related facts and qualify any negative interpretations. Some of the cases observed show that major obstacles to employment were indeed overcome thanks to the attendance and intervention of the employment mediator:

Mrs D (47, on RMI for 22 months) was given an interview for a home help job, during which she fell asleep due to her alcohol problem. The employer nevertheless gave an 'agreement to start' but in the end Mrs D was not interested in the job. She later had an interview for a chambermaid's job. The employer noticed her alcohol problems but still took her on a trial basis, remarking 'as long as she does her work, it's not a problem'.

Mr N (60, on RMI for 14 months) cannot read and write and did undeclared sewing work. Despite his illiteracy, the employment mediator organised an interview with an alterations company, and he was hired on a trial basis. But the employer saw that Mr N did not really know how to sew, 'he only knows one stitch', and decided not to employ him.

In both these cases, obstacles to employment such as illiteracy, alcoholism or falling asleep in an interview were not the reasons for the failure to get the job.

In a third stage, the employment mediators try to negotiate placement in a work situation, allowing the candidate to actually see the workstation, gauge the tasks involved and meet with future colleagues. This gives the worker and the employer the maximum amount of information for their decision, and shows that the method sees the agents' environment as a decisive support for judgement. Moreover, CASTRA and PASCUAL (2003) show that organizing tripartite interview at the work place is more efficient for the confirmation of contract, especially if the candidate can converse with employed staff.

Finally, altering recruitment channels has an impact on the rationality of the assessment, which is 'situated' [START_REF] Hutchins | Cognition in the wild[END_REF][START_REF] Laville | La cognition située : une nouvelle approche de la rationalité limitée[END_REF] in that the employer's rationality is based on information from the environment. The judgement differs according to the devices it relies on: it is more selective when it is made from a distance and based on a CV than when it is face to face in a working situation, with negotiation over factors emphasised by a person who is seen as 'guarantor'.

Committing firms to a high-quality integration and permanent changes in practices

One essential factor in successful job integration is follow-up monitoring of the job placement, from the initial agreement to the confirmation of the full-time, permanent contract. This takes the form of regular scheduled meetings with the worker and employer separately (which are positively correlated with confirmation of the contract according to [START_REF] Castra | L'insertion professionnelle des publics précaires: une alternative au recrutement concurrentiel[END_REF]), to raise any problem encountered by either, and negotiate solutions. The employment mediator thus reassures workers who lack self-confidence, and can, by acting as guarantor, reverse certain hasty decisions by the employer to stop the trial period. Certain cases provide concrete illustrations of the role of monitoring: Mrs D was hired as a chambermaid on a trial basis, and did not turn up for work after three days. The employment mediator talked to her and the employer, who then agreed to continue the employment although he complained that she was 'slow'. This gave Mrs D self-confidence, and the employer praised her work and remarked 'she doesn't smell of drink any more'. The permanent contract was confirmed, and the manager claimed to be 'very pleased with her work'.

Mr P (37, on RMI for 34 months) easily found a job as a re-potter at a nursery, but his trial period did not go well. He too was 'too slow' according to his team leader, and the employment mediator had several conversations with the manager, who wanted to end the trial period. In the end, Mr P was moved to watering work under a different team leader. The integration process had come close to failure on several occasions, and intensive monitoring was necessary to validate the permanent contract. The same nursery also hired another worker put forward by the IOD team, Mr B (36, on RMI for 75 months).

In parallel to this monitoring, the employment mediator encourages employers to devote some time to the integration of employees and development of management practices favourable to confirmation of contracts, for instance appointing a mentor who helps the worker integrate, mainly by on-the-job training and being available to answer questions. The employment mediator also negotiates the intensity of work, the difficulties of tasks, progressive self-sufficiency and responsibilities in the job, and working days and hours.

Through negotiation, Mrs M-J (47, on RMI for 62 months), who was afraid she would not be able to 'keep up', was allowed reduced-level tasks and working hours when she started, to move progressively on to a full-time permanent contract.

Finally, another factor in successful integration is negotiation of development prospects (training and promotion, job profile, salary, working conditions).

For Mrs B (33, on RMI for 1 month), company-provided training was negotiated to enable her to achieve promotion from administrative clerk to personal assistant.

As such, [START_REF] Castra | L'insertion professionnelle des publics précaires: une alternative au recrutement concurrentiel[END_REF] show that negotiation of a contract term (as working hours or selected criteria) with employer has a positive effect on the confirmation of the contract.

The action taken by IOD teams engages the employer in new behaviour, which is a source of change in representations by post-hoc rationalisation, whether in hiring decisions, recruitment policies, employee integration or career prospects.

The receptivity of certain companies was observed at the round table organised by Evry's IOD team. To foster closer collaboration with businesses, the team presented themselves as being at their service ('a service for your business: from analysis of your personnel requirements to long-term integration of your employee'), while they are primarily at the service of the workers. The team underlined the coherence of the various stages in their service for successful integration of the new employee, and proposed that participants should share and discuss their own experiences of the IOD service: Mr C, representing an office furniture company S, thinks that placing the worker in the real-life working situation at the interview built 'commitment in the workplace: discussions focus on the reality of the job, whereas in more traditional methods, the candidate discovers their job the day he joins the company'.

Regarding integration of the newly-hired worker, Mr N from company K explained: 'after the second visit, we introduce the person to a mentor who will train him -a machine operator. It was a deliberate choice to appoint a peer, because a machine operator can train the new recruit better, plus, the task raises their own standing, which means he can develop too: the mentor can realise he's capable of a supervisory job'. Mr M, manager of a chain hotel, proposed that 'the employment mediator should be present for longer, spend a day in the company to get a better understanding of the job and details of the tasks'.

For these companies, recruitment efficiency indeed appears to rely above all on employee integration. It challenges the quality of information and rationality of decision-making in highly selective and remote (from candidates) recruitment processes.

The IOD teams' work could have a socio-economic impact: changes in practices in business networks could over time be applied to the benefit of other jobseekers, not just those assisted by the teams. The outlook touched on at the end of the round table confirm this: Mr N said his company's aim was to 'continue and step up the collaboration, particularly as we plan to take on about thirty staff in the coming months', and wished to 'talk about it with businesses from other sectors', while Mrs M from company O (council housing management) said she would like to talk 'to others from the same sector because as a landlord we have serious difficulties: the salaries are low and there are no prospects'.

Encountered difficulties

The IOD team leader says that people living on RMI are 'the furthest from the labour market and the most 'damaged': they have tried everything else on offer and IOD is their last chance.' In the employment mediators' opinion, this distance from employment, which prevents the development of self-confidence, is a difficulty that needs to be overcome. Sometimes, candidates fail to come to the interviews fixed by the team, or do not show up for their first day at work. To reduce this distance, the point is not to 'adapt' the jobseeker to the market by working on self-awareness, but to re-establish contact with employment, and take on the 'idea of going to work every day under a full-time permanent contract, with pay at the end of the month'. Being put rapidly into direct contact with the employer, and visiting the workstation, are the main levers to achieve this. But other tactics can also be useful in matching the worker with a work situation: Mrs M-J, afraid she would not be able to 'keep up' with a full-time job, did not keep her appointments and said she had several allergies. The IOD team manager persuaded her to promise to come to the job centre every morning, note any job offers that might be of interest and give them to the team. She finally found a fulltime, permanent job as a chambermaid and her employer is very satisfied with her work.

The most receptive businesses are mainly small and medium-sized companies, which often have turnover problems with unqualified staff, probably because the work is hard and the pay low, or because staff are overqualified. The team's network of businesses also includes 'socially responsible' or more 'caring' companies (for instance, company K), which are aware of the problems currently encountered by the unemployed and are open to innovative methods. Large companies governed by recruitment procedures are more difficult to convince, although it is possible to 'get into big groups by the back door': a worker was hired by a hotel group through the intermediary of one of its hotels that was in charge of recruitment. The programme's failures can be explained by employers' lack of patience, leaving the workers almost no chance when they are very rapidly judged inefficient, or by poor integration monitoring.

Mrs R. was hired on a trial basis as order preparer in a sandwich shop. After three hours, the employer wanted to end the trial: 'she's inefficient and therefore not a good investment'. Mrs R later found a full-time permanent job as a chambermaid.

Mrs P was hired on a trial basis as an accounts clerk, but only worked one week. The employment mediator analysed this failure as the result of poor monitoring, considering he had waited too long to fix a follow-up meeting.

Discussion and conclusion

This study shows that labour demand cannot be considered as an objective fact in a rational selection procedure. Treating hiring and integration practices as social constructs that can be modulated and transformed gives the job mediator back a genuine intermediation position, at the intersection of supply and demand. In this respect, job accompaniment focuses here more on job placement through tripartite negotiations rather than job search centred on jobseekers' personal difficulties. One major conclusion of the observations is that the long-term unemployed and RMI beneficiaries, who often suffer discrimination, are not as 'unemployable' as generally thought. The companies' change in hiring behaviour is another strong finding, confirmed by evaluation of Transfer's activities at national level in 2005 (Transfer, 2006) which shows that in more than 60 % of confirmed permanent contracts, some selection criteria have been neutralized: professional experience duration, education level, patronymic; and work conditions have been negotiated to give less vulnerability. In more than 80 % of confirmed permanent contracts, the recruitment was made without a CV, after a tripartite interview, and with one single candidate being presented (no competition). A progression in job task or wage or responsibilities has been negotiated in more than 50 % of confirmed, permanent contracts.

In appraising the wider applicability of these findings, this evaluation shows that the IOD method gives relatively good outcomes and does not introduce prohibitive costs. In 2005 indeed, the back-to-work rate was 67 % (72% in 2002), the rate of return to permanent confirmed work was 41% (46 % in 2002), and 75 % of these permanent contracts have been confirmed within 6 months; 800 workers, beneficiaries of minimum income benefit for 24 months, have found a job. Between 2003 and 2005, the work of IOD teams with 6,000 firms enabled 10,000 jobseekers to find a permanent job. The relative cost is 2,400 € per person (a budget of 16,500,000€ for 6,963 people) and 5,500 € per person returned to permanent confirmed work. Comparisons with other back-to-work policies for long-term unemployed are difficult in the absence of common basis. The back-to-work programmes as part of the PARE give a back-to-work rate of 30% for 2005 [START_REF] Crépon | Un bilan de l'accompagnement des chômeurs[END_REF] and the costs are about 750€ for a 3 months programmes. But the mean cost of longer privately operated back-to-work programmes is 2,300€ (source: ANPE, Klein, Renard and Traversier, 2006, p.2-3).

While this analysis concerns the French context to a large extent, the discussed hypotheses and the achieved results relate to the general, transnational problem of reducing long-term unemployment and professional exclusion. As such, promoting contact with employers and speedy return to a work situation are the main levers common to both the IOD method and the American Welfare-to-Work programmesunlike coercive aspect of these latter (benefit payments are conditional on having a job) that can have potentially damaging effects in terms of poverty and social exclusion [START_REF] Weir | The Uncertain Future of Welfare Reform in the Cities[END_REF]. It seems that lessons learned from the IOD programme could be extended, on the one hand, to other countries which have the same concerns and are ready to accept mediators' intervention; and on the other hand to vulnerable jobseekers with qualifications that are not always legible on a CV and for whom the tactics used might be slightly adapted.

The interventionist approach is not the only valid back-to-work method and a degree of worker's adaptation is sometimes required, but it remains too rarely considered at both theoretical and practical levels of employment policies. The IOD method proposes innovative devices that are promising for the most vulnerable unemployed and that can lead to new public policy guidelines. The findings of our study have some theoretical implications. According to the 'labour quality convention' approach, observations show that the employability of the long-term unemployed -and the definition of labour quality -depends above all on the context, selection methods and recruitment tools: recruitment processes based on a negotiation between the employer, the applicant and an intermediary, without CV, allows to redress the balance of competition and focuses on emergent and distributed skills. It also prevents from employers' over-selection and enables long-term unemployed return to work more promptly. This finding confirms experimental psychology research by [START_REF] Castra | Mécanisme implicites de prises de décision dans la situation de recrutement[END_REF] which shows that the outcomes of simulated classic hiring interviews vary a lot with the selection methods and tools implemented. Indeed, our study shows that the rationality of assessment of labour quality is situated: taking into account the real context of the vacancy often allows to reorient the selection in favour of the outcasts.