Valérie-Inès De

L A Ville

Eléonore Mounoud

CHAPTER 12 A narrative approach to Strategy as Practice: strategy making from texts and narratives

The narrativizing of practices is a textual 'way of operating', having its own procedures and tactics. […] Shouldn't we recognize its scientific legitimacy by assuming that instead of being a remainder that cannot be, or has not yet been, eliminated from discourse, narrativity has a necessary function in it, and that a theory of narration is indissociable from a theory of practices, as its condition as well as its production. (de Certeau 1988: 78)

Introduction

The Strategy as Practice approach requires a close and detailed scrutiny of practitioners' activities. Such a micro-level approach enables us to depart from the conventional perspective and delve 'inside the process to examine intimately the kind of work that is actually being done' (Whittington and Cailluet 2008: 244), to study in more details 'individual' rather than 'organizational' performance [START_REF] Samra-Fredericks | Strategising as lived experience and strategists' everyday efforts to shape strategic direction[END_REF]. Moving attention away from macro-processes towards various aspects of the minutiae of strategy making has changed the discourse used by researchers to explain how strategy is conceived, explained and communicated [START_REF] Whittington | Strategy practice and strategy process: Family differences and the sociological eyes[END_REF]. In practice, strategy is still essentially considered as micro-processesi.e. the actual activities carried out by individuals within their organized contexts: "strategy is something that people do"1 (Jarzabkowski and Whittington 2008: 282). In that vein, the research conducted by [START_REF] Nordqvist | Strategic planning champions: social craftspersons, artful interpreters, and kown strangers[END_REF] examines in depth the activities held by strategic planning champions through which they become effective strategy practitioners within complex organizational contexts.

Although social practice theory tends to emphasize the tacit and informal dimensions of practices and praxis, Strategy as Practice research has focused on "the work, the workers and tools of strategy" (Jarzabkowski and Whittington 2008: 285), leading to privilege explicit practices, especially on operating procedures and standards [START_REF] Jarzabkowski | Strategy as practice: Recursiveness, adaptation and practicesin-use[END_REF](Jarzabkowski , 2005)), norms of appropriate strategic behaviour set by industry recipes [START_REF] Spender | Industrial recipes[END_REF]) and legitimizing discourses [START_REF] Barry | Strategy retold: Toward a narrative view of strategic discourse[END_REF]. Futhermore, while social practice theory advocates 'agency' for everyone in everyday life, Strategy as Practice research pays attention mainly to special events (Hendry and Seidl 2000) and top management personnel [START_REF] Samra-Fredericks | Strategising as lived experience and strategists' everyday efforts to shape strategic direction[END_REF]. Thus the approach's achievement has been a change in the method of observing a phenomenon's processes, and not the basic categories of thought (Jarzabkowki et al. 2007[START_REF] Johnson | Strategy-as-Practice: Research Directions and Resources[END_REF][START_REF] Whittington | The practice turn in organization research: towards a disciplined transdisciplinarity[END_REF]. However, so far Strategy as Practice research has mainly focused on the visible part of the iceberg: people, events and explicit tools. The actual practice in itself that "involves a constant parsing out of the individual, the local and the societal" (Whittington 2011: 185), has not been sufficiently investigated yet.

Focusing on micro-activities leaves the macro-micro distinction intact, but raises the subsequent problem of linking individual actions to macro outcomes. Making a 'practice turn' in strategy research requires not only knitting together 'micro-practices' and 'macro-outcomes', but also avoiding being caught in the trap of considering practices as just something people do. Practices are construed as social skills that have been culturally acquired, hence unconsciously absorbed and embodied. This compels us to take the dynamic and emerging fields of practices as the starting point for analysis, thereby getting by with the usual macro-micro distinction. Hence, [START_REF] Chia | Post-processual challenges for the emerging strategyas-practice perspective: Discovering strategy in the logic of practice[END_REF] call for shifting the focus of analysis 'from individual strategists to the historically and culturally transmitted fields of practice'. [START_REF] Schatzki | The sites of organisations[END_REF] proposes that we should view practices as relational sites in which events, entities and meanings compose one another. Gherardi emphasizes that 'theories of practice view actions as 'taking place' or 'happening', as being performed through a network of connections-in-actions, as lifework and dwelling ' (2009: 115). The challenge is then to overcome the prevalent individualistic focus on micro-level managerial activities and roles, which leaves a mass of larger social issues melting into the under-theorized, all-encompassing category of 'context' [START_REF] Tsoukas | What is management? An outline of a metatheory[END_REF][START_REF] Willmott | Rethinking management and managerial work: Capitalism, control and subjectivity[END_REF]).

Following the Heideggerian view, Chia and Holt argue that the dominant 'building' mode of strategy making, in which actors are distinct entities deliberately engaging in purposeful strategic activities, is actually derived from a more basic 'dwelling' mode in which strategy making emerges non-deliberately through everyday practical 'coping'. Practical 'coping' is rooted in social practices. Social practices are identity-forming and strategy-setting activities. They provide individuals with resources to interpret and improvise their role; they shape the scope and the extent of their exploratory activities and initiatives to cope with the ongoing flow of organizational development [START_REF] Chia | Strategy as practical coping: A Heideggerian perspective[END_REF]. Mundane practical 'coping' can produce unexpected and strategically important outcomes, as shown in the famous example of Honda's success in the USA [START_REF] Pascale | Perspectives on strategy: The real story behind Honda's success[END_REF], in [START_REF] Regnér | Strategy creation in the periphery: Inductive versus deductive strategy making[END_REF] uncovering of local improvisation at the periphery of corporate reach, in de La [START_REF] De La Ville | Collective learning processes in high tech firms: Enablers and barriers to the innovation process[END_REF] work on emerging technological strategies in a start-up, and in [START_REF] Rouleau | Micro-practices of strategic sense-making and sense-giving: How middle managers interpret and sell change everyday[END_REF] analysis of strategy formation in everyday interactions. These studies show the importance of recognizing how much of strategy formation is rooted in the non-deliberate practical action of 'coping' that escapes the logic of planned and intentional action. For [START_REF] Sandberg | Grasping the logic of practice: theorizing through practical activity[END_REF] the challenge in order to grasp practice, it is to escape the modern scientific rationality that pervades management theoretical frameworks, and to elaborate the premises of an alternative practical rationality that considers entwinement as the cornerstone of existence. Entwinement means that being and doing become intelligible when included in a relational scheme articulating concomitantly the 'embodied other' and a specific 'socio-material' world. Moreover, [START_REF] Feldman | Theorizing practice and practicing theory[END_REF] point out the conceptual creativity needed to elaborate a language as well as a logic that tolerates ambiguity and adequately express the dynamic, recurrent and relational nature of everyday practices. This chapter builds upon the distinction between the 'building' and the 'dwelling' modes in order to introduce a narrative approach to Strategy as Practice. We contend that Strategy as Practice research is still mainly imbued with the conceptual categories of the dominant 'building' mode. We contend that the recognition and integration of the 'dwelling' mode into strategy formation, as well as the combination of the 'building' and the 'dwelling' modes in strategy-making, are the key challenges for research analysis. In order to include in the picture the hidden creativity embedded in mundane practical 'coping', closer scrutiny and better accuracy in methodology need to be achieved as 'practices are difficult to access, observe, measure or represent because they are hidden tacit, and often linguistically inexpressible in propositional terms' (Gherardi 2009, p.116). We therefore propose a narrative approach to Strategy as Practice. This approach relates strategy making to using texts and narratives, and also provides the conceptual and methodological means to deal with the challenges mentioned above. A narrative approach enables strategy research to engage more deeply in the 'practice turn' and to develop a 'certain research sensibility to the unspoken, the inarticulate and even the often unconscious aspects of strategy-making' [START_REF] Chia | Post-processual challenges for the emerging strategyas-practice perspective: Discovering strategy in the logic of practice[END_REF]see also Raelin 2007).

This chapter is organized in four sections. The first section describes the various perspectives on narratives brought into strategy research. Beyond the overall functionalist interest in good stories, it shows the importance of texts in strategy and management. The second section, on the basis of the work of Paul Ricoeur, develops the implications of this very notion of text. The third section follows Michel de Certeau's analysis of practices to identify a narrative way of forming strategy. In line with Chia's distinction based on Heidegger, we now consider producing texts as the dominant 'building' mode of strategy making. This mode is actually derived from a more basic 'dwelling' mode, in which strategy formation emerges through reading texts and producing daily narratives. The last section draws the implications of our conceptual framework of 'strategy-making from texts and narratives', which is based upon the dynamics of reading and writing 'texts'. This offers a perspective in which all organizational actors participate in strategy formation when producing and dealing with texts produced by others as well as in reading these texts and producing mundane narratives, thus engaging in bricolage of strategy.

Narratives in strategy research

Since the publication of [START_REF] Barry | Strategy retold: Toward a narrative view of strategic discourse[END_REF] article on the narrative aspects of strategic discourses, it has been generally accepted that strategyboth organizational strategies and theories of strategyconsists of stories told by key people, generally leaders, to other people such as shareholders, members of the organization and other stakeholders. This work highlighted the double nature of strategynarrative production and process of narrationby which various stories about strategic choices are connected, tested, reinforced or weakened. It also related strategic change processes to the romantic genre, the adventure novel of ordeal and to realistic fiction. With a certain degree of irony, the authors underlined the epic, even hagiographic, character of several strategic discourses of leaders. For example, the promotion of neoSchumpeterian heroes in entrepreneurial strategies created a demiurgic drift in many research accounts of new venture founding (de La Ville 2006).

Why are stories and narratives so interesting? The basic function of a story is to organize a series of events and actors into a common, acceptable and comprehensible temporal framework. By reorganizing events in a temporal framework, stories preserve and build the continuity of actions. The perception of the stakes of the present situation enables us to reorganize past events into a story. Restructuring a group of relationships creates retrospective senses, hence enabling further action. This faculty of generating sense has led researchers to become interested in stories told within organizations. Research on organizational culture and identity considers both big storiesmyths, texts and discoursesand smaller ones such as stories, storytelling, gossip and narratives [START_REF] Gabriel | Storytelling in organisations Facts, fictions and fantasies[END_REF][START_REF] Boje | The storytelling organisation: A study of story performance in an office-supply firm[END_REF][START_REF] Boje | Stories of the storytelling organization: A postmodern analysis of Disney as "Tamara-land[END_REF][START_REF] Boyce | Organisational story and storytelling: A critical review[END_REF] as important in analysing and understanding organizational life.

Stories and storytelling have now pervaded management, strategy and marketing research areas [START_REF] Salmon | Storytelling, la machine à fabriquer des histoires à formater les esprits[END_REF] and have put in the forefront a new array of consultants and gurus. Good stories are hence considered an effective factor in implementing strategic ideas. Strategy formulation involves a narrative production of an integrative story that enables the leaders to reorganize past events according to a plausible and desirable logic. What is at stake is the capacity of stories to construct a persuasive and stimulating message to facilitate memorization and training or to convince stakeholders of the relevance of a strategy. Leaders need to be good storytellers, i.e. be able to tell good stories which must be both coherent to gain credibility and stimulating to facilitate its reception and implementation. In a functionalist view, the construction of a good story supposes an overall intentionality, meaning total control of the plot through to its final outcome. However, it does not take into account such organizational phenomena as improvisations or routine activities, to which it is difficult to attribute intentionality due to their takenfor-granted nature.

Thus, the functionalistic view of strategic stories fails to capture the complexity of strategic processes and practices. It prevents us from widening the field of analysis to include the ordinary narratives of mid to low-level organizational members in relationship with the higher-level 'visionary' strategy produced by senior executives. However, is the intrinsic quality of a good story able to dissolve the integrative difficulties inherent in the strategic exercise? Moreover, can the integrative strategic narrative be considered effective without including the interpretations of people to whom it is addressed? To escape this over-simplistic view of storytelling management, we need to account more accurately for the narrative perspectives brought into strategy research.

On the contrary, the interest of social scientists in narratives is based on the way people organize knowledge in their daily life. It is suggested that people organize their experience in the form of scripts about goal-based events that include people, places and events, and these scripts are recounted in the form of stories. On the one hand, it has become fairly accepted that narrative is a universal form in which people construct, represent and share experience [START_REF] Bruner | Actual minds, possible worlds[END_REF]). On the other hand, experience shows how deep cultural narratives are, how powerful stories are as a socializing agent and, conversely, how much they reveal about the values, beliefs and thought processes of a given culture or community. [START_REF] Bruner | Actual minds, possible worlds[END_REF], among others, has argued that it is difficult to distinguish between the stories children learn and the stories they build from their direct experience and knowledge. The narrative ability to create stories develops during childhood through reminiscing and engaging in symbolic play [START_REF] Engel | The stories children tell[END_REF]. Narratives do not merely convey fantasies or the representation of unusual feelings or experiences, but also provide a fundamental intra-and interpersonal process, through which children make sense of themselves in the world. Storytelling is a deep social activity and a powerful private activity. Children tell stories when alone, they tell stories that have private meanings, and they use stories as much for their internal thoughts and feelings as they do to communicate. What researchers have learned so far is that children create stories in much the same way as they create play scenarioswith the pleasure of creativity. It is important to keep in mind that the form and content of children's stories are tied to the context in which they are told and the purpose for which they are told [START_REF] Engel | Narrative analysis of children's experience[END_REF].

In conclusion, following Czarniawska's distinction between three different modes of mobilizing narratives, we acknowledge three narrative perspectives in strategy research that we detail in the next section. It is possible for the researcher either to build explanations out of 'narratives from the field', or to build his own 'narrative in the field' and even to define 'organising as narration' (Czarniawska 1997, p. 25). The first mode is visible in the interactional perspective developed in communication science, the second is at play when strategy is portrayed as a story of domination and discipline, and the third when strategy formation is seen as narration.

Strategic narratives as meta-conversations

The interactional perspective highlights the vital importance of communication in organizational life in general and strategy formation in particular. For followers of this approach, ordinary activities develop through conversations, which constitute coherent discursive units in themselves. Giroux describes this process as a 'chain of conversations' spread out in time and space. She considers a dialogical mode of production of strategy, 'through a polyphonic vision of the community where several voices are heard, and where the heteroglossia (the simultaneous presence of several languages) is accepted' (Giroux 1998, p. 7, our translation). The formulation of strategy is then conceived as a narrative process that organizes polyphony. The concept of polyphony recognizes the coexistence, interaction and mutual definition of various logics. In this polyphonic process, strategy formulation is never controlled by one single author, so it is particularly complex. Strategy is worked out gradually by negotiation within a 'meta-conversation' [START_REF] Giroux | Communication organisationnelle et stratégie[END_REF] dedicated to strategy formation, and leads to the drafting of a strategic text. [START_REF] Taylor | Finding the organisation in the communication: Discourse as action and sensemaking[END_REF] suggest that for organizational members to interact, they must construct a shared language, embodied in a text which enables them to cooperate. This begins with everyday conversation with mutual interaction, which is a prerequisite of organized activity. The resulting narratives constitute secondary productions, which formalize the interpretations constructed in conversation and carry them toward future actions. Not only does the text produced retain the traces of the original conversations, it frames subsequent actions by offering interpretative frameworks for the sensemaking of ongoing events. This view relates the concept of text to that of the framework of interaction, which is inspired by Erving Goffman and has previously been used in analysing strategy formation (de La Ville 2001).

This proposition is based on the analytical distinction between the two dimensions of discourse as text (what is said) and conversation (what is accomplished in the saying): 'Conversation refers, in other words, to the interactive, situated "eventfulness" of language use; text refers to the semi-otic artefact (oral or written) produced in the use of language, which may persist as a trace and record of past conversations' (Robichaud et al. 2004). A meta-conversation is then defined as 'a conversation that embeds, recursively, another conversation' [START_REF] Robichaud | The meta-conversation: The recursive property of language as the key to organizing[END_REF]). The meta-conversation simultaneously incorporates and reconstructs the local discussions within the organization into an encompassing conversation, where the identity of the organization as a whole is continuously regenerated. The process at work is the production of a metanarrative that enfolds and transcends the narratives of the different communities comprising an organization.

Strategic narratives as discourse of domination

Inspired by the work of Foucault (mainly 1971Foucault (mainly , 1976)), the critical organizational discourse perspective [START_REF] Vaara | On the discursive construction of success/failure in narrative of post merger integration[END_REF][START_REF] Phillips | Discourse analysis: Investigating processes of social construction[END_REF][START_REF] Fairclough | Critical discourse analysis, organisational discourse, and organisational change[END_REF] focuses on discourses as linguistically mediated constructions of social realities. Discourses are important means through which beliefs, values and norms are reproduced and at times transformed in social life [START_REF] Fairclough | Analyzing discourse: Textual analysis for social research[END_REF]. This perspective is one of the various approaches to discourse analysis (van Dijk 1997) and to organizational discourse analysis in particular [START_REF] Hardy | Discourse and power[END_REF][START_REF] Grant | Handbook of organisational discourse[END_REF]).

These studies highlight the disciplining power of discourses on the ordinary practices of organization members, stemming from their capacity to impose and legitimize certain interpretative frameworks at the expense of others. Foucault warns that it is a question 'of no longer treating the discourses as sets of signs (of meaningful elements which refer to contents or representations), but as practices which systematically form the objects about which they speak' [START_REF] Foucault | The archeology of knowledge[END_REF]). Discourses should be considered 'surreptitious objectivations' (objectivations subreptices): they appear to be built by induction and serve to describe the world, but in fact they actually constitute the world. More generally, the language used on a daily basis within an organization is itself a bearer of logics of domination, which direct ordinary interactions and activities and legitimize power relations [START_REF] Hardy | Scaling up and bearing down in discourse analysis: Questions regarding textual agencies and their context[END_REF]).

Strategy discourse is thus considered to be a complex set of meanings constituting this body of knowledge [START_REF] Knights | Corporate strategy, organisations and subjectivity: A critique[END_REF], as well as a part of the complex set of social practices formulating strategy as an organizational practice. Moreover, critical discourse analysis enables to identify how specific conceptions of strategy work are reproduced and justified in organizational strategy formation. The idea that strategy includes a disciplining dimension emphasizes the importance of the stakes of power and legitimization invoked in the strategic exercise.

Critical theorists [START_REF] Alvesson | Doing critical research management[END_REF][START_REF] Putnam | Alternative perspectives on the role of text and agency in constituting organisations[END_REF][START_REF] Gherardi | The critical power of the 'Practice Lens[END_REF]) offer a distinctive point of view on key documents, such as regulations, procedures and memorandums. Discourses are selected, perpetuated and subsumed in texts, which are registered, preserved and memorized in accordance with the disciplinary function of the organization. These texts do not result from interaction between organization members; they rather influence strategy formulation by virtue of their structured and permanent character that enables organizations to survive [START_REF] Mcphee | Text, agency and organisation in the light of structuration theory[END_REF]. Discourses and texts mobilize mechanisms of domination based on legitimized rationality and the invoked scientific nature of the discipline. They result in practices of monitoring and controlling, but also aim at influencing the subjectivity and identity of organization members. Hardy and Phillips (2004) highlight how certain actors are able to mobilize economic, cultural and social capital to legitimize their power. From this point of view, the very notion of discourse includes domination and is opposed to the ordinary, fragmentary, situational narratives being built during the course of the everyday activities of organization members and bearing the stamp of subjectivity and of emotion. Mantere and Vaara's analysis (2008) shows that strategy as practice involves alternative and even competing discourses that have fundamentally different kinds of implications for participation in strategy work.

Organizations and strategies as narration

The third view is grounded in the claim made by [START_REF] Mcintyre | Whose justice? Which rationality[END_REF] that 'it is useful to think of an enacted narrative as the most typical form of social life' (cited in [START_REF] Czarniawska | Interviews and organisational narratives[END_REF]. Its initiator, Barbara [START_REF] Czarniawska | Narrating the organisation -Dramas of institutional identity[END_REF], has a deep interest in the daily activities of the organization members, which result in the creation of the organization itself. She identifies two types of conversations: those allowing for the confrontation of personal experience or actions between two parties, and those manufacturing texts beyond the personal experience of the individual by imposing standards of behaviour and decision. This coexistence results in fierce competition between the 'stronger' orderthat of the official discourse which reinforces institutional domination by controlling interpretations -and the 'weaker' orderthat of the ordinary narratives which try to make sense of daily activities. Her work suggests an ironic stance with regard to the impact of strategists, as she finds strategy to be a relatively artificial discursive construction, far removed from the realities experienced by organization members and geared to institutional concerns for domination and justification. Without any impact on the future of organizations and with no control over its daily activities, strategy appears in her descriptions to be a kind of meaningless ritual (de La Ville and Mounoud 2003). The severity of this assessment is partly explained by Czarniawska's focus on public organizations where the distance between official discourses and actual practices might be particularly perceptible. In Czarniawska's view, everyday life within the organization takes shape through ordinary narratives in which individuals select events, organize temporalities, typify key characters, build identity relationships, structure their experience, and construct and transform their interpretations. Drawing on Bruner's point that 'there is an availability, or a predisposition to organise experience in narrative form by building intrigues' [START_REF] Bruner | Actual minds, possible worlds[END_REF], we estimate that the continuity of existence may be understood by recounting this same existence, a narrative process of fashioning one another's identities. Through the spoken word, exchanged and retained among themselves, organization members construct and perpetuate their identities and their organized activity. Language, speech, plot production, mere stories and ordinary narrations are experienced and consubstantial with organizing itself. The construction of activities, knowledge and identities is thus structured in and through a complex interlacing of narrative processes, which is always spontaneous, related to unforeseen events and socially organized [START_REF] Czarniawska | A narrative approach to organisation studies[END_REF]).

In the two following sections, we will develop our view of strategy as narration, including narrative production and the process of narration, in which the future is created through a collective narrative that is dispersed and fragmented, being the subject of partial developments, major transformations and inscriptions perpetuated in texts. Strategy-making, when considered as directing the future and leading organization members to comply with this direction, results partly in the production of texts. Nevertheless, not all texts can be qualified as 'strategic', nor is strategy formation confined to the processes of creating or monitoring the effects of 'strategic' texts. We will first consider the implications of this production of texts.

Strategy formation as producing texts

Strategic texts constitute forms of mediation, in and through which organizational actors reflexively understand their situations, give meaning to their actions, and anticipate their futures. Produced strategic texts thus have a double relation with the context (the preceding texts with which they interact) and the situation (the mundane organizational activities and practices to which they relate and help organize).

Texts organize relationships of intertextuality and polyphony

The production of a strategic text relies on a group of scriptural prerequisites. To be described as 'strategic', the text must bring together appropriate standards, rules and criteria that explicitly connect it to the discipline of management and to various genres relevant to strategy, such as management reports, business plans, development plans, refocusing plans, asset redeployment plans, etc. Processes of institutionalization accompany and support the production of strategic texts while differentiating them from other textual productions. MBA programmes, specialized academic courses, consulting firms and trade associations legitimize strategists and increase their influence. Strategic activity is seen through textual productions that communicate to shareholders the relevance of the strategic project and the strategic team's control. For example [START_REF] Vaara | On the force potential of strategy texts: a critical discourse analysis of a strategic plan and its power effects in a city organization[END_REF] identified five central discursive features that could be conceived as distinctive features of the strategy genre. They argue that these discursive features have important implications for the textual agency of strategic plans and their performative effects. They identify their impact on power relations and their ideological implications.

Strategic texts are embedded in intertextual relations, with pre-existent strategic texts that are themselves governed by the instituted kinds of organizational productions, and by discursive orders based not only on strategic management as a discipline [START_REF] Hardy | Scaling up and bearing down in discourse analysis: Questions regarding textual agencies and their context[END_REF]), but also on objectives and strategies derived from the constitutive values of the local social system. In a documented essay, [START_REF] Whittington | Opening strategy: evolution of a precarious profession[END_REF] depict the progressive structuring of strategy since the 1950's as the emergence of a precarious professional field, including top executives, strategic planners, consultancy companies, academics, and middle managers, that is shaped permanently by changing organizational, societal, cultural and technological forces. Since strategy formulation is directly embedded in an institutional environment, it inevitably includes an ideological dimension, because it reproduces the inequalities of the capitalist society, extends Western managerial structures and presents the objectives of dominant elites as universal goals. Being institutionally inscribed, strategic texts propose worlds that include a disciplining function founded both on legitimized scriptural standards and on institutionalized value systems.

Because they present a proposal for a relation with the world, strategic texts cannot ignore the multiplicity of voices, actions and narratives within the organization [START_REF] Giroux | Communication organisationnelle et stratégie[END_REF]. The very production of strategic texts organizes a polyphonic relationship among voices, which always remain singular and develop autonomously, but answer one another, oppose one another and contribute to proposing new worlds [START_REF] O'connor | Plotting the organisation: The embedded narrative as a construct for studying change[END_REF][START_REF] Hardy | Scaling up and bearing down in discourse analysis: Questions regarding textual agencies and their context[END_REF]). Strategy formation proceeds from the application of strategic apprenticeship, which goes beyond the order of discourse and conversation to integrate a body of knowledge into explicit activities and tacit tactics. Furthermore, the ordinary practices of managers and the texts that underlie them, through the resistance that they express, continually nourish the inventiveness of the organizational actions and form an ongoing, emerging and vital part of the strategic activity. Either these practices are gradually recognized, named and defined so as to be integrated into the strategic text, or they remain invisible or exterior (perhaps because they occur outside official channels). Thus, strategic texts operate a selection and organization of mundane organizational narratives.

The notion of 'intertextuality' allows us to appreciate writing as a permanently creative flux integrating previous standards and conventions in order to produce texts, which are likely to be readable, understandable and recognizable by an audience. It was described by Julia Kristeva (1980, p. 69) as a reaction to the tendency to analyse texts as discrete and closed units, whose meaningfulness lay in their internal structure. Drawing on the dialogue perspective proposed by Mikhail [START_REF] Bakhtin | Rabelais and his world[END_REF] in literary theory, she contends that texts become meaningful if they are considered as a fragment relating to former texts. Shared codes allow both the writer and the reader to recognize, situate and appreciate the text in the continuum of literary production. It is worth noting that this post-structuralist perspective considers that every text is under the dominance of previous texts that impose a universe of codes in relation to which it will be read and understood by certain audiences. This suggests a drastic shift in the method of analysing reading and writing by focusing the effort on studying the process of structuration through which the text comes into being. By questioning the romantic roots that lead to the invention of the notion of 'authorship', this perspective lays special emphasis on the fact that writers are compelled to use pre-existing concepts and conventions to communicate with an audience. Their individual creative skills are socially founded in shared language and scriptural conventions. That is why Roland Barthes defines text as a tissue of quotations, a creative art consisting in weaving former codes, references and genres [START_REF] Barthes | S/Z: An Essay[END_REF].

Texts draw upon a large range of codes and social norms that allow them to be assigned to a particular genre. Genres are situated and evolving conventions that enable us to classify texts and outline their relationship with each other. Literary theorists have demonstrated that the definition of genres is quite fluid and relates to ongoing changes and social renegotiations, leading to a permanent blurring of borders and a constant mitigation of their distinctive characteristics. We are fully aware that such a brief presentation of the complexities linked to the notion of 'intertextuality' and its use in cultural studies and literary analysis is a risky undertaking. Nevertheless, in the context of this chapter, we aim at transposing this notion into a managerial perspective, in an attempt to offer some guidelines to support managers' efforts in mastering the complex stakes of 'intertextuality' needed to exploit strategically the creativity hidden in mundane organizational activities.

Texts call for reading

To analyse the dynamics of texts, we draw on Paul Ricoeur, for whom the concept of text covers a limited category of signs: those which comprise a form of fossilization comparable with that produced by writing [START_REF] Ricoeur | From text to action: Essays in Hermeneutics II[END_REF] which allows the conservation and the linearization of the conversation. When writing is added to a previous statement, it modifies the relationship with the utterances, which is called the 'ostensive reference' by Ricoeur, i.e. the object with which one expresses oneself. Writing creates a different relationship from that of interlocution: the reader is absent from the writing and the author from the reading. The text is thus the product of a simultaneous eclipsing of the reader and the author. In this view, the nature of the text is underlined. Because of its fossilization into a medium, because of the lack of association between the intention of the author and the intention of the text, because of the use of 'non-ostensive' references and the substitution of unknown readers for a visible listener, the text must be differentiated from a face-to-face or situated discourse.

Consequently, 'the text awaits and calls for reading' [START_REF] Ricoeur | From text to action: Essays in Hermeneutics II[END_REF]. Ricoeur distinguishes two ways of understanding reading: to explain and to interpret. 'To explain is to bring out the structure, i.e. the internal relations of dependence, which constitute the static of the text. To interpret is to follow the path of thought opened up by the text and to start heading towards the orientation of the text' [START_REF] Ricoeur | From text to action: Essays in Hermeneutics II[END_REF]. This dualism suggests a dialectic in the activity of reading, as movement between these two attitudes produces interpretation. The open nature of the text is made salient: references are offered to propose a 'world' and build a new meaning. Reading is possible because text is not closed in on itself; it is open to other things. Reading is thus a creative activity that prolongs the creation of writing. As stated by [START_REF] Ricoeur | From text to action: Essays in Hermeneutics II[END_REF], 'to read is, in any hypothesis, to conjoin a new discourse to the discourse of the text'.

Strategic texts are characterized by their plurivocity: their significance is unresolved as for any ext, because of the distance caused by its written form, is open to alternative readings and constructions depending on the situations of readers. While interpreting strategic texts, organizational actors propose their relations with the world. This process of appropriation, which takes place in the narrative register, as we will show in the next section, is complex, dense, emergent and dynamic.

We have underlined the 'building' mode of strategy formation as producing strategic texts. It is important to keep in mind that these texts are themselves embedded in a 'context' of previous texts and are derived from the polyphony of situated narratives. It is now possible to envisage the more basic 'dwelling' mode of strategy formation, the everyday practical 'coping' with the rules and texts of the organization. The relationship of this 'dwelling' mode with the 'building' one is similar to that of reading with writing.

Narratives as practical coping with strategic texts

The creativity of reading, put forward by Ricoeur, is shared by Michel de Certeau, who argues for a greater emphasis on the activity of reading to oppose the excessive importance placed on writing in contemporary society, a society that he finds 'increasingly written, organised by the capacity to modify things and to reform the structures through scriptural models (scientific, economic, political), and gradually transformed into combined "texts" (administrative, urban, industrial, etc.)'. He strives to show that reading is not a passive activity; it modifies its object, reinvents beyond the intention of the text, and builds a different 'world', which belongs to the reader in place of the author, 'to make the text liveable'. Readers carry out 'a reappropriation of the other's text: he poaches there, he is transported there, he becomes plural there' [START_REF] De Certeau | The practice of everyday life[END_REF].

Reading as consuming texts

According to Michel de Certeau, everyday life is distinctive from other practices of existence because it is repetitive and unconscious. An interesting point is the distinction he makes between the concepts of strategy and tactics. De Certeau links 'strategies' with institutions and structures of power, while 'tactics' are utilized by individuals to create space for themselves in environments defined by strategies. For example, he describes 'the city' as a 'concept', generated by the strategic manoeuvring of governments, corporations and other institutional bodies, who produce things like maps that describe the city as a unified whole experienced by someone looking down from high above. By contrast, a walker on the street moves in ways that are tactical and never fully determined by the plans of organizing bodies. He may take shortcuts or meander aimlessly, rather than follow the utilitarian layout of the grid of streets. This concretely illustrates de Certeau's assertion that everyday life works by a process of poaching on the territory of others, recombining the rules and products that already exist in culture in a way that is influenced, but never wholly determined, by those rules and products.

For de Certeau, consumption supposes the acceptance of an offer of products but not a passive one. Consumers are active; they take pleasure in consuming and consider themselves free and creative in doing so. Under the apparent banality of ordinary gestures and routine actions lurks an extraordinary creativity often ignored by theory. Individuals show a great capacity for 'making do'. They exhibit inventiveness in terms of shrewd ploys and stratagems to work out their own way of doing things, whether it is cooking, strolling through a town or shopping, etc. Being analysed superficially, certain routine behaviours reveal a form of submission. Through in-depth analysis, they reveal ongoing experimentations filled with resistance and creativity. The relationship between reading and writing is of a comparable nature: texts, just like the goods offered on the market, are produced by manufacturers who offer them to consumersthe readerswho decide upon their significance and use them in their own ways. De Certeau's analysis of consumption is oriented towards the ordinary practices of consumers, who are defined as 'users of goods imposed upon them by producers'. Indeed, in offering products to consumers, producers assume a position of domination, against which consumers resist by developing inventive attitudes and practices. By mirroring consumption and reading, de Certeau reveals the two sides of consumption. On the one hand, consuming entails a form of acceptance of an imposed offer of goods. On the other, consumers are neither passive nor docile; they experience freedom, creativity and pleasurejust as readers do. Commenting on empirical investigations of several situational social practices such as reading, talking, dwelling, cooking, wandering around, etc., de Certeau explores scientific literature in order to clarify the purpose of his theoretical undertaking:

It may be supposed that these operationsmultiform and fragmentary, relative to situations and details, insinuated into and concealed … within devices, whose mode of usage they constitute, and thus lacking their own ideologies or institutionsconform to certain rules. In other words, there must be a logic of these practices. [START_REF] De Certeau | The practice of everyday life[END_REF]

Narrativity in strategy formation

Thus, strategy making can be understood as a permanent creative process including not only what strategists produce/write, such as texts, budgets, plans, matrices, charts and strategies, but also the ways in which organization members consume/read these productions. This conceptual framework leads us to question how organizational actors read, that is, use and transform strategic texts in their daily activities.

Reading takes place through the mobilization of innumerable fragmentary, instantaneous, opportunistic tactics (de La Ville and Mounoud 2001b). 'These tactics also demonstrate the degree to which intelligence is inseparable from the struggles and the daily pleasures which it articulates [. . .] Because of its intangible nature, a tactic depends on time and remains vigilant to catch any possibilities of profit. It does not keep what it gains. It is necessary for it to play constantly with the events to transfer them into opportunities' [START_REF] De Certeau | The practice of everyday life[END_REF]. Being incapable of capitalizing voluntarily on their achievements to control temporality and the course of events, these tactics, which are peculiar to the art of reading, may produce tangible and sometimes irreversible strategic effects, such as delays in implementation, side-tracking from the main objectives, operational diversions, more or less continuous symbolic rejections or the subversion of authority.

Adopting this view provides a new way of looking at organizational practice, because it enables us to accept strategic discourses as a production and an offer of a (cultural) good: a text. Thus, we might be able to suggest new ways of explaining how people read, use and transform this particular cultural product. [START_REF] Linstead | On reading organisational culture[END_REF] contrast the production of corporate culture with the creative consumption of organizational culture by organization members. Using this conception requires supplementing the analysis of the discourse of strategy (representation) and of the time spent attending strategic meetings (behaviour) with a study of what middle managers and employees actually 'make' or 'do' during that time and how they use these discourses. With their 'making' or 'doing' being devious and dispersed, it remains difficult for the researcher to analyse. In organizations, employees and managers do not adopt, adhere to or share the 'strategic' vision or intent of their 'charismatic leaders'. In their everyday activities, they actively interpret, criticize, learn and experiment with possible attitudes and microdecisions in order to implement or resist the multiple implications of strategic changes imposed on them.

Practice expresses creativity, a capacity 'to put up with', to subvert imposed rules and create room for manoeuvre. Practice includes the subconscious part of creativity, seen in clever devices and inventions. This creativity is also evident in attempts to negotiate meanings of actions and events among organization members, i.e. in ordinary and everyday narratives. The narrative register indeed enables the practical art to express itself, to experiment, to improvise and to resist the domination of a disciplining totality envisioned by some strategic texts. This readingor consumptionof strategic texts constitutes a second-order production, which de Certeau calls a fabrication, i.e. a narrative which is added to the intention of strategic texts. Employees often do not adhere to, embrace or share the strategic vision or the worlds produced by strategists or top management. In their daily activities, managers and employees learn, test and demonstrate critical thinking to take micro-decisions, be they to implement or resist strategic mandates. This conceptualization makes it possible to comprehend the complexity and the creativity of strategy formation and to reconsider the problematic bond between the 'emergent' and the 'deliberate'. On the one hand, processes of institutionalization accompany and support the emergence of integrative organizational discourses that become strategic texts. On the other, innumerable readings ensue in a disorderly way, gradually giving shape to a multiplicity of tactics that constitute strategic practice.

Implications for research

As summed up in Table 12.1, we have defined strategy formation as the interplay between producing strategic texts and reading them, thus, producing daily narratives. The writing of strategic texts implies the use of standards, which authorize the inscription of the text in the strategic genre. Strategic texts are based on the institutional 'ruling' order and combine together to produce the dominant discourse of strategy. Strategic texts proceed from a selection and polyphonic organization of mundane organizational narratives. But strategy formation also includes the creative reading of strategic texts, producing unpremeditated tactics for resisting their domination. For [START_REF] Rasche | Researching strategy practices: a genealogical social theory perspective[END_REF], the practice of strategy research needs to give a stronger emphasis on an ethnographic approach directed towards uncovering the contextual and hidden characteristics of strategy-making.

Thus, it is important to develop more research on the consumption side of strategy making. These reading practices revealed by narratives can be reconstructed by the researcher from qualitative inquiry based upon observations and conventional unstructured and semi-structured interviews. De Certeau and Ricoeur help us in defining what we should be looking for. De Certeau identifies three places where this practical creativity of ordinary accounts can be seen: the 'games' that formalize the organizing rules of 'actions', the 'game recipes' that teach the practices available, and the "tales and legends" that expose the available good and evil tricks. This aspect of consumption, included in strategic activity because of its dispersion, surreptitiousness and deviousness, evades the eye of both the researcher and the manager. The concept of plot developed by Paul Ricoeur helps us to bring to light the various narratives produced while organizational members consume strategic texts. [START_REF] Ricoeur | Time and narrative[END_REF] built his concept of 'emplotment' (mise en intrigue) around Aristotle's sentence that 'the plot is the imitation of the actionfor by plot, I here mean the arrangement of the incidents' (Poetics, part VI). For Ricoeur, the narrative defined as 'emplotment' combines the Aristotelian concepts of mimesis (imitation) and muthos (arrangement of the incidents): 'With the narrative, the semantic innovation consists in the invention of a plot, which is also a work of synthesis: through the plot, objectives, causes, incidents are brought together under the temporal unity of an action that is complete and whole' (Ricoeur, our translation). Thus, narrative is defined as a 'synthesis of the heterogenous'. The narrative perspective gives way to the analysis of the consumption/production interplay across three levels of analysis as in Table 12.1. Following the seminal work of [START_REF] Floyd | Building strategy from the middle: reconceptualising strategy process[END_REF], research on middle managers has shown a growing interest in their role and participation to strategy formation [START_REF] Rouleau | Micro-practices of strategic sense-making and sense-giving: How middle managers interpret and sell change everyday[END_REF][START_REF] Fauré | The strategic competence of accountants and middle managers in budget making[END_REF][START_REF] Rouleau | Middle managers, strategic sensemaking and discursive competence[END_REF].

Through a fine-grained study of daily conversations held by accountants in order to set up a budgeting control procedure in a construction firm, [START_REF] Fauré | The strategic competence of accountants and middle managers in budget making[END_REF] analyze how accountants and middle managers engage in various forms of discretionary tactics aimed at re-defining their respective accountabilities within the new context of a strategic partnership imposed on them. The mutual tactic aimed at reducing the gap between forecasts and actual achievements consisted of putting forward the acceptability of numbers for the new partner rather than strictly applying the procedures that make budgetary control reliable. These tactics sometimes led to smoothed figures, clandestine and dilatory arrangements justified by the need to render some figures plausible within this new way of setting up budgets required by the partnership strategy. This has drifted research away from top management teams and helped anchoring it in daily practices. [START_REF] Rouleau | Middle managers, strategic sensemaking and discursive competence[END_REF] have studied the way middle managers enact the strategic roles allocated to them. They identify two situated, but interlinked, discursive activities, critical to this accomplishment. If language use is key, it has to be combined with an ability to devise a setting in which to perform the language by drawing on contextually relevant verbal, symbolic, and sociocultural systems. Their final conclusion is that "this is turn suggests that we need to teach strategy differently, taking a more discursive and less analytical approach" in line with the work of Jazarbkowski and Whittington (2008) and Raelin (2007).

The consumption of dominant discourse, strategic texts and formal practices can be tracked within the management fashion framework [START_REF] Abrahamson | Management fashion[END_REF][START_REF] Sturdy | The adoption of management ideas and practices: Theoretical perspectives and possibilities[END_REF]). [START_REF] Corbett | Looping the loop: The consumption and production of knowledge management ideas and practices[END_REF] developed such an analysis. Their study encompasses the ruling order and the direction conveyed in the official discourse, as well as a political view focusing on the instrumental use of strategies to secure power. Strategies are adopted not only because of their supposed effectiveness, but rather because they 'provide a potentially comforting sense of order and identity and/or control' [START_REF] Sturdy | The adoption of management ideas and practices: Theoretical perspectives and possibilities[END_REF]. Strategies are related to the language devices and tricks used by management gurus and other suppliers of ideas to convince the somewhat naïve manager. Focusing on daily narratives allows them to grasp all the contradictions and tensions brought by strategy in the daily activity. In turn they show how individuals are able to play with the texts. Practice is the singular art of coping through combination, inventiveness and 'Do it yourself!' techniques, i.e. 'a way of thinking invested in a way of acting […] which cannot be dissociated from an art of using' [START_REF] De Certeau | The practice of everyday life[END_REF].

Conclusion

Drawing from the narrative perspective in organization studies, we address the strategic role of mundane stories and narratives that give meaning to daily experiences. In particular, we consider the fundamental role of reading as a process of comprehension of texts. We propose a model for strategy formation that states how strategic texts are created recursively, starting from the mundane narratives which influence daily practices (de La Ville and Mounoud 2001a). We also clarify the relationships that these mundane narratives have with texts produced by dominant stakeholders. The strategic text is thus involved in a double relationship with the context (the body of the preceding texts to which it relates) and with the situation (the ordinary activities it accounts for and helps organize).

This framework highlights the mediation role of strategic texts between institutional contexts and organizational situations and clarifies the processes involved in strategic textual productions. Strategy making has much to do with the capacity to master the skills of discussion. However, the practice aspect of strategy-making appears to be immersed in the narration of human experience. We consider strategic documents that organizations produce, such as written plans, as texts. Thus, they may be considered as 'being read' by organization members. Understanding strategy making based on reading and writing is useful in order to understand the complexities of strategy formation.

Strategy formation brings into play complex processes of interaction between organizational productions of a contrasting nature. It may be understood by using the text as a model of 'judicious' or sensible action. The latter 'becomes a subject of science on the condition that a kind of objectivity equivalent to the fossilization of the discourse through writing exists' [START_REF] Ricoeur | From text to action: Essays in Hermeneutics II[END_REF]. Ricoeur thus equates ordinary action with speech and conversation: action is also a representation anchored in the present, whose structure resembles that of speech acts and utterances. Conversely, the judicious action, associated with strategic action, perpetuates itself, leaves traces and becomes memorable. An action leaves its mark when it contributes to the emergence of significant configurations. A process of recording transforms it into a 'document' or 'archive' of organizational action, which brings it closer to the textual form and distinguishes it from the conversation. The judicious action results from emancipation with regard to the initial context and develops meanings that can be actualized or completed under new and different circumstances.

Consequently, the analysis of strategy formation must not be centred only on the conversations or the interactions described as 'strategic'. Strategy making should be considered as the combination of the production of texts and their creative consumption in daily activities. Consumption can be understood as the dominated production of second-order narratives. The descending order of the dominant discourse of strategy and the ascending order of the resisting narrative, two realms of strategy making and strategic texts are their point of intersection and articulation. This meeting shows the complexity of strategy formation, i.e. an ongoing process of becoming, through which the practice of strategy is brought into being at every instant of organizational life (Langley and al. 2013, p. 5). The context dominates and informs the strategic text because it provides the rules for it to form itself. In return, the strategic text, fuelled by ordinary accounts of organization members' practices, is subject to creative readings and resistant consumption. 'Human action is open to whoever can read' [START_REF] Ricoeur | From text to action: Essays in Hermeneutics II[END_REF]. Through this double role of mediation, the strategic text gathers meaning and becomes effective.

Table 12 .1 Strategy making from texts and narratives Consumption / Production interplay

 12

	Ruling order:	Consuming social practice / Producing
		dominant discourses (discipline)
	Strategic texts	Consuming dominant discourses
		(intertextuality) / Producing strategic texts
		(strategic genre) / Consuming everyday

Emphasis added by the authors.


Anthony Busson
email: anthony.busson@ens-lyon.fr

Lynda Zitoune
email: lynda.zitoune@esiee.fr

Véronique Vèque
email: veronique.veque@lss.supelec.fr

Bijan Jabbari
email: bjabbari@gmu.edu

Outage Analysis of integrated Mesh LTE Femtocell Networks

Keywords:

The femtocell -Wi-Fi integration is a promising approach to solve the problem of inter-tier or intra-tier interference in heterogeneous networks. In this paper, multimode femtocell base stations are deployed which form a Wi-Fi mesh network to communicate between themselves while deploying cellular technology (e.g., LTE) for communications with mobile users, thus ensuring ultimately connectivity between mobile users and their macro base stations to improve the network coverage. We propose a tractable model for coverage/outage to evaluate the benefits of such integration in terms of SINR and received signal strength. Our work is based on point processes in twodimensional plane that models locations of femtocell -Wi-Fi (also referred to as multimode) nodes. The proposed model is more realistic than the classical Poisson point process, as the distribution of points is more homogeneous and it ensures that the nodes are not too close to each other. The derivation of coverage/outage formula allows us to determine operational parameter ranges for the Wi-Fi network to form a mesh network. In addition, it helps in the design of the femtocell network to ensure a suitable coverage for users in terms of SINR and received signal strength. LTE/Wi-Fi LTE/Wi-Fi LTE/Wi-Fi

I. INTRODUCTION

Femtocell networks and more generally small cell networks are promising solutions to address the growth of the user's traffic density and coverage and diversity. The subject has received considerable attention in recent years [START_REF] Andrews | A tractable approach to coverage and rate in cellular networks[END_REF]- [START_REF] Wang | Analytical evaluation of coverageoriented femtocell network deployment[END_REF] from both academia and industry. Typically, femtocells base-stations (BS), operating in the licensed spectrum, are used to reduce the distance between the mobile user and the macro BS to which it belongs, using an efficient spatial reuse spectrum mechanisms [START_REF] Andrews | Femtocells: Past, present, and future[END_REF], [START_REF] Wang | Cognitive radio enhanced interference coordination for femtocell networks[END_REF]. Consequently, while indoor users may experience higher quality wireless services, the outdoor users can gain access to higher capacity.

Femtocells used with macrocells together form a heterogeneous network (also called k-tier network) to improve the network performance in terms of coverage and capacity. However, in practice communication suffers from the interference induced by femtocell BSs when used in 1-tier network alone or in the 2-tier case. The interference is due to the spectrum sharing and the random location of the femto BSs being user dependent. Several techniques have recently been deployed to handle the interference problem between the macro and small cells including power control, multiple antennas, adaptive FAP (Femtocell Access Point) access scheme, cognitive radio and spectrum allocation [START_REF] Cheung | Throughput optimization, spectrum allocation, and access control in two-tier femtocell networks[END_REF].

Other technical and economic/regulatory challenges are still present within femtocell networks when applied in outdoors, these include cell association and biasing, mobility and soft handoff, self-organizing (see [START_REF] Andrews | Femtocells: Past, present, and future[END_REF] for more details). In [START_REF] Bennis | When cellular meets wifi in wireless small cell networks[END_REF], the authors state that to take advantage of femtocells, innovative solutions must be developed to deal with the challenges cited above, and propose to integrate different radio access technologies, for example the integration of cellular (LTE) and Wi-Fi technologies. Thus, it is not surprising that the next generation of small cell BS is expected to be multi-mode. Consequently, the femtocell-Wi-Fi integration may resolve the problem of inter-tier or intra-tier interference by offloading some of the traffic to the unlicensed and shared-band of Wi-Fi. Conversely, when contention increases causing throughput reduction on the shared Wi-Fi band, some of the traffic can be switched to cellular links. This integration may provide benefits resulting from these two technologies, as summarized in [START_REF]Running for the coverage: A review of femtocells[END_REF].

In this paper, we aim to study coverage and outage of an integrated femtocell-Wi-Fi network. The network architecture is depicted in Figure I. We assume that femtocells implement both a cellular (e.g., LTE), and Wi-Fi technologies. The cellular network allows the mobile users to access the femtocell network. The Wi-Fi mesh network is used to ensure the connectivity between mobile users and their macro BS. Data from the mobile users is carried through the Wi-Fi mesh network to the macro BS.

We propose an innovative spatial point process to model this network. It differs from the classical Poisson point process and other work on femtocells [START_REF] Andrews | A tractable approach to coverage and rate in cellular networks[END_REF]- [START_REF] Cheung | Throughput optimization, spectrum allocation, and access control in two-tier femtocell networks[END_REF], [START_REF] Wang | Analytical evaluation of coverageoriented femtocell network deployment[END_REF] because points are more regularly distributed in the plane leading to a more uniform coverage. Furthermore, we prevent the presence of femtocells which are too close to each other. This modeling effort provides insight on the coverage and outage of the networks with multi-tier architecture. The present work may be applied in two contexts: 1) a dimensioning tool to evaluate ideal/optimal outdoor deployment of femtocells and 2) in green-networking where certain femtocells have to be switched-off to save energy. For the latter, our model offers analytical capability to evaluate location and number of femtocells that are needed to be kept on, while ensuring an accurate coverage of the cellular network and the connectivity of the multi-hop Wi-Fi network.

A. Related work

Stochastic geometry is extensively used to develop more tractable analytical models to study the performance of heterogeneous or k-tier cellular networks, in terms of the probability of coverage, outage and throughput. Practically, most of modeling papers consider Poisson Point Process (PPP) to describe the position of the femtocell BSs and the mobile users.

In [START_REF] Andrews | A tractable approach to coverage and rate in cellular networks[END_REF], the authors developed a general expression of the coverage probability in a 1-tier cellular network where the interference fading/shadowing follows an arbitrary distribution. They study the coverage through the signal on interference plus noise ratio (SINR), a region being covered if a typical user experiences a SINR greater than a threshold with a certain probability. They consider Rayleigh fading, and ignore the thermal noise. The authors derive the mean achievable rate and study coverage and rate in order to find the required frequency reuse to reach a specified coverage probability.

The paper [START_REF] Dhillon | A tractable framework for coverage and outage in heterogeneous cellular networks[END_REF] extends the model of coverage probability of [START_REF] Andrews | A tractable approach to coverage and rate in cellular networks[END_REF] to consider a multi-tier cellular network, by modeling downlink SINR. This new model has been compared to an actual 4G macro-cell network to validate its accuracy.

In [START_REF] Jo | Heterogeneous cellular networks with flexible cell association: A comprehensive downlink sinr analysis[END_REF], the same authors evaluate the impact of different cell association policies on metrics like the minimum average user throughput and the average ergodic rate. They assume that a mobile user connects to the femtocell BS that offers the best long-term averaged received power rather than the greatest instantaneous SINR. In this work, the outage probability is also calculated, and they observe that neither the number of BS nor tiers change the outage probability and the ergodic rate in an interference-limited fully-loaded heterogeneous cellular network with unbiased cell association. In [START_REF] Wang | Analytical evaluation of coverageoriented femtocell network deployment[END_REF], the authors argue that interference is more important in the "inner regions" close to the macro BS. So, they propose to deactivate femtocell BSs in zones where there is sufficient macrocell coverage. They show the benefits of their solution on the downlink coverage.

The authors in [START_REF] Wang | Analytical evaluation of coverageoriented femtocell network deployment[END_REF] define an analytical model which describes the coverage probability at a randomly located mobile user. In the first step, the model (same as [START_REF] Dhillon | A tractable framework for coverage and outage in heterogeneous cellular networks[END_REF]) describes the coverage probability for uniform femtocell deployment, where all the femtocell BSs remain active.Then, they derive another model for the overall coverage probability by defining the coverage probability in both the inner (where femtocell BSs are inactive) and outer regions (where femtocell BSs are active). This new model depends on the radius of the inner region. Monte Carlo simulations are also conducted to validate the model.

The model of [START_REF] Andrews | A tractable approach to coverage and rate in cellular networks[END_REF] is also used in [START_REF] Cheung | Throughput optimization, spectrum allocation, and access control in two-tier femtocell networks[END_REF] to handle the problem of inter-tier interference between a macrocell BS and femtocell BSs in case of severe frequency reuse. It aims to assess the impact of spectrum allocation and the femtocell access policies on the link reliability of each tier and on the total network throughput.

B. Approach and Contributions

We consider a set of multimode (LTE/Wi-Fi) femtocell BSs distributed arbitrarily over the plane. Our aim is to switch off some of them in order to save energy and at the same time to reduce interference on mobile users in the dense regions. The switching off process must guarantee the Wi-Fi connectivity between the remaining femtocells. As a result, we form a mesh network of femtocells that serves as an access network of the mobile nodes which are distant from the macro base station.

The point process we propose aims to model locations of the femtocells that are active. In order to ensure an accurate coverage, femtocells cannot be switched off randomly and independently of each other, because it could lead to uncovered regions or regions with femtocells interfering with each other. Consequently, the Poisson point process is inaccurate in this context. Locations of the femtocells being known, it is possible to keep a set of femtocells that covers the plane/region more or less regularly. Therefore, we split the plane into a set of squares of same size, forming a partition. For each square, we keep only one femtocell on to ensure a uniform coverage of the plane. But, two femtocells in two adjacent squares may still be arbitrarily close to each other generating redundant coverage and harmful interference. As the choice of active femtocells may be planned in advance, and with the knowledge of the femtocells location, this kind of situations should not appear. The idea is then to consider that these femtocells are distributed in the core of each square and not on the edges. This type of point process belongs to the family of the so-called hard-core point process. With these point processes, the distance between two points cannot be less than a given threshold. The most used hard-core point processes in the Telecommunication domain are the Simple Sequential Inhibition [START_REF] Busson | Capacity and interference modeling of csma/ca networks using ssi point processes[END_REF], or Matèrn [START_REF] Stoyan | Stochastic geometry and its applications[END_REF], but for which analytical derivations of Interference or SINR distribution are intractable. The point process that we propose has the benefit that it models realistically the femtocell selection (saving energy while ensuring a good coverage), and is mathematically tractable.

The remainder of the paper is organized as follows. In section II, we present the point process used to model the integrated femtocell-Wi-Fi network. In section III, we provide tractable analytical formulas of SINR and received signal strength at a mobile user. We present the numerical results in Section IV. Finally concluding remarks are made in Section V.

II. FEMTO-WI-FI COVERAGE MODEL

The proposed point process may model both the femtocell and Wi-Fi networks. Path-loss and transmission power levels can be adapted with respect to the considered technology. In the following, we shall use the term node or point rather than femtocell or Access Point, as the nodes implement these two technologies. The point process represents the node locations for nodes that have not been switched-off. We consider a partition of the plane formed by a grid of size r × r. In order to keep the process stationary, the grid is not centered at 0, but is centered at a point randomly distributed in the interval [0, r] × [0, r]. In each of these squares, we set a sub-square of size l × l (with 0 ≤ l ≤ r) at the center. A point is then uniformly distributed in each sub-square. When l < r, this process is a hard core point process, as the points cannot lie at a distance less than r -l. In our context, it guarantees that points in two adjacent squares cannot be too close to each other. It limits interference between adjacent cells. Figure 2(a) illustrates the construction of this process and the different notations. The intensity of this point process is then 1 r whatever the value of l. Mobile users are set according to a Poisson point process distributed in the plane. Conditioned on the presence of a user in a square, this mobile user is thus uniformly distributed within this square. Without loss of generality we assume that this point is located at the origin (by construction the origin is uniformly distributed in the square covering it). Also, we assume that a mobile user associates and communicates with the closest femtocell. Each femtocell is thus responsible for users distributed in its Voronoï cell. These Voronoï cells are more or less regular. It depends on the ratio l r between small and big squares. The impact of this ratio may be observed in Figure II, where we plotted the Voronoï cells of this point process for different l r ratios. We focus on the downlink between the femtocell and the mobile user. Interference is then computed at the user location. Interference at a femtocell can be derived in the same way, but is not considered in this paper. Interference will be mainly generated by the femtocell within the adjacent squares of the mobile user. Consequently, we estimate interference only from these squares. For convenience, we shift the center of the square where the mobile user is located at the origin. As shown in Figure 2(b), the squares are numbered from 0 (square at the origin) to 8. Locations of the associated point are denoted X 0 , X 1 , .., X 8 . The corresponding r × r and l × l squares are denoted R 0 , R 1 , .., R 8 , and L 0 , L 1 , .., L 8 respectively. The mobile user location is denoted with the random variable U . It follows a uniform distribution in the square 0

([-r 2 , r 2 ] × [-r 2 , r 2
]). In our example, the closest femtocell from the user is the point in the square 0. For this example, the transmission takes place between the point at U and X 0 , and interference are generated by points at X 1 , .., X 8 .

Let K (K ∈ {0, .., 8}) be the discrete random variable equal to the index of the closest femtocell/points from U , and I(U ) the interference at the user, we get:

I(U ) = 8 i=0 P t ξ i l ( U -X i ) 1 l K =i (1)
where P t is the transmission power (it is assumed to be the same for all femtocells), (ξ i ) i is a sequence of i.i.d. random variables modeling fading, l(.) is the path-loss function and 1 l . is the indicator function. The Signal over Interference plus Noise Ratio (SINR), is then given by:

SIN R = ξ K l( X K -U ) N + I(U ) ( 2
)
where N is a random variable modeling the noise. In the following, we consider a Rayleigh fading where (ξ i ) i are independently and exponentially distributed with parameter 1.

III. PERFORMANCE EVALUATION A. Coverage/Outage

We consider the distribution of two main quantities that impact the design of the integrated femtocell-Wi-Fi network: the SINR and the received signal strength. The proof is given only for the SINR distribution. The other computations are very similar.

Proposition 1. The complementary cumulative distribution function (CCDF) of the SINR is given by:

P (SIN R > β) = 1 r 2 l 2 R 0 k=0,1,5 C k L k E e - βN P t l( x k -u ) × 8 i=0;i =k E   1 l X i / ∈B(u, x k -u ) 1 + β l( X i -u ) l( x k -u )   dx k du (3)
with C 0 = 1, and C 1 = C 5 = 4. The CCDF of the received signal strength is given by:

P (ξ K Ptl( X k -U ) > β) (4) = 1 r 2 l 2 R 0 k=0,1,5 C k L k e - β P t l( x k -u ) (5) × 8 i=0;i =k P (X i / ∈ B(u, x k -u )) dx k du (6)
or when we consider the signal strength without fading:

P (Ptl( X k -U ) > β) = 1 r 2 l 2 R 0 k=0,1,5 C k L k 1 l P t l( x k -u )>β × 8 i=0;i =k P (X i / ∈ B(u, x k -u )) dx k du (7)
Proof.

P (SIN R > β) = P P t l( X K -U )ξ N + I > β (8) = P ξ > β(N + I) P t l( X K -U ) (9) = E e - β(N +I) P t l( X K -U ) (10) = k=8 k=0 E e - β(N +I) P t l( X i -U ) 1 l K=i (11)
By simple symmetric arguments, we can see that the terms in the sum of Equation [START_REF] Stoyan | Stochastic geometry and its applications[END_REF] are equal for all possible values of K in {1, 2, 3, 4} and {5, 6, 7, 8}. Therefore, we can distinguish three different cases: K = 0, K = 1, and K = 5. If we set the constant C 0 = 1 and C 1 = C 5 = 4, we get,

P (SIN R > β) (12) = k=0,1,5 C i E e - β(N +I) P t l( X k -U ) 1 l K=k (13)
We condition by U , and each term of the sum by the transmitter location, (X 0 , X 1 or X 5 ):

P (SIN R > β) (14) = 1 |R 0 | 1 |L 0 | R 0 k=0,1,5 C k L k E e - β(N +I) P t l( x k -u ) 1 l K=k dx k du (15)
Computation of the expectations can be done as follows. Let k ∈ {0, 1, 5}, we obtain:

E e - β(N +I) P t l( x k -u ) 1 l K=k (16) = E e - βN P t l( x k -u ) E e - βI P t l( x k -u ) 1 l K=k (17) = E e - βN P t l( x k -u ) E e - β 8 i=0;i =k ξ i P t l( X i -u ) P t l( x k -u ) 1 l K=k (18)
The second term is as follows:

;i =k ξ i P t l( X i -u ) P t l( x k -u ) 1 l K=k (19) = 8 i=0;i =k E e - βξ i l( X i -u ) l( x k -u ) 1 l Xi / ∈B(u, x k -u ) (20)
= 8 i=0;i =k E   1 l Xi / ∈B(u, x k -u ) 1 + β l( Xi-u ) l( x k -u )   (21)
Finally, we obtain:

P (SIN R > β) (22) = 1 |R 0 | 1 |L 0 | R 0 k=0,1,5 C k L k E e - βN P t l( x k -u ) (23) × 8 i=0;i =k E   1 l X i / ∈B(u, x k -u ) 1 + β l( X i -u ) l( x k -u )   dx k du (24)
If we assume that the noise follows a Gaussian distribution with mean µ and variance σ 2 , we get:

E e - βN P t l( x k -u ) (25) = e -1 2 σβ P t l( x k -u ) 2 - µβ P t l( x k -u ) (26)
IV. NUMERICAL EVALUATION Our model aims to determine values r and l, that verifies the different constraints of the femtocell and Wi-Fi networks. In order to save maximum energy, i.e. to switch-off maximum number of nodes, we need to choose the greatest r that satisfies these constraints. If λ f is the initial femtocell intensity, we can easily express the ratio between the remaining femtocell and the number of initial femtocell. as 1 λ f r 2 . It may give a precise estimate of the saved energy, but this point is not developed in this paper.

The constraints on r are manifold. r must be bounded in order to keep the Wi-Fi network connected. It suffices to guarantee that nodes into two adjacent squares are in the radio range of each others. Therefore, we can choose r to guarantee a maximum distance between two nodes, or ensure that the received signal strength will be greater than a given threshold with a certain probability (as it is developed below for the femtocell network). Interference does not have to be considered here, as the CSMA/CA mechanism used in the Wi-Fi network ensures that two interfering nodes are not transmitting at the same time.

On the other hand, in the femtocell network the medium is shared by nodes lying in adjacent squares. A transmission from a femtocell to a user will be properly received if both the SINR and the received signal strength are sufficiently great. The second criterion is linked to the receiver device sensitivity. For instance, in Figure 4(a) we assumed a fixed receive power target of -100.0 dBm. The other parameters are given in Table I. We have plotted the CCDF of the received signal strength without fading as given by Equation ( 7) for β = -100 dBm. We aim to choose r in such a way that 95% of the users will experience a signal strength greater than this threshold. This is shown through the horizontal line in the figure . The maximum values of r with respect to this constraint varies from 400 to approximately 570 meters. There is thus an important gain in terms of coverage with respect to the parameter l.

Also, we compared these results with the Poisson point process with same intensity (λ = 1 r 2 ) in the same figure. Due to the fact that distance between the user and its closest node is not bounded for Poisson (the user may be arbitrarily far from the closest node), CCDF of the received signal strength is less for Poisson than for our model. It involves that for a given threshold on this CCDF, the coverage distance is less for Poisson.

The second criterion is the SINR. We need to set r and l in such a way that P (SIN R > β) > 1 -. In Figure 4(b), we plot the SINR CCDF for r = 400.0 and different values of l (as given by Equation ( 3)). We can observe the impact of l on the SINR. Small values of l lead to a significant improvement of SINR. Poisson still leads to a less efficient coverage as SINR is likely to be smaller than for our process.

The SINR CCDF for a given value of β (P(SIN R > β)) does not vary with r. It is not plotted here due to lack of space, and because curves simply consist of horizontal line for both processes. As it has been shown for the Poisson point process [START_REF] Andrews | A tractable approach to coverage and rate in cellular networks[END_REF], when the noise is negligible, this quantity stays constant with respect to r (and P t ) due to the ratio between received signal strength and interference.

Other criteria can be taken into account to set l and r values. l cannot be choose arbitrarily small as it has to be chosen in such a way that there is a femtocell in the l × l square with a high probability. Given the initial spatial distribution of the nodes (before they have been switched-off), we may choose l such that we have a reasonable probability to have a femtocell in a square of size l ×l. Also, r can be set according to the mean number of users associated with a femtocell. As the femtocell intensity is 1 r 2 , the mean size of a Voronoï cell is r 2 . If the users intensity is λ u , then the mean number of associated users is λ u r 2 , and 0.95λ u r 2 if we consider only users meeting the criterion on the received signal strength.

V. CONCLUSION

We proposed a new point process that is more realistic than the Poisson point process to model an integrated femtocells- Wi-Fi network. It has the benefit to offer a more regular coverage, and inhibit the property of hard-core point processes where points cannot be arbitrarily close to each other. Coverage and outage have been derived for this model, offering some insights on the deployment of such networks.

We have shown that this more realistic model exhibits a better coverage than a Poisson point process with same intensity both in terms of SINR and received signal strength. Our point process depends on two main parameters: r which is related to the point intensity, and l that set the minimal distance between the points. The parameter r mainly impacts the received signal strength at a receiver whereas l impacts SINR distribution. It is thus possible to propose dimensioning rules of the femtocell networks according to these two criteria. Moreover, this work may help in the design of algorithms that switch-off certain nodes to save energy while ensuring the proper operation of the network in terms of connectivity and coverage. A direct extension of this study might involve combining the proposed point process within a model allowing us to evaluate precisely the gain in energy when the femtocells-Wi-Fi nodes are switched-off.

Fig. 1 .

 1 Fig. 1. Femtocell and Wi-Fi mesh network architecture.

  Fig. 2. Notations

Fig. 3 .

 3 Fig. 3. Impact of the ratio l r on the Voronoï cells.

  P (Received signal strength > -110 dBm) for a typical user CCDF of the SINR.

Fig. 4 .

 4 Fig. 4. CCDF of SINR and received signal strength