Antoine Vernet

Esther Berner

Philipp Gonon

Solving the Crisis. VET as an Economic Policy (France, from the Long Depression to the Second Oil Crisis)

Keywords: public policies, local authorities, economic crisis, employment

In modern France, economic crises have presented an opportunity for administrations to intervene directly in economic and social affairs. On these occasions, the vocational education and training system was used as a policy instrument to address the difficulties of the time, i.e. the necessity to revive the French industry during the Long Depression, the will to direct the workforce toward disadvantaged professional sectors during the crisis of 1930s, and the requirement to facilitate the professional integration of youth into the labour market during the Oil Crises of the 1970s. This paper is thus concerned with the diversion of vocational training practices for the benefit of these issues, both at legislative and regulatory levels, as well as in a local context, provided by the industrial district of Saint-Étienne.

Highlighted through the works of Gary Becker [START_REF] Becker | Human Capital: A Theoretical and Empirical Analysis with Special Reference to Education[END_REF], the concept of human capital has turned the issue of education into one of the most relevant means for socioeconomic prosperity. Robert Lucas used human capital by applying it, not to individual career paths, but rather to states [START_REF] Lucas | On the mechanics of economic development[END_REF]. He modelled its influence on workers' productivity, and as such on the economic growth of countries. However, neoclassical stances are particularly limited in their analysis of social phenomena, and do not reflect the whole complexity of human rationality. They fail to explain how the different categories of collective actors involved in these processes are able to negotiate and create educational paths. Historical institutionalism, on the other hand, is more likely able to present those relationships [START_REF] Thelen | How Institutions Evolve: the Political Economy of Skills in Germany, Britain, the United States[END_REF].

Education is not only considered to be a way of fostering economic development, at individual and territorial levels. Its promotion also occurs during harsher times like economic crises. Since 2008 and the so-called Great Recession, investment in education looks more than ever looks likely to be one of its key remedies. The OECD in particular promotes the efficiency of such a solution (OECD 2010). Literature written on this specific subject exists, both for education in general [START_REF] Heyneman | Economic crisis and the quality of education[END_REF]; Ewing/Hicks 2006) and more specifically on vocational education and training (VET) [START_REF] Koudahl | Vocation education and training: dual education and economic crises[END_REF]. But however, these studies relate mainly to Anglo-Saxon countries, while the French case, for instance, has not been addressed in this regard.

Contrary to the British workplace-based training and the corporatist German dual model [START_REF] Greinert | Mass vocational education and training in Europe[END_REF], the French VET system is characterized, by state intervention. From the liberal Second Empire to the post-1945 welfare state [START_REF] Kuisel | Capitalism and the State in Modern France: Renovation and Economic Management in the 20 th Century[END_REF][START_REF] Rosanvallon | L'État en France de 1789 à nos jours[END_REF], and from the dirigiste economic-planning to the État brancardier (stretcher-bearer state) [START_REF] Cohen | L'État brancardier : politiques du déclin industriel 1974/1984[END_REF], the VET network developed along two interactive ways: first, through the establishment of a regulatory framework by the public authorities [START_REF] Chapoulie | L'École d'État conquiert la France. Deux siècles de politique scolaire[END_REF] and second, through certain local initiatives, more or less efficient, depending upon the financial support of administrations [START_REF] Bodé | L'offre locale d'enseignement. Les formations techniques et intermédiaires, XIX e -XX e siècles[END_REF]. Both aspects responded, according to the level of political intervention in economic matters.

When considered as a historical process, the relation between VET and economic policy raises the following questions. Firstly, when did the use of VET as an economic intervention device begin? Secondly, who amongst administrations, local authorities and employers is the main actor behind these VET changes? The consequences in the education/training debate arise from this leadership. And thirdly, what is the sustainability of such organizational changes? In response to these questions this paper will consider three major economic downturns since the late 19 th Century: the Long Depression, the Great Depression and the Oil Crises. It will consider the education/training debate. The diverse range of public receiving training must also be taken into account. To explain the challenge that crisis situations present for VET policies, questioning the local/national relations, particularly between the national and local ones, proves helpful. Therefore, the national chronology will be compared with examples drawn from a case study devoted to the organization of VET in an industrial region: the industrial district of Saint-Étienne, in the Loire department.

The Long Depression (1873-1885): industrial concerns rather than economic competition

Debated on its status and named after a disputed expression, the Long Depression was actually more of a slowdown in economic growth rather than a real depression. Prices dropped globally, which led to a decrease in economic activity with this being particularly acute in the French situation. While the decline was only relevant when compared to foreign competition, it therefore became especially important when comparing with Germany [START_REF] Asselain | Histoire économique de la France du XVIII e siècle à nos jours, tome 1, De l'Ancien Régime à la Première Guerre mondiale[END_REF]. Owing to market, agricultural and demographic factors, the Long Depression revealed the diminishing effects of the First Industrialization and its main activities, mainly in textiles and metals. The progressive mechanization of industrial production continued and the ever greater need for scientific and technical knowledge affected labour organization. In the meantime, increased competition in international trade raised a significant economic problem that the political field would have to solve.

The debate surrounding vocational education and the "crise de l'apprentissage"

The first part of the Third Republic was challenging. From the downfall of the Emperor Napoléon III in early September 1870, to the stabilization of the Republican government in 1877, any want for institutional reform faced significant resistance.

Once the situation was resolved, the legislative work began. For example, the Ferry laws (1881-1882) imposed mandatory, secular and free primary education, though this was not the sole example. Vocational education, a major oversight of the schooling system reforms during the 19 th Century, was finally enacted through its founding text. The 11 th December 1880 Act implemented the écoles manuelles d'apprentissage [START_REF] Brucy | Histoire des diplômes de l'enseignement technique et professionnel[END_REF][START_REF] Chapoulie | L'École d'État conquiert la France. Deux siècles de politique scolaire[END_REF]. They came under the control of the Ministry of Trade and Industry, though the status mainly applied to other existing schools, attached to the Ministry of Public Instruction, known as the écoles primaires supérieures (upper primary schools). Established by the Guizot law of 1833, then theoretically abolished in 1850, these schools experienced a new dynamism following the Ministerial Circulaire of 16 th May 1878 [START_REF] Briand | Les collèges du peuple. L'enseignement primaire supérieur et le développement de la scolarisation prolongée sous la Troisième République[END_REF]. This double administrative tutelage slowed the development of vocational schools for ten years.

The text of the law did not offer up any economic justification for its inception (Charmasson/Le Lorrain/Ripa 1987). However, it could only be understood through the growing debate surrounding the crise de l'apprentissage (apprenticeship crisis) [START_REF] Chapoulie | L'École d'État conquiert la France. Deux siècles de politique scolaire[END_REF][START_REF] Lembré | L'école des producteurs. Aux origines de l'enseignement technique en France[END_REF]. The economic downturn and German rivalry were therefore particularly serious. The instruction of vocational training was discussed at the Congrès international du commerce et de l'industrie, organized alongside the World Exposition of Paris in 1878. Defenders of the apprenticeship renovation argued against those partisan to the development of vocational schools. While the debate was partly solved with the 1919 Astier Law [START_REF] Brucy | Un siècle de formation professionnelle en France : la parenthèse scolaire ?[END_REF], in both cases, crisis awareness was not the main motivation for these positions. Know-how, skills and social relations within workshops, especially for men, mattered more. The crisis situation does not fully explain the occurrence of institutional change, however certain elements of it do (technological and organisational evolutions, quest for competitiveness).

From the legislative framework to local initiatives

While Gérard Bodé characterizes the 1815-1880 period as the time of local initiatives, the next one cannot yet be regarded as marked by systematic state intervention [START_REF] Bodé | L'enseignement technique dans le département de la Loire entre 1815 et[END_REF]. Municipalities had to finance the opening of vocational schools. Some localities had already established such institutions, such as in Paris and Le Havre, while others took advantage of employers' initiatives, namely in Lyon and Mulhouse. In Saint-Étienne, an attempt in 1865 to install vocational courses for apprentices, the Société d'enseignement professionnel de la Loire, was patterned after the Lyon model, though it collapsed in 1872 due to lack of municipal support and failing in the employers' philanthropy. The 1870s continued to experience demand for the technical training of future workers, concerning almost exclusively men. The city of Saint-Étienne demanded in 1879 for the establishment of an école d'arts et métiers. A subscription was put into place, which involved the major municipalities in the department and the chamber of commerce1 . Despite these efforts, competition was tough and the administration eventually chose to locate the school in Lille.

This setback did not stop local aspirations, and in the same year, the radicalsocialist municipality of Saint-Chamond, an industrial and medium-sized city close to Saint-Étienne, opened an école primaire supérieure2 . It was intended to be as a vocational school, which would prepare candidates for the anticipated arrival of the école d'arts et metiers. While its first years were middling, the formula quickly became so convincing that Saint-Étienne recruited the school director to create its own school in 18823 . In following, the socialist municipality simply dismissed the Brothers of the Christian Schools from its école primaire supérieure for boys, and as a response, local Catholic employers supported the opening of a new school run by the brothers. Its purpose was to train highly-skilled workers who would then go on to become "excellent Christian foremen4 ".

The opening of these schools occurred while the creation of such institutions was on the policy agenda. Skills and industrial activity were its main motivation, however it was the notion of economic competition that applied to another school. As it was directly related to traditional activities like the ribbon and weapon industries, the Municipal drawing school greatly interested the city council. A 28 th June 1880 debate outlined its economic challenges5 . Foreign competition was characterized not only by a cheaper workforce, but also by the "good taste and art" of the contending cities, illustrating the "state of suffering" of Saint-Étienne's industries. Local activities were able to maintain their superiority "provided that, from generation to generation, worship and science of this good taste and that art are profusely extended to the working class". The fear of foreign competition motivated the reorganization of the school in 1884, which was run by both the city and the Beaux-Arts administration. Resembling a series of evening classes more than an actual day school, the new école régionale des arts industriels (regional school of industrial arts) brought together many already existing vocational courses, with a number of them taking place at the école primaire supérieure 6 . Ultimately, while the economic situation partly explained the creation of schools, the Long Depression was not considered by the actors to be a decisive criterion. This argument was implicit, perhaps because the issue of unemployment had not yet been construed as a category of public policy, contrary to during the 1930s [START_REF] Salais | L'invention du chômage[END_REF][START_REF] Topalov | Naissance du chômeur : 1880-1910[END_REF]. The acknowledged value of vocational schools, as well as the constant support of municipalities and administrations helped to stabilize them during the crisis and beyond. Indeed, these schools would once again become relevant during the 1930s crisis.

The Great Depression (1929-1939): training for employers' needs

The Wall Street Crash of 1929 was not immediately reflected in the French economy. However from 1931, the inadequacies of the production system come to light [START_REF] Caron | Histoire économique de la France XIX e -XX e siècle[END_REF]. Moreover, despite its late entry into the crisis, when compared to its main competitors, France's recovery also occurred late. The French governments were primarily obsessed with monetary stability, as there was no real economic policy before 1935. The fight against unemployment was also slowed by serious difficulties, related to the inefficiency of the recording of jobless workers and inadequacies between the creation of certain categories and the actual situations (Salais/Baverez/Reynaud 1986). The effects of the economic slowdown were initially diminished by the limitation of the foreign workforce and the return of dismissed workers to rural areas. The deepening crisis mainly affected unskilled and semiskilled workers. As a result, administrations were concerned about apprenticeship, which they tried to highlight anew. However, this was not the most innovative aspect of the period. With the spread of scientific management [START_REF] Moutet | Les logiques de l'entreprise. La rationalisation dans l'industrie française de l'entredeux-guerres[END_REF], the skills required in larger metalworking firms evolved and yet another training pathway developed during the 1930s: the retraining of unemployed workers.

From mass unemployment... The Great Depression was the first large-scale opportunity in which a traitement social du travail (literally social treatment of unemployment) could be applied, as Keynesian views on public spending in the economic field developed [START_REF] Desrosières | Prouver et gouverner. Une analyse politique des statistiques publiques[END_REF]. For their part, employers' organizations, such as the Union des industries métallurgiques et minières (UIMM -Metalworking and Mining Industries Union) considered the treatment of unemployment to be a major issue linked to the regulation of the labour market [START_REF] Fraboulet | Quand les patrons s'organisent. Stratégies et pratiques de l'Union des industries métallurgiques et minières 1901-1950[END_REF]). The problems were so important that the employers' delegates at the Work Placement Administrative Commission of the Loire department suggested, during the 24 th February 1931 meeting, that unemployed people should use their spare time to acquire professional knowledge that would help them find new jobs 7 . This recommendation primarily targeted young workers aged between 18 and 35 years, who were considered to be less affected by routine and bad habits. The envisioned training courses should also be optional. However the burden of supporting such an organization and the problem of providing unemployment benefits during training prevented any realization. Public vocational schools still kept jobless youth busy over the age requirement for compulsory courses 8 .

Subsequently, the legislative work began. A 15 th October 1932 Ministerial Circulaire provided measures for the adaptation of unskilled workers in vocational schools [START_REF] Bodé | L'enseignement technique de la Révolution à nos jours[END_REF]. Another Circulaire from the 14 th January 1933 imposed that unemployed youth, who were recipients of municipal funds, must follow vocational courses. However, school principals were reluctant to connect their students with workers of questionable morality 9 . Furthermore, there was a lack of workforce-poor industries therefore unemployed people would have to be oriented towards professions with high levels of foreign labour. In a letter to the Prefect of the Loire department written on the 6 th December 1932, the President of the Chamber of Commerce in Saint-Étienne questioned the effectiveness of such a policy10 . He was particularly sceptical regarding the interest of unemployed workers in attending the vocational schools and mandatory courses. Despite such reluctance, the formula became more definite. A Circulaire dated the 29 th November 1934 specified the intervention methods for Vocational Education administration in the training of unemployed workers. The decrees of the 30 th and 31 st October 1935 involved the Ministry of Labour in the approval of retraining centres, which at the time were more focused on training than education per se. The UIMM participated directly in this regulatory work [START_REF] Bonnet | La formation professionnelle des adultes : une institution et ses formateurs[END_REF][START_REF] Fraboulet | Quand les patrons s'organisent. Stratégies et pratiques de l'Union des industries métallurgiques et minières 1901-1950[END_REF]). In the Saint-Étienne region, employers initially required the lack of any constraint on the placement of workforce. In April 1936 the Departmental Labour commission responded to a survey by the Ministry of Labour 11 . It believed that unemployed youth should be oriented towards new occupations, without encouraging the establishment of dedicated retraining centres. Existing vocational schools and apprenticeships should be privileged. The Front populaire's ministry, which governed from May 1936 to April 1938, did little to change the process. A census of unemployed people was initiated through the application of a 26 th September 1937 decree. The aim was focused as much on placing the skilled workforce as retraining the unskilled one. Joint Committees were implemented at the local level and mobilized vocational education staff, which included employers and workers completing inspection duties. These commissions were intended to assess professional skills of jobless persons before directing them to placements 12 .

... to mass production

The situation then evolved quickly with the economic crisis making room for the arms race. Due to a lack of skilled labour, war industries necessitated the implementation of accelerated training. The 12 th November 1938 décret-loi (decree-act) increased the funding for retraining centres set up by private initiatives. The first centres, created as early as 1935 at the instigation of metalworking employers' organizations such as the UIMM, connected to labour in the Paris region, even though they were located outside [START_REF] Fraboulet | Quand les patrons s'organisent. Stratégies et pratiques de l'Union des industries métallurgiques et minières 1901-1950[END_REF]). While such a centre was recognized as being valuable for the metalworking industry in the Saint-Étienne region in June 1938 13 , its implementation was not achieved until the end of 1939 due to a lack of available premises 14 . The local employers therefore favoured private or firms' vocational schools.

Despite the Battle of France in June 1940, the training path introduced during the 1930s crisis remained. The former accelerated training centres hosted unemployed youth from the summer of 1940 and after the war, they became centres d'apprentissage (apprenticeship centres, now lycées professionnels). The institutionalization of skilled workers training marked the finest hours of the parenthèse scolaire (schooling parenthesis) [START_REF] Brucy | Un siècle de formation professionnelle en France : la parenthèse scolaire ?[END_REF]. For its part, adult accelerated training grew in significance from 1944 as it had to provide the skilled workforce needed to rebuild the country and the national economy. Even though many companies or employers' associations' centres closed thereafter, the establishment of worker advancement practices opened the way for the development of Training Within Industry, in large firms or dedicated agencies. The Great Depression offered an opportunity to extend the practice of training to new audiences, and this pattern was once again seen at work during the Oil Crises.

The Oil Crises (1973-1982): the dual training cure

The First Oil Crisis in 1973 ended what the French economist Jean Fourastié called the Trente Glorieuses (the Glorious Thirty, roughly from 1945 to 1975). Much like during the Great Depression, France experienced a slower start in its shift to the crisis [START_REF] Boyer | La spécificité de l'industrialisation française en quête de théories : essor et crise d'une variante étatique du modèle fordiste[END_REF]. Economic problems did not stop at the simple matter of oil prices. Dependence on state intervention in certain sectors, a lack of support for innovative industries like capital goods, the decline of public procurement and the low competitiveness of French products in export as well as on the domestic market were all major factors used to explain the severity of the situation. Despite its size, the crisis was initially experienced as a classic cyclical economic crash [START_REF] Caron | Histoire économique de la France XIX e -XX e siècle[END_REF]. After the difficulties of 1974-1975, the economy temporarily resumed until the second oil shock in 1979. Meanwhile, technological advances, the globalization of trade and the slowdown of traditional industries in Western countries caused a real downturn in the productivity of capital and labour. The crisis of the Fordist model then forced the reconsideration of both employment opportunities and the skills required by firms, which tended to disappear in favour of competencies. This change accompanied that of work organization and processes [START_REF] Stroobants | Savoir-faire et compétences au travail. Une sociologie de la fabrication des aptitudes[END_REF], in part motivated by the willingness of companies to control professional certification [START_REF] Zarifian | Le modèle de la compétence. Trajectoire historique, enjeux actuels et propositions[END_REF].

Integrating unemployed youth into the labour market

The impact of economic difficulties primarily affected the most vulnerable groups, namely the foreign workforce, women, older workers and young people, especially those who were unskilled. Despite compulsory education being extended to the age of 16 in 1967, youth access to the labour market was blocked. At the same time, diplomas were seemingly becoming increasingly disconnected from job openings. These factors became the base for the concept of insertion professionnelle (professional integration) (Nicole-Drancourt/Roulleau-Berger 2006). This concept allowed treating a specific statistical category that, apart from qualifications and recognized skills, was relatively undifferentiated in its characteristics. In the wake of work conducted by the Commissariat général au Plan commissions, public policies now had to deal with flows of people in order to get them into employment [START_REF] Tanguy | L'introuvable relation formation-emploi[END_REF]. Vocational integration could only be effective if trained workers were adaptable and suitable to labour market needs. Therefore, employability became a key concept.

The VET reforms, especially the 16 th July 1971 laws on apprenticeship and continuous training, dramatically changed the educational landscape. Vocational training now benefited from regular funding from administrations [START_REF] Chapoulie | L'École d'État conquiert la France. Deux siècles de politique scolaire[END_REF]. At the same time, the administrative machinery of education was reformed. The 1971 acts endorsed administrative regionalization of VET [START_REF] Terrot | Histoire de l'éducation des adultes en France[END_REF]. A major production of statistics on education was needed for planning, and was conducted through organizations like Céreq (Centre d'études et de recherches sur les qualifications). Through these studies, public authorities began to realize the disparities between skilled and unskilled youth facing unemployment. From 1974, professional integration thus becomes a national issue, inseparable from VET.

Public policies henceforth sought to establish a match between VET and employment, called adéquation formation-emploi [START_REF] Tanguy | L'introuvable relation formation-emploi[END_REF]; Giret/Lopez/Rose 2005; Chapoulie 2010). However the real challenges were found on the margins of the school system. The pressing problem of youth leaving school without a degree or a qualification was now on the policy agenda. A 5 th July 1977 law instituted the first Pacte national pour l'emploi des jeunes (National pact for youth employment). Throughout the length of the crisis, a total of five campaigns occurred from 1977 to 1982. They were perceived as a way of encouraging employers, especially smaller ones, to recruit [START_REF] Charlot | Histoire de la formation des ouvriers[END_REF]. The main actions organized through the Pactes were: social welfare tax exemptions on apprenticeship and youth recruiting, internships, contrats emploi-formation (contracts involving both employment and atwork vocational training, especially for unskilled youth and women) and dual training. Some of these actions already existed before 1977, though the initiative was also a way of communicating the struggle for employment. While the first Pacte was a clear success thanks to the participation of employers, the results of the following campaigns were somewhat mixed. Placement rates tended to gradually decrease [START_REF] Gaspard | Les effets des pactes nationaux pour l'emploi sur l'évolution du chômage[END_REF] with financial conditions and length of training also worsening with each new Pacte. Various support measures were also viewed as falling victim to the deadweight effect [START_REF] Charlot | Histoire de la formation des ouvriers[END_REF].

Pactes thus appeared increasingly ineffective to employers and lost some of their legitimacy. The final one (1981)(1982), launched after the socialist victory in the presidential elections of 1981, even changed its name to Plan Avenir Jeunes (Youth future plan) before succumbing to a major overhaul. The system is nevertheless retained. Bertrand Schwartz, special adviser to the Prime Minister, later introduced a social dimension to professional integration [START_REF] Schwartz | L'insertion professionnelle et sociale des jeunes[END_REF]. Educational aspects once again mattered with youth employability leaving the single statistical approach and instead focusing on individual pathways [START_REF] Quenson | Une socio-histoire des relations formation-emploi[END_REF]. However the highlighting of dual training through the Pacteswhich also occurred within vocational schoolsput an end to the parenthèse scolaire. Therefore dual training became the new benchmark for VET policies [START_REF] Dubar | La formation professionnelle continue[END_REF].

Top-down policy and local VET system

The previously mentioned administrative regionalization did not present local actors with further more decision-making powers. Rather, from a rational regional planning perspective, it appeared to be more like technocratic devolvement than true decentralization [START_REF] Pasquier | Le pouvoir régional. Mobilisations, décentralisation et gouvernance en France[END_REF]. For VET, the dual purpose of regionalization was to enable the coordination of policies with new levels of consultation that were more in tune with the evolution of the modes of representation of professional organizations [START_REF] Terrot | Histoire de l'éducation des adultes en France[END_REF]. Local VET bodies could only provide dual training courses adapted to the needs of employers, whether public or agreed by a Ministry -National Education or Labour and Social Affairs. Departmental observation groups (GOD), comprised of only administrations representatives, selected between the proposals, which were then forwarded to the regional level, where the distribution of allocated funds would be decided15 . Multiple criteria were used, from the employment situation of each department to the estimated value of the various training supplies. Internships were approved by the regional Prefect, and candidates were recruited through local agencies of the Agence nationale pour l'emploi (National employment agency). The role of employers in this decision-making was weak. They could dialog or participate in existing training institutions, directly organize vocational training for the largest ones like Creusot-Loire, or create bodies linked to local trade associations and chambers.

In general, training institutions cooperated in the development of a local VET supply adapted to job opportunities. Following on from the second Pacte, administrations encouraged the implementation of SAS d'orientation (literally Guidance airlock) 16 . It introduced a general testing period for all trainees in order to improve their placement and to share costs. While some form of competition between training providers may have remained, public actors such as universities and GRETA (groupements d'établissements, schools groups dedicated to further education) coexisted alongside to private organizations, that were closer to professionals, in order to share the burden. In Saint-Étienne's case, one institution was symptomatic of the relationship between public policy and private actors.

The Centre interprofessionnel de promotion de la Loire (CIPL) was a joint training organization composed of employers, trade unionists, administrations' and local authorities' representatives. Its actions appeared similar to the experience of the Nancy-based CUCES (Centre universitaire de cooperation économique et sociale) [START_REF] Laot | La formation des adultes[END_REF]). The CIPL organized many courses for promotion sociale (upward mobility based on lifelong learning) to the benefit of regional skills and competencies development [START_REF] Vernet | Du développement économique à la lutte pour l'emploi : la formation en région stéphanoise (1964-1982), study day of the Gremmos, Penser et agir face à la crise dans les "années 1968". Les luttes ouvrières dans le bassin stéphanois[END_REF]. Its actions were funded by government subsidies and a specific taxation on employers. A reduction in economic activities however reduced available funds and, following the systematization of training courses agreement, drove the CIPL to become merely an extension of public actors17 . From a resource for local economic development during the 1960s, it became a remedy for vocational integration. Meanwhile, administrations using local VET actors for labour purposes were inclined to favour the initiatives of employers' trade associations and as a result, corporatist interests prevailed over the common good.

As it relied on the employment possibilities within firms, the dual training formula became problematic when job opportunities decreased due to factory closures and economic downfall. Vocational integration could not help all young job seekers and such a policy could not replace a comprehensive reform of initial vocational education. The 1980s thus experienced major reforms, such as the creation of the baccalauréat professionnel in 1985 and the extension of apprenticeships to baccalauréat and higher education levels in 1987.

This study has allowed us to consider two types of crisis: with or without mass unemployment, since technological and organizational changes permanently remain. VET was used in many different ways to assist economic recovery, such as improving workers' skills, adapting to industrial needs and integrating into the labour market. These initiatives generally survived the experience of the crisis and proved their sustainability, sometimes at the expense of further adjustments. The Long Depression necessitated the opening of vocational schools. The Great Depression required the commitment of employers for retraining. The Oil Crises demanded an adaptation of the training supply. In each of these cases, the means required the coordination of national policies with local resources. The changing nature of the local actors involved should also be noted: municipalities and employers; employers and devolved administrations; devolved administrations and VET institutions. Local practices had a tendency to precede legislative and regulatory changes and the creation of new VET streams used these local initiatives. These crises acted as critical junctures and revealed the need for new pathways, even if they difficultly came ex nihilo and were more readily related to employment policies than economic ones. Unemployment created this confusion, as employability does not mean employment. The small number of people thus trained also limited the effects of VET as an emergency fix. The paths opened by these institutional changes were later used to improve the availability of skills and competencies to the labour market. Therefore in the current French context it is somewhat confusing that the government continues trying to emphasize apprenticeship, despite the economic situation being disadvantageous to its extension.

7

  ADL, 10 M 195: meeting of the Work Placement Administrative Commission of the Loire department, 24 th February 1931. 8 ADL, 123 W 29: letter from the Director of the École pratique d'industrie de garçons in Rive-de-Gier (Municipal school of industrial practice for boys) to the Prefect of the Loire department, 14 th February 1932; letter from the Directress of the École pratique de commerce et d'industrie de jeunes filles in Firminy (Municipal school of trade and industry practice for girls) to the Prefect of the Loire department, 23 rd February 1932. 9 ADL, 123 W 29: meeting of the Loire Commission on the retraining of unemployed workers within vocational education schools, 20 th January 1933.

Departmental Archives of the Loire (ADL), 9 M 123: subscription for the establishment of an école d'arts et métiers in Saint-Étienne, [1879].

Municipal Archives of Saint-Chamond, 1 Dsc 15: register of Municipal Council debates, 1877-1879.

Municipal Archives of Saint-Étienne (AMSE), 9 C2 2: Municipal Council debate from 17 th July 1882.

Lasallian Archives (Lyon), archival fonds from the École Sainte-Barbe: Saint-Étienne École professionnelle, sommaire des événements1882-1886, s.d.

AMSE, 1 D

61: Municipal Council debate from 28 th October 1880, report from the Deputy Mayor Montegu on the reorganization of the drawing school. 6 ADL, T 2092: report from the director of the École régionale des arts industriels to the Prefect of the Loire department, May 1921.

ADL, 123 W 29: letter from the President of the Chamber of commerce of Saint-Étienne to the Prefect of the Loire department, 6 th December 1932.

ADL, 1192 W 50-56: files from the Pactes nationaux pour l'emploi des jeunes' enforcement in theLoire department, 1977Loire department, -1982. .

ADL, 1192 W 53: CIPL, Action intégrée 50 jeunes, 21 st June 1979.

ADL, 1192 W 50: CIPL, Note sur les conséquences financières prévisibles entrainées par la mise en place de la loi du 5 juillet 1977, 22 nd July 1977.


Zaaraoui
email: hind.zaaraoui@orange.com

Zwi Altman
email: zwi.altman@orange.com

Eitan Altman
email: eitan.altman@sophia.inria.fr

Tania Jimenez
email: tania.jimenez@univ-avignon.fr

Forecast scheduling and its extensions to account for random events

Keywords: Forecast scheduler, alpha-fair, high mobility, Radio Environment Maps, geo-localized measurements, random events, trajectory uncertainty

Technology evolutions make possible the use of Geo-Localized Measurements (GLM) for performance and quality of service optimization thanks to the Minimization of Drive Testing (MDT) feature. Exploiting GLM in radio resource management is a key challenge in future networks. The Forecast Scheduling (FS) concept that uses GLM in the scheduling process has been recently introduced. It exploits long term time and spatial diversity of vehicular users in order to improve user throughputs and quality of service. In a previous paper we have formulated the FS as a convex optimization problem namely the maximization of an α-fair utility function of the cumulated downlink data rates of the users along their trajectories. This paper proposes an extension for the FS model to take into account different types of random events such as arrival and departure of users and uncertainties in the mobile trajectories. Simulation results illustrate the significant performance gain achieved by the FS algorithms in the presence of random events. a

I. INTRODUCTION

The use of GLM to improve network performance and profitability is receiving growing interest by network operators. The reason is threefold: First, it allows the operator to better know what is the real Quality of Service (QoS) provisioning to customers at any location (and not only at cell level). Second, it provides significant levers to optimize the network performance; and third, it allows personalized, user centric optimization. GLM can feed new Radio Resource Management (RRM) algorithms, Self-Organizing Network (SON) algorithms, and in general, a management entity responsible to configure, optimize and troubleshoot the network. This view of a This work has been partially carried out in the framework of IDEFIX project, funded by the ANR under the contract number ANR-13-INFR-0006.

GLM utilization corresponds to the general trend in 5G networks, namely the utilization of data from different sources in order to improve network operation. The data can feed applications on top of the Operation Support System such as a centralized SON server or directly feed virtual network functions in the virtual radio access network.

The perspective of having GLM has opened an active research and development domain, namely the construction of Radio Environment Maps (REMs) using spatial interpolation techniques [START_REF] Farnham | Radio environment map techniques and performance in the presence of errors[END_REF]. [START_REF] Braham | Spatial prediction under location uncertainty in cellular networks[END_REF] for example utilizes coverage prediction algorithms based on geo-statistics Fixed Rank Kriging algorithm which is adapted to handle geo-location errors. The REM can be created and updated in a MDT server in the management plane and be downloaded into each Base Station (BS). It can provide maps for different quantities such as the received signal strength or Signal to Interference plus Noise Ratio (SINR). The BS can then use the REM to derive policies, to optimize different RRM algorithms such as association, handover or resource allocation, or manage interference and coverage problems. It is noted that in spite of the potential plethora of applications provided by REMs, most of the research has focused on the creation of the REM itself.

The capability of User Equipments (UEs) to report GLM to the network finds its roots in the introduction of MDT in the Long Term Evolution (LTE) standard [START_REF] Hapsari | Minimization of drive tests solution in 3GPP[END_REF]. The term MDT was motivated by the need to replace costly drive tests in order to manage and to troubleshoot the network using GLM generated by UEs. The MDT feature is presently available in mobile chipsets and can be activated by mobile operators.

The purpose of this paper is to design a scheduler, namely the FS that, by utilizing a REM, can benefit from long-term time-space diversity. The basic concept of the FS has been introduced in [START_REF] Zaaraoui | Forecast scheduling for mobile users[END_REF] with application to data type of services. The FS allocation is formulated as a convex optimization problem, namely the maximization of an α-fair utility function of the cumulated rates of the mobile users along their trajectories. Similarly to the classical α-fair scheduling such as the Proportional Fair (PF) [START_REF] Mo | Fair end-to-end window-based congestion control[END_REF], [START_REF] Combes | Scheduling gain for frequency-selective Rayleigh-fading channels with application to self-organizing packet scheduling[END_REF], the forecast scheduler is an opportunistic scheduler with a degree of fairness depending on the choice of the α-fair parameter. However, the scheduling gain is not related to short term user diversity in fast fading states (measured in a millisecond timescale) as in classical α-fair scheduler, but to the long term user diversity along the trajectory. An important result of [START_REF] Zaaraoui | Forecast scheduling for mobile users[END_REF] that motivates the FS approach is its robustness to interference: The interference condition used to generate the REM with respect to the actual one experienced by the users has little impact on the scheduler decision, and negligible impact on the allocated rates.

Several contributions in the area of anticipatory or proactive scheduling have been recently repported (see for example [START_REF] Tsilimantos | Anticipatory radio resource management for mobile video streaming with linear programming[END_REF] and references therein), with particular focus on video streaming applications. In [START_REF] Tsilimantos | Anticipatory radio resource management for mobile video streaming with linear programming[END_REF], using the play-out buffer state and future channel states, the authors optimize spectral efficiency while avoiding or minimizing stalling durarion.

This paper generalizes the FS formulation to include random events such as arrivals and departures of users, or uncertainty in the predicted trajectories. The contributions of the paper are the following:

• The α-fair concept is extended to the FS fairness,

• A multiclass version of the FS is formulated,

• Heuristic solutions for the FS are developed to take into account random events such as users' arrivals and departures and uncertainties in their trajectories.

The paper is organized as follows: Section II recalls the basic FS model and shows how it extends the standard α-fair scheduling. Section III generalizes the FS model to the multiclass case, and proposes heuristic solutions to take into account random events. Numerical results for the different FS formulations are described in Section IV followed by concluding remarks in section V.

II. BASIC MODEL

In this Section we briefly recall the basic formulation of the FS as presented in [START_REF] Zaaraoui | Forecast scheduling for mobile users[END_REF]. Then, using Karush-Kuhn-Tucker (KKT) conditions, we show the relation between the FS and the α-fair scheduling.

A. Forecast scheduling formulation

Consider a macro-cell (BS) surrounded by interfering BSs. A REM is deployed in the BS and provides SINR values corresponding to the mobile location. It is recalled that a REM can provide the metric values (SINR in our case) at any point of the map thanks to interpolation algorithms, and hence any scheduling periodicity can be considered.

Consider n full buffer users moving at a constant speed during a time interval T -the scheduling period, over which n is considered constant. Suppose that time is in a discrete space: t ∈ {1, 2, .., T } = [|1, T |] and let i denote the user number, i ∈ {1, 2, .., n} = [|1, n|]. We suppose that during the scheduling duration there are no arrivals or departures of users (this assumption is later on relaxed).

A scheduling period T (typically of the order of seconds) is divided into scheduling time slots denoted here for simplicity as time units (e.g. of 1 ms), during which the bandwidth is shared among the scheduled users. Let a i (t) denote the bandwidth proportion allocated to a user i at time t, a i (t) ∈ [0, 1], according to the scheduling strategy, where ∀t, n i=1 a i (t) = 1, and W -the total bandwidth. Using the Shannon equation, we write the throughput as a function φ of the SINR of user i as follows ai(t)φ(SIN Ri(t)) = ai(t)W log2(1 + SIN Ri(t)). [START_REF] Farnham | Radio environment map techniques and performance in the presence of errors[END_REF] Denote by S t i the predicted SINR (i.e. the one provided by the REM). The FS allocation policy is defined by the following optimization problem, with α = 1:

maximize : f (a) = n i=1 ( T t=1 ai(t)φ(S t i )) 1-α 1 -α (2) subject to : ∀i, ∀t, ai(t) ≥ 0 ∀t, n i=1 ai(t) = 1
and for α → 1, the optimization problem with the same constraints reads:

maximize : f (a) = n i=1 log( T t=1 ai(t)φ(S t i )). (3)
Both equations ( 2) and (3) have concave functions f for α ≥ 0, and can be solved using convex optimization. For example, one can use the convex optimization solvers such as CVX [START_REF] Research | CVX: Matlab software for disciplined convex programming, version 2.0[END_REF]. The size of the optimization problem is defined by the number of unknown variables, namely n × T .

The interpretation of ( 2) and ( 3) is the following: resources are shared fairly among the users according to the data-rate variation in their future trajectories. For example, if a user has a large enough coverage hole in his future trajectory, the forecast scheduler will take this into account and may allocate this user as much data as possible before reaching the coverage hole so as to remain fair with respect to the other users.

B. KKT for computing the FS

We briefly present the KKT optimality conditions for the forcast scheduling problem [START_REF] Braham | Spatial prediction under location uncertainty in cellular networks[END_REF]. It is known to provide necessary and sufficient optimality conditions. We have been using this approach to obtain closed form solutions in the special case of two users.

The objective and constraint functions in (2) are continuously differentiable for any a = (a 1 (1), ...a 1 (T ), a 2 (1), ..., a n (T )) ∈ R nT , then there exist multipliers λ k,j and ν j , where k ∈ [|1, n|] and j ∈ [|1, T |], called KKT multipliers ( [START_REF] Boyd | Convex optimization[END_REF], Chap.5) with the following Lagrangian function:

L(a, ν, λ) = f (a)+ T j=1 ν j ( n k=1 a k (j)-1)+ k,j λ k,j a k (j), (4)
where λ k,j ≥ 0.

We define the Lagrange dual function as the maximum value of L over a. Let a * maximize the Lagrangian function (4) for the optimal multipliers λ * k,j and ν * j , where k ∈ [|1, n|] and j ∈ [|1, T |]. The gradiant at this point is null:

∇L(a * , ν * , λ * ) = 0 (5)
hence for all i ∈ [|1, n|] and t ∈ [|1, T |] the following KKT conditions should be verified:

∂f (a) ∂a i (t) + ∂ ∂a i (t) T j=1 ν j ( n k=1 a k (j) -1) + ∂ ∂a i (t) k,j λ k,j a k (j) = 0, a i (t) ≥ 0, n i=1 a i (t) = 1, λ i,t a i (t) = 0, λ i,t ≥ 0, which is equivalent to : φ(S t i )( T j=1 a * i (j)φ(S j i )) -α + ν * t + λ * i,t = 0, (6)
a * i (t) ≥ 0, (7)
n k=1 a * k (t) = 1, (8)
λ * i,t a * i (t) = 0 (9) λ * i,t ≥ 0. (10)
We note that from [START_REF] Combes | Scheduling gain for frequency-selective Rayleigh-fading channels with application to self-organizing packet scheduling[END_REF], at any time t and for all users i and w, w = i we have

φ(S t i )( T j=1 a * i (j)φ(S j i )) -α + λ * i,t = φ(S t w )( T j=1 a * w (j)φ(S j w )) -α + λ * w,t . (11)
Similarly, from [START_REF] Combes | Scheduling gain for frequency-selective Rayleigh-fading channels with application to self-organizing packet scheduling[END_REF], for all user i and time t and u:

λ * i,t + ν * t φ(S t i ) = λ * i,u + ν * u φ(S u i ) (12)
since ν * t does not depend on the users, and T j=1 a * i (j)φ(S j i ) does not depend on time. Equality (11) explicits the resource balancing among users at each time relative to α in the sense of equalizing the two expressions of each two users.

We deduce from [START_REF] Tall | Virtual sectorization: design and self-optimization[END_REF] that the choice of α impacts the user selection:

• When α = 0, (11) is equivalent to φ(S t i ) + λ * i,t = φ(S t w ) + λ * w,t which means that the scheduled user at a future time t is the one who reaches the highest data rate at t due to equation [START_REF] Boyd | Convex optimization[END_REF]. Interestingly, this particular case is the same as the normal α-fair scheduling since the maximum of the sum in the utility function is the sum of the maximum in this case.

• When α -→ 1 the FS becomes the forecast proportional fair scheduler. • When α -→ ∞ the FS becomes the max-min forecast fairness scheduler.

Consider the case where an optimal policy uses a * i > 0 for all i in some set I * and uses a * w = 0 for w / ∈ I * . Then for all i, k ∈ I * and w / ∈ I * , and by ( 9) that states that λ * i,t = 0 we have

φ(S t i ) ( T j=1 a * i (j)φ(S j i )) α = (13) φ(S t k ) ( T j=1 a * k (j)φ(S j k )) α = φ(S t w ) ( T j=1 a * w (j)φ(S j w )) α + λ * w,t .
Since λ w,t ≥ 0, we have

φ(S t i ) ( T j=1 a * i (j)φ(S j i )) α ≥ φ(S t w ) ( T j=1 a * w (j)φ(S j w )) α .
The above formulation suggests a solution using a water filling type algorithm for this problem, and has enabled us to obtain an explicit solution for the special case of two users only. b

III. MULTICLASS AND RANDOM EVENTS FS PROBLEMS

This Section generalizes the optimization model [START_REF] Braham | Spatial prediction under location uncertainty in cellular networks[END_REF] in order to take into account arrivals and departures of users as well as different classes of users such as fixed and mobile, real time and non-real time services or users having different random trajectories.

A. Multiclass problem

Denote by C 1 the set of real-time active users and by C 2 -the set of non-real time (elastic) users. Let T 1 be the minimum scheduling period for a real time user. T 2 is the FS duration for all users in class C 2 , which is subdivided into minimum scheduling periods of T 1 (namely T 2 >> T 1 ).

Static or low speed users can be included in the set C 1 where users can benefit from fast fading. It is noted that if service differentiation is sought, weighting coefficients w s(i) (s(i) being the service of the user i) can be introduced as in Weighted Fair Queueing scheduling. The new FS model including the real-time class is written follows:

maximize : f (a) = i∈C 2 ( m t=1 ai(t)φ(S t i )) 1-α 1 -α + i∈C 1 m t=1 w s(i) (ai(t)φ(S t i )) 1-α 1 -α (14)
subject to : ∀i, ∀t, ai(t) ≥ 0 ∀t,

i∈C 1 ∪C 2 ai(t) = 1
where m = T 2 /T 1 .

We can have as many classes as types of users and types of trajectories. For example, users approaching a traffic junction with a distance below d are attributed to a new class, denoted as C 3 in Fig. 1. The corresponding duration T 3 for users in C 3 , T 3 < T 2 , is defined as a function of d. The corresponding term added to the objective function of the optimization problem (14) b Research report in preparation.

during the period T 3 is denoted as Restricted Forecast Scheduling (RFS). At the end of T 3 , the users arriving next to the random point with a distance less than d to it are switched to the set C 1 due to both lower speed and trajectory uncertainty (users can turn left, right or continue straight, see Fig. 1).

Fixed

Deterministic fading gain α-fair scheduler C 1

B. Arrivals and departures problem

The extension of the optimization model (2) to include arrivals and departures is described presently. One can make the same extension for the optimization problem (14). New users can be integrated in the set C 1 at each arrival time, however they will not benefit from the FS.

A heuristic solution consists of initializing the optimization problem (2) or (14) at each user arrival and departure. To remain fair among all users, including those who have not yet been scheduled, we recompute the forecast scheduler at each event, taking into account the received past data. This new heuristic scheduling solution is denoted the Updated Forecast Scheduling (UFS) and is inspired by the rolling horizon approach [START_REF] Sethi | A theory of rolling horizon decision making[END_REF]. It is noted that optimizing the problem (2) or ( 14) for each time step or for each random event occurrence time (random variation of speeds, trajectories, number of users), taking into account the received past data, gives the same result, however the latter has significant lower complexity.

When restarting the scheduling algorithm, it is important to reinject the data already received in the last scheduling period in order to remain fair among all users. In Fig. 2 we explicit the scheduling algorithm for the particular optimization problem (2):

f N (a) = n i=1 ( u N -1 t=1 b t i (t)φ(S t i ) 1 -α + T t=u N a i (t)φ(S t i )) 1-α ) 1-α 1 -α (15)

IV. NUMERICAL RESULTS

We present in this Section the numerical simulations obtained using a Matlab simulator. Users are moving with a speed of 50 km/h. It is recalled that at this speed, due to too short coherence time, one cannot exploit fast fading to achieve opportunistic scheduling gain. For this reason we consider the Round Robin (RR) as a base line to the different approaches. The spatial resolution of the REM is of 1m (it is recalled that the REM interpolates GLM), and in 50km/h it corresponds to a 70 ms time intervals over which the SINR is considered constant. Hence the time resolution of the FS is of 70 ms. During this time interval, a fixed allocation is applied, namely the same users are scheduled at a time interval depending on the technology (e.g. 1 ms for LTE). In the scenarios considered in this Section, a Virtual Small Cell (VSC), namely a remotely created small cell using a Large Scale Antenna System (LSAS) [START_REF] Tall | Virtual sectorization: design and self-optimization[END_REF] is considered to enhance spatial SINR diversity along the trajectory.

A. CVX resolution

The objective function of the optimization problem ( 2) is a convex function that calls for convex optimization solver. The CVX library implemented in Matlab to resolve this kind of problems has been used (see [START_REF] Research | CVX: Matlab software for disciplined convex programming, version 2.0[END_REF] and [START_REF] Grant | Graph implementations for nonsmooth convex programs[END_REF]). The CVX resolution process verifies the convexity of the problem and solves it using SDPT3 or SeDuMi. SDPT3 is a MATLAB implementation of infeasible pathfollowing algorithms for solving conic programming problems whose constraint cone is a product of semidefinite cones. It uses a predictor-corrector primal-dual pathfollowing method, with different types of search direction. SeDuMi is a linear/quadratic/semidefinite solver for Matlab and Octave.

Simulation parameters are depicted in Table II.

B. FS with randomness

Two different types of randomness are studied in the following: trajectory randomness and a user arrival in the network. We analyze the impact of a random event occurrence on five types of schedulers:

• The basic FS which does not take into account any random event during the scheduling duration T (section II-A); • UFS which stops at each random event occurrence and integrates the past data allocated by the FS before reiterating (Section III-B); • RFS which stops at T < T and integrates the past data allocated by the FS before reiterating. This scheduling is usefull when we know when the random event will occur (any randomness along the trajectories such as a crossroad) (section III-A); • Seer Forecast Scheduling (SFS) is a kind of oracle that sees the future and knows when and what will occur in the future. This last scheduling is used to compare how perfect are the others cited schedulings and has same formulation as the basic FS knowing all the random events. • RR scheduling. The two schedulers FS and UFS assume that all the users will take the Road 1 with the VSC (Figure3).

1) Trajectories randomness: The impact of randomness in users' trajectories for the above five schedulers is studied presently. account the trajectory randomness. The UFS assumes the hypothetical users trajectory of Road 1 in this example. The UFS will stop as soon as a user takes a trajectory different than the expected one and will then take into account the attenuated signal in Road 2 as explained in Section III-B. In Figure 4, the first five users in the trajectory who arrive first to the random point, turn right into Road 2 (this information is not known) and the last five users take the Road 1 with the VSC. We denote this case as Scenario 1. The first five users will not receive as much data as the last five users. Even the SFS (red bars) cannot be fair enough for the users since the first five users do not have much time to be scheduled before taking the Road 2 (bars "Before Crossroad" in Figure 4). In the right side of Figure 4 ("After Crossroad"), the four forecast schedulers give pratically all the resource to the last five users. The SFS gives the priority to the first five users before the crossroad as they will experience lower signal after passing it, while the last five users will reach in the future the VSC area with high SINR.

The UFS and the basic FS give also the priority to the first five users before reaching the crossroad but not for the same reasons as the SFS. Users 2 to 5 are approaching the VSC and experience higher SINR so the schedulers allocate most of the resource to them. User 1 will not receive any resource as he does not have time to be scheduled before reaching the crossroad. The last five users will not be allocated as they are far from the VSC.

The resources allocated by the RFS to the users grow monotonically as a function of the sojourn time in the left Section of Road 1. User 10, the last one in the road, stays longer time before the crossroad than the other users.

In the second scenario, the last five users who arrive last to the random point, are taking the Road 2 (this information is not known). The UFS and the basic FS do not give to the last five users any data (bars "Before Crossroad" in Figure 5) since they assume that the users continue straight along the main road and cross the VSC coverage. When the first five users arrive to the VSC, the schedulers give them all the resources (bars "After Crossroad in Figure 5).

The RFS (cyan bars) and the UFS are therefore the best schedulers to choose in this case. They achieve the best throughput and fairness according to the α-fair utility (recall that the SFS is just an oracle scheduler). The main reason for the difference between these schedulers is that only the RFS has the knowledge on the occurence time of the uncertain event. The RFS applies its scheduling policy during shorter intervals when an uncertain event occurs, thus remaining fair for all users. The UFS on the other hand will enhance fairness in the next scheduling interval by condidering past allocation in the scheduling policy. The RR scheduler (grey bar) underperforms all the forecast schedulers.

2) Random user arrival: An arrival of a user in the middle of the forecast scheduling period T is investigated presently. We consider the same users' model as in the previous case but with 9 users, with user 10 arrival as shown in Figure 6. A VSC is also deployed in the users' trajectory. Only four scheduling strategies are considered as we do not know the event occurrence time, namely the RFS is not relevant here. The impact of user 10 arrival is depicted in Figure 7. The Key Performance Indicator (KPI) studied is the same as in Section IV-B1. User 10 arrives at time T /2 where we suppose in this case that T = 400 it. (recall that 1 it. = 70 ms).

In Figure 7, user 10 arrives at time t = 200 it. The main observation is that the UFS and the SFS give almost the same dowloaded data during the trajectories for all the users, even for the one that arrives randomly at time T /2 = 200 it. In fact, the UFS takes into account the arriving user that has never received any data and tries to enforce fairness between the new arrival and the active ones by integrating the past downloaded data in the utility function and optimizing the new allocation.

The basic FS (yellow bars) does not see the arrival of user 10 since it calculates the optimal scheduling for the entire period T without interruptions. Hence user 10 has to wait the next FS period time T to be scheduled.

V. CONCLUSION

This paper has presented extensions of the FS that has been recently proposed in the literature. The FS utilizes GLM, namely rate or SINR, in order to exploit long term time and spatial diversity of vehicular users in mobility. The problem is posed as a convex optimization problem that can be solved using KKT in conjunction with a convex optimization solver.

It is shown that random events such as arrivals and departures of users, or uncertainties in their trajectories can be taken into account by the FS by integrating past received data as soon as a random event occurs. Knowing the time and the type of the random event occurence (e.g. from the distance to a traffic junction) allows to implement the the FS during restricted time horizons. The different types of users, services, mobility conditions and uncertainties can be handled using the multiclass FS formulation proposed in the paper. Numerical results that compare the different FS solutions together with a baseline RR scheduling illustrate the important benefits of the FS.

Fig. 1 .

 1 Fig. 1. Forecast scheduling with different classes of traffic

1 )

 1 At time t = 1 we maximize the function f of the optimization problem (2) denoted by f 1 over the period T ; 2) We find b 1 = (b 1 1 (1), ..., b 1 1 (T ), ..., b 1 n (1), ..., b 1 n (T )) the optimal solution of the function f 1 ; 3) For the first event (arrival for example) at time t = u 2 , we replace a i (1), ..., a i (u 2 -1) by b 1 i (1), ..., b 1 i (u 2 -1) for all users i in the function f 1 . We obtain a new function f 2 to optimize at time t = u 2 (see Fig.2). 4) We proceed iteratively with the optimization of f N at the event number N -1 for N ∈ [1, T ]:

Fig. 2 .

 2 Fig. 2. FS algorithm taking into account arrival and departure of users

Figure 3

 3 shows users arriving to a cross road. If they continue straight, they reach the coverage zone of a VSC (Road 1 in the Figure), whereas if they turn right, due to propagation condition they experience signal attenuation of the order of 10dB (Road 2 in the Figure). Figures 4 and 5 depict the normalized downloaded data for each user during the period T for the five scheduling strategies. The basic FS (yellow bars in the Figures) and the UFS (black bars) do not take into

Fig. 3 .

 3 Fig. 3. Mobile users arriving to a cross road, with the possibility to drive straight or turn right.

Fig. 4 .Fig. 5 .

 45 Fig. 4. Impact of random trajectories with different scheduling strategies: Scenario 1, before and after the crossroad for each user

Fig. 6 .

 6 Fig. 6. Random arrival time of user 10

Fig. 7 .

 7 Fig. 7. Impact of an arrival in the middle of the FS duration in the 4 schedulers

Table I

 I summarizes the types of schedulers with the corresponding types of mobility and channel behaviours.

TABLE II NETWORK

 II AND TRAFFIC CHARACTERISTICS

	Network parameters
	Number of macro BSs	1
	Number of interfering BSs	6
	Macro-cell layout	hexagonal omni sectors
	Intersite distance	500m
	Bandwidth	20M Hz
	Channel characteristics
	Thermal noise	-174dBm/Hz
	Macro Path loss (d in km)	128.1 + 37.6 log 10 (d) dB
	Mobility traffic characteristics
	User speed	50km/h
	Number of users	10
	File size σ	full buffer (∞)
	One iteration = Scheduling delay	70ms