Khalil Assala

Suela Bylykbashi

Professor Gilles Roehrich

M Gerard Cliquet

How To Measure Competitive Intensity?

Keywords: Competitive intensity, Competitive dynamics, New product, Strategic decisions, Tactical decisions

In this research, we analyse the internal structure of competitive intensity on the basis of competitive dynamics. We propose a measure of competitive intensity based on two dimensions: strategic and tactical. This two-dimensional design makes it possible to gain a better understanding of the competitive battle, allowing managers to improve operations and the allocation of resources, according to both dimensions. It also provides a better understanding of the relationship between competitive intensity and other variables.

Introduction

A dynamic interpretation of competition is one of the recent trends in strategic management research (Chen and Miller, 2012). With this approach, competitive intensity is identified as a threat factor affecting the ability of firms to maintain a long-term competitive advantage [START_REF] D'aveni | Hypercompetition: Managing the Dynamics of Strategic Maneuvering[END_REF], and influencing the performance and success/failure of new products (Cooper, 1979;Cooper, 1984;Cooper and de Brentani, 1991;[START_REF] Cooper | New Products: What Separates the Winners from the Losers[END_REF][START_REF] Cooper | New product success factors: A comparison of 'kills' versus successes and failures[END_REF]Gonzales-Benito et al., 2014;[START_REF] Lee | The Impact of Communication Strategy on Launching New Products: The moderating Role of Product Innovativeness[END_REF][START_REF] Muller | Stratégie d'innovation, concurrence et performance des nouveaux produits[END_REF][START_REF] Song | The determinants of Japanese New Product Successes[END_REF]. Despite the importance of competitive intensity, its internal structure has been neglected. Nevertheless, an improved knowledge of its workings provides for a better understanding of the competitive environment in a market, and leads to more appropriate management decisions (Ketchenet al., 2004). The present research attempts to fill this gap by studying the internal structure of competitive intensity, through the identification of its dimensions. Competitive intensity allows the competition observed in any given market to be characterized. It corresponds to the degree of competition exerted by competitors in a market (Chen, 1996). Competitive battle in a market leads to two types of action: strategic and long-term actions involving major investments, which are generally designed to make an offer that is more attractive to buyers than that proposed by competitors [START_REF] Abell | Defining the Business: The Starting Point of Strategic Planning[END_REF]Ailawadiet al. 2001;Bowman and Gatignon, 1995;Chen and Lii, 2005;Chen et al., 1992;[START_REF] Lemmink | Competitive Reactions to Products Quality Improvements in Industrial Markets[END_REF][START_REF] Ramaswamy | Competitive Marketing Behavior in Industrial Markets[END_REF][START_REF] Thompson | Organizations in Action[END_REF][START_REF] Urban | Design and Marketing of New Products[END_REF], and tactical actions leading to only minor modifications. This is a question of short-term investments, whose purpose is either to curb competitors' sales, or to temporarily boost a company's own sales. Strategic actions, on the other hand, require a greater mobilization of resources and are accompanied by major changes in the company's strategic orientation [START_REF] Thompson | Organizations in Action[END_REF] and in the definition of its sphere of business [START_REF] Abell | Defining the Business: The Starting Point of Strategic Planning[END_REF]. In the short term, these expenses often have a negative impact on profits, whereas their long-term impact can be extremely positive. This research suggests that competitive intensity has a two-dimensional nature, because it occurs at two different levels. However, the literature dealing with the operationalization of competitive intensity, through the observation of actions and responses in a market, reveals a rather one-dimensional posture and makes no distinction between strategic and tactical decisions [START_REF] Cooper | New product success factors: A comparison of 'kills' versus successes and failures[END_REF]Gonzales-Benito et al., 2014;[START_REF] Jaworski | Market Orientation: Antecedents and Consequences[END_REF][START_REF] Lee | The Impact of Communication Strategy on Launching New Products: The moderating Role of Product Innovativeness[END_REF]Pulendranet al., 2000). Nonetheless, strategic and tactical decisions do not have the same temporalities and consequences (Chen and Miller, 1994;Smith et al., 1991). According to [START_REF] Lee | The Impact of Communication Strategy on Launching New Products: The moderating Role of Product Innovativeness[END_REF], for example, a high level of competitive intensity corresponds to an intense battle over price, distribution or advertising. Pulendranet al. (2000) consider this same battle in terms of price and promotion. Finally, according to [START_REF] Muller | L'influence de la réaction concurrentielle sur la performance des nouveaux produits et le rôle modérateur des caractéristiques du marché[END_REF], although this author accepts that there is a correlation between competitive intensity and the degree of competition in a market, the instruments used by competitors are not specified. The aim of this research is to study the internal structure of competitive intensity, and to explore the possibility of developing a two-dimensional structure. To do this, we firstly present the methods used to measure competitive intensity in previous research. We then expand the notion of competitive intensity using a qualitative study, and present our approach to the development of a measurement scale. Finally, we discuss the theoretical and managerial implications, as well as some thoughts about the limitations of this study.

Literature Review

Competitive intensity has been central to research on strategic groups [START_REF] Porter | The Structure Within Industries and Companies' Performance[END_REF]Caves and Porter, 1977;Cool and Dierickx, 1993;Peteraf, 1993) or multi-market competition [START_REF] Amine | Intensité concurrentielle entre lignes de produits rivales : Un éclairage par la théorie de la concurrence multimarchés[END_REF][START_REF] Fuentelsaz | Multipoint Competition, Strategic Similarity and Entry into Geographic Markets[END_REF][START_REF] Gimeno | Reciprocal Threats in Multimarket Rivalry : Staking Out "Spheres of Influence[END_REF]Gimeno and Woo, 1999;Jaychandranet al., 1999). Although it is widely used in management sciences, with 1100 publications noted at the end of 2014 (Kwiecinski, 2017), very few authors have focused on defining this concept. According to [START_REF] Porter | Competitive Strategy[END_REF][START_REF] Porter | The Five Competitive Forces That Shape Strategy[END_REF], one of the founders of the structuralist conception of competition, competitive intensity is identified as one of the five forces determining the attractiveness of an industry and expressing the exchange of competitive movements2 . Along similar lines, [START_REF] Auh | Balancing exploration and exploitation: The moderating role of competitive intensity[END_REF] define competitive intensity as a situation where competition is fierce, due to the number of competitors and the lack of growth opportunities in the market. In contrast to this approach, Chen (1966) relies on a "behavioural" perspective in which competition is considered to be a set of decisions (Jacquemin, 1985;[START_REF] Foss | La recherche en stratégie et la perceptive de processus de marché[END_REF]Le Roy, 2004;Poracet al., 1995). In line with the works of D' Aveni (1994) and his concept of hyper-competition, Chen (1996) defines competitive intensity as the degree of aggressiveness and the speed of actions and responses taken by firms to compete in a market. Using individual competitive movements as a unit of analysis, it proposes to analyse the competitive battle as a chain of actions and reactions between companies or brands in a situation of competitive interdependence (Chen et al., 1992). Finally, according to [START_REF] Muller | L'influence de la réaction concurrentielle sur la performance des nouveaux produits et le rôle modérateur des caractéristiques du marché[END_REF], competitive intensity reflects the number of companies competing in the market and the fierce competition they face in this market. This author takes into account, in the definition of competitive intensity, its partial nature, i.e. the fact that in some cases competitive intensity may not be relevant to all competitors in the market.

In this research we study the competition between brands in a given market. The competitive battle finds its origins in the fact that brands must share the market, and that with the aim of maximizing profits, each competitor tries to increase its sales. An increase in sales can have two origins: either the conquest of new consumers, or the conquest of consumers from other brands, leading to an increase in market share. Competitive intensity is thus a sign of the difficulty experienced by brands in increasing their sales, other than by increasing their market share. This conflict for market share can lead to two types of action: the conquest of superior positioning, or that of improved attractiveness resulting from positioning emphasis. We thus adopt the following operational definition for competitive intensity: competitive intensity is the degree to which competitors fight to improve their market share; it is expressed either by the search for superior (strategic) positioning, through the use of a more effective (tactical) supply support policy, or through a combination of both of these. While it is rare to encounter a definition for competitive intensity, there is abundant management science literature dealing with its operationalization. In previous studies we have identified different approaches to measuring the degree of competitive intensity. They differ in several respects: the notion of competition (structuralist or behaviourist), the level of analysis (micro or macro), the dyadic (two competitors) or market-level (all competitors) approach, the unit of analysis (brands or businesses); and finally the analytical perspective (behaviour of consumers or competitors). With the structuralist approach, competitive intensity is measured either by the number of competitors in a market, or through the use of different concentration ratios (Abramoet al., 2012;Becker and Dietz, 2004;Caves et al., 1984;Chen et al., 2015;[START_REF] Fischer | Measuring Competition in the U.S. Airline Industry Using the Rosse-Panzar Test and Cross-Sectional Regression Analyses[END_REF][START_REF] Giachetti | Detecting the relationship between competitive intensity and firm product line length: Evidence from the worldwide mobile phone industry[END_REF]Jermias, 2006;[START_REF] Ju | Behind organizational slack and firm performance in China: The moderating roles of ownership and competitive intensity[END_REF]Lijesenet al., 2002;[START_REF] Porter | Competitive Strategy[END_REF][START_REF] Vroom | Ownership form, managerial incentives and the intensity of rivalry[END_REF][START_REF] Scherer | Industrial Market Structure and Economic Performance[END_REF][START_REF] Souare | Canada -US productivity gap: the role of competition intensity differential[END_REF][START_REF] Wu | Technological collaboration in product innovation: The role of market competition and sectoral technological intensity[END_REF][START_REF] Wu | The bidirectional relationship between competitive intensity and collaboration: Evidence from China[END_REF]. The most commonly used index is that of Herfindahl, calculated by summing the squares of the market shares of n competitors. The higher the value of this indicator, the more concentrated and less competitive the sector. In this approach, the actual behaviour of competitors is not taken into account (Le Roy, 2004). Measuring competitive intensity is equivalent to determining the structural factors that determine its degree [START_REF] Oster | Modern competitive analysis[END_REF][START_REF] Porter | Choix stratégiques et concurrence[END_REF]. In the same vein, O' Cass and Ngo (2007) and O'Cass and Weerawardena (2010) measure competitive intensity using the five sectorial forces defined by Porter [START_REF] Porter | Towards a dynamic theory of strategy[END_REF]. In a more recent behaviourist approach, which is at odds with the static approach, the core of competitive intensity lies in the interactional "dynamics". In this approach, market concentration is considered as one of the antecedents of competitive intensity. With this concept, which places interactions between competitors at the centre of the debate, intensity is measured more in terms of its consequences, such as change in margin (change in the cost/price ratio) [START_REF] Feinberg | Sales-at-Risk : A Test of the Mutual Forbearance Theory of Conglomerate Behavior[END_REF][START_REF] Gimeno | Hypercompetition in a multimarket environment: the role of strategic similarity and multimarket contact in competitive de-escalation[END_REF], the number of competitors entering or exiting from the market [START_REF] Baum | Competitive Dynamics of Interfirm Rivalry[END_REF]Corn, 1996), 1999;[START_REF] Barnett | Strategic Deterrence Among Multipoint Competitors[END_REF], or the transfer of market share between competitors [START_REF] Li | The Impact of Market Knowledge Competence on New Product Advantage: Conceptualisation and Empirical Examination[END_REF]. Other authors measure the degree of competitive intensity by its impact on consumer behaviour. The competitive intensity between two brands can thus be measured by studying transfers (Carpenter and Lehman, 1985;[START_REF] Grover | A Simultaneous Approach to Market Segmentation and Market Structuring[END_REF], inter-purchase periods [START_REF] Fraser | Competitive Market Structure Analysis: Principal Partitioning of Revealed Substituabilities[END_REF][START_REF] Grover | Inferring Competitive Market Structures Based on a Model of Interpurchase Intervals[END_REF], simultaneous brand considerations (Chandon and Strazzieri, 1986), revealed preferences [START_REF] Merunka | Competitor : Un Modèle de Positionnement Concurrentiel des Marques Appliqué à des Données de Panel Consommateur[END_REF] or even penetration and duplication indexes [START_REF] Dawes | Analyzing the intensity of private label competition across retailers[END_REF]. These authors study competition at the individual level [START_REF] Shocker | Modelling Competitive Market Structures : Practices, Problems, Promise[END_REF] and are more interested in the underlying reasons for competition than competition itself (Merunkaet al., 1999). "These measures help to understand the similarities and differences between brands that may explain competitive intensity measured elsewhere" (p. 11). Another research group focuses on the dyadic of action and response (Chen et al., 1992;Chen, 1996, Chen andMiller, 2012) and measures the degree of competitive battle through direct observation of the competitors' actions and responses. However, these measures remain limited to two competitors. Finally, another group measures competitive intensity at the market level by including all competitors. Some measures used by this group provide no information concerning the instruments used (Bosoet al., 2012[START_REF] Mahapatra | A contingent theory of supplier management initiatives: Effects of competitive intensity and product life cycle[END_REF][START_REF] Muller | L'influence de la réaction concurrentielle sur la performance des nouveaux produits et le rôle modérateur des caractéristiques du marché[END_REF]. Competitive intensity is considered by [START_REF] Muller | L'influence de la réaction concurrentielle sur la performance des nouveaux produits et le rôle modérateur des caractéristiques du marché[END_REF], for example, to be "strong" when the respondent indicates a highly competitive market, and "weak" when the respondent indicates a "moderately competitive market" or a "weakly competitive market". Other measures focus on the instruments used by all competitors in a market, through the use of various scales (Chan et al., 2012;Chen et al., 2015;[START_REF] Cooper | New product success factors: A comparison of 'kills' versus successes and failures[END_REF][START_REF] Cui | The influence of competitive intensity and market dynamism on knowledge management capabilities of multinational corporation subsidiaries[END_REF]Gonzales-Benito et al., 2014;[START_REF] Jaworski | Market Orientation: Antecedents and Consequences[END_REF][START_REF] Lee | The Impact of Communication Strategy on Launching New Products: The moderating Role of Product Innovativeness[END_REF]Leonidouet al., 2013;Navarro-Garcia et al., 2015;Pulendranet al., 2000;[START_REF] Tsai | Cross-Functional collaboration, competitive intensity, knowledge integration mechanisms, and new product performance: A mediated moderation model[END_REF][START_REF] Tsaur | Personal ties, reciprocity, competitive intensity, and performance of the strategic alliances in Taiwan's travel industry[END_REF]. However, we believe that these scales measure market dynamics only partially, because they do not take into account all the instruments used in the competitive battle, and do not distinguish between strategic and tactical instruments. Table 1 summarizes all of these scales.

Reference

Measure used Aim of the research

Bosoet al. (2012)

One dimension (3 items): 1. Our export markets are known for competition between companies. 2. There is substantial competition between competitors in our export markets. 3. There is intense competition between competitors in our export markets.

To study the impact of entrepreneurship and market orientation on the success of a new export product, under different levels of competitive intensity and financial capital.

Chen (1996)

Respondents are asked to indicate, in order of importance, from a list of 13 competitors, the five airlines with which the most intense rivalry is experienced.

To study the impact of multi-market competition and strategic similarity, on rivalry between two competitors.

Chen et al. (2015)

One dimension (3 items): 1. Promotional warfare is intense in our industry. 2. Every time a competitor does something, the others quickly do the same. 3. In our industry, price is the main component of the competitive conflict.

To study the moderating role of competitive intensity and entrepreneurship between the capacity of technological information and the performance of product innovation. [START_REF] Cooper | New product success factors: A comparison of 'kills' versus successes and failures[END_REF] One dimension (3 items): 1. Number of competitors. 2. The intensity of competition. 3. The degree of price competition.

To determine the success factors for new products.

Gonzales-Benito et al.

(

) 2014
One dimension (4 items): 1. Our competitors are very aggressive in pricing decisions 2. Our competitors are constantly proposing new products or improved products for our target. 3. Our competitors propose products / services that can easily be substituted.

4. Our competitors are larger.

To study the moderating role of environmental characteristics in the market-orientation / performance relationship. One dimension (6 items): 1. Competition is fierce in our industry. 2. The promotional war is intense in our industry. 3. Every time a competitor does something, the others quickly do the same. 4. In our industry, price is the main component of the competitive conflict.

5. We often hear about a new competitive manoeuvre. 6. Our competitors are relatively slow.

To determine the antecedents and consequences of market orientation.

Lee and O'Connor (2003)

One dimension (5 items): 1. The number of competitors. 2. The intensity of price competition 3. Competitive intensity in the industry 4. The intensity of the main competitors' distribution system.

The intensity of the main competitors'

advertising.

To study the moderating role of product novelty in the communication of new products.

Li and Calantone (1998)

One dimension (4 items): This product's market: 1. Is predictable / not predictable 2. Is not competitive / highly competitive 3. Market shares are stable / volatile 4. Has few / many new competitors

To study the impact of market knowledge skills on the advantage of new products.

Luschand [START_REF] Laczniak | The evolving marketing concept, competitive intensity and organizational performance[END_REF] One dimension (3 items): 1. Businesses will spend a higher proportion of each dollar on marketing, due to increased competition. 2. Companies in our industry will fight aggressively to maintain their market share. 3. Competition will be more intense.

To study the evolution of the concept of marketing, competitive intensity and organisational performance.

Molina-Castillo et al. (2011)

One dimension (3 items): 1. Competitive intensity on the market is intense.

Businesses will aggressively fight to

maintain their market share. 3. Companies have increased their marketing expenses due to competitive pressures.

To study the impact of operating and skills exploration strategies on the performance of new products.

Muller (2002)

Only one item: Respondents are asked to indicate whether the market is very competitive, moderately competitive, or not very competitive. Competitive intensity is "strong" when the respondent indicates a highly competitive market, and "weak" when he/she indicates a "moderately competitive market" or an "uncompetitive market".

To study the influence of a competitive reaction on the performance of new products and the moderating role of market characteristics.

Pulendranet al. (2000)

One dimension (5 items): 1. Competition in our industry is fierce. 2. There is an intense promotional war in our industry. 3. Every time a competitor does something, the others quickly do the same. 4. In our industry, price is the main component of the competitive conflict.

5. We often hear about a new competitive manoeuvre.

To determine the antecedents and consequences of market orientation.

Song and Parry (1997) One dimension (3 items): 1. Potential consumers of this product were very loyal to the products of competitors in this market. 2. There is a competitor who dominates the market (with a very high market share). 3. Potential consumers for this product were very satisfied with the competitors' products.

To determine the success factors for new products.

Tsai and Hsu (2014) One dimension (3 items): 1. Promotional conflict is fierce in our industry. 2. Every time a competitor does something, the others quickly do the same.

We often hear about a new

competitive manoeuvre.

To study the moderating variables between transverse collaboration in a business and the performance of new products.

Tsaur and Wang (2011) One dimension (3 items): 1. The number of competitors in your category, within the alliance. 2. The extent of price competition in price competition, within the alliance.

It should be noted however that this scale measures competitive intensity, using both structural variables, such as the number of competitors, as well as behavioural variables.

To study the role of reciprocity and competitive intensity in the relationship between personal characteristics and the performance of alliance strategies in Taiwan's travel industry. Despite the significance of this research, the measures generated by these studies nevertheless appear incomplete to us. Although the literature review suggests that competitive battle leads to two types of action, strategic and tactical, can the competitive intensity characterising this conflict have a two-dimensional structure? And if this were confirmed, how should it be measured? These are the questions we try to answer in the following section.

AProposal ForThe Measurement Of Competitive Intensity

The scale we propose is built on the basis of the Churchill paradigm (1979), updated by Gerbing and Anderson in 1988. We proceed in two steps: the first is the creation of a scale with the specification of the constructed domain and the creation of a sample of items; the second concerns its refinement and validation. Although the Churchill paradigm has been criticized [START_REF] Rossiter | The c-oar-se procedure for scale development in marketing[END_REF], it is still relevant because it offers precise and simple rules for the construction of reliable measurement scales [START_REF] Mansouri | La construction dune échelle de mesure des problématiques de lenvironnement tétranormalisé de lentreprise Application du paradigme de Churchill. 5 ème Congrès de lADERSE[END_REF]. However, we have taken into account the remarks and developments formulated by [START_REF] Rossiter | The c-oar-se procedure for scale development in marketing[END_REF][START_REF] Rossiter | Reminder: A horse is a horse[END_REF], in an effort to improve this procedure, by systematically comparing each item with the definitions of the construct.

Specifications ForThe Domain Of The Construct

In this step, we follow Churchill's recommendations (1979) through a dual approach: theoretical, by studying the literature and researching existing measures, and empirical, by carrying out qualitative exploratory studies (individual or group interviews) with the dual objective of providing a definition of the construct to be measured, and identifying any internal dimensions of this construct. In order to further develop the notion of competitive intensity and determine its internal structure, we base our approach on an exploratory qualitative study [START_REF] Bardin | L'analyse de contenu[END_REF][START_REF] Wacheux | Méthodes qualitatives et recherche en gestion[END_REF]. Our corpus is composed of texts corresponding to transcripts from a series of semi-directive interviews with 9 product managers. We interviewed product managers with market responsibilities in various sectors: telecommunications, information systems, public works, and ski equipment, in order to collect a variety of information (Table 2). Our corpus is homogeneous in terms of temporality, as the interviews were conducted over a two-month period. The interview guide is structured around a central question: "How does competitive battle function in your market?" Follow-up actions made it possible to clarify the modalities of the battle. Interviews with product managers lasted one hour and a half, on average. Redundancy and crosschecking of responses during the last two interviews indicated a posteriori that there was thematic saturation at the end of the ninth interview (Allard-Poesiet al.,2004). After transcribing the interviews, manual thematic content analysis was carried out, firstly by dividing the corpus into recording units; these were grouped into categories to facilitate the development of our analysis grid. We then conducted a vertical analysis to study in depth each interview as well as a horizontal analysis to compare the different discourses. This technique is well suited to exploration in a poorly known field (Mileset al., 2014). This content analysis made it possible to reveal the existence of two major themes. Regardless of their sector, the managers confirmed that competitive battle is indeed exerted at two different levels: strategic and tactical, with very different instruments for each level. Table 3 shows the main statements made during the interviews, for each theme.

Sector of activity

Main responses to the question: "How does competitive battle function in your market?" Theme 1 -The competitive battle in strategic terms -"we compete essentially in terms of new products" -"the market we're in is a very competitive one. In this market all competitors are launching new products" -"our competitors propose products that are very, very good and have technical capacity" -"you can't always slash prices to gain market share. Many innovation programs have been developed in recent years, in an effort to improve the quality of our products. The competitive battle is being fought at this level" Theme 2 -The competitive battle in tactical terms -"it's a highly competitive market. We have to make promotional offers" -"everyone is trying to be present in advertising campaigns, in magazines, websites, i.e. in marketing" -"our competitors do not earn much with their products, rather with their after-sales services" -"at every level: promotional offers, team management, in the shops, advertising is huge. The principle is to increase visibility, to maximize visibility in all communications media" -"the competitive battle is exerted at the level of prices, speed of service, and quality" -"indeed, we have products that are increasingly difficult to differentiate with respect to our competitors (because everyone is able to manufacture the same product), this is the reason for which we compete with prices, and with the offer of complementary services"

Table 3: The main responses arising from individual interviews

The results derived from this qualitative exploratory analysis confirmed our belief that competitive intensity should be considered as two-dimensional. Measuring competitive intensity thus corresponds to measuring the intensity of the effort provided by competitors, in each of the two dimensions of this battle: strategic and tactical. The items on our scale are based on the existing scales listed in Table 1 as well as the results of interviews with product managers. Indeed, although the existing scales are not perfectly adapted to our approach, some of their items are compatible. These items are presented in Table 4.

Creation OfThe Items Of The Competitive Intensity Scale

Items

Assigned dimension Reference

publicity battle Tactical [START_REF] Lee | The Impact of Communication Strategy on Launching New Products: The moderating Role of Product Innovativeness[END_REF] publicity battle at the level of sales promotion Tactical [START_REF] Jaworski | Market Orientation: Antecedents and Consequences[END_REF]; [START_REF] Pulendran | Antecedents and Consequences of Market Orientation in Australia[END_REF] publicity battle at the level of distribution Tactical [START_REF] Lee | The Impact of Communication Strategy on Launching New Products: The moderating Role of Product Innovativeness[END_REF] price competition Tactical [START_REF] Jaworski | Market Orientation: Antecedents and Consequences[END_REF]; [START_REF] Lee | The Impact of Communication Strategy on Launching New Products: The moderating Role of Product Innovativeness[END_REF] The qualitative interviews allowed us to complete this list of items (Table 5). In the case of the items taken from Anglo-Saxon measures, these were translated from English into French, and then back translated, in order to check the quality of their translation. Then, for these items and for those taken from the exploratory interviews, content analysis was used to classify them into the different dimensions. Finally, a selection was made of the finally retained items, according to their dimension. Pretesting of these items was done in two phases: 1) face-to-face interviews with three lecturers in management science, and face-to-face interviews with four managers. At the end of each phase, these items were modified while taking their comments into account. At the end of the second pre-test, and in the absence of additional remarks from the managers, the questionnaire was ready for release.

Items Assigned dimension

Battle to improve the offer of complementary services Tactical

Battle in terms of sales force Tactical

Rhythm of the launch of new products Strategic

Rate of product improvement Strategic Battle to improve the quality of products Strategic

Battle to launch new products Strategic Table 5: Items of competitive intensity derived from the qualitative study In our approach, this scale includes two sub-dimensions: the actions related to the "strategic" dimension and the actions related to the "tactical" dimension. The former corresponds to items 1, 2, 5, 6 and 10, and the second to items 3, 4, 7, 8 and 9.

Data Collection

Three data collection methods were used: mailing, hand-delivery and online survey. Our target population included executives with a marketing function (i.e. product manager, marketing manager, sales manager, sales engineer). In practice, 546 questionnaires were sent to managers working in the fields of electronics, the automotive industry and plastics. They were contacted in advance by telephone in order to increase their response rate [START_REF] Yu | A Quantitative Review of Research Design Effects on Response Rates to Questionnaires[END_REF]. Two weeks after the first contact, we again contacted the people concerned. Finally, 42 questionnaires were returned. At the same time, questionnaires were hand-delivered to members of the target group through trainees and apprentices from a business school. Out of 69 distributed questionnaires, 12 were returned. Finally, the questionnaire was placed online using the Sphinx software. On the basis of various diploma directories and files found on the Internet, 1745 persons were contacted. A total of 107 questionnaires were collected. Overall, these three procedures allowed us to collect 161 completed questionnaires. The use of three different data-collection methods made it possible to reduce the influence of the search method on the results obtained [START_REF] Mitchell | An Evaluation of the Validity of Correlational Research Conducted in Organisations[END_REF][START_REF] Bagozzi | Multitrait-Multimethod Matrices in Consumer Research[END_REF][START_REF] Williams | Method Variance in Organisational Behaviour and Human Resources Research : Effects on Correlations, Path Coefficients and Hypothesis Testing[END_REF]. We eliminated 21 questionnaires, thus restricting our final data analysis to 140 questionnaires.

Refinement AndValidation Of The Scale

Testing of the structure of the two-dimensional scale of competitive intensity was carried out in two steps: an exploratory factorial analysis (EFA) first made it possible, thanks to the use of principal component analysis with Promax rotation, to refine the measure by successively eliminating all items that were not correctly assigned. Confirmatory factorial analysis (CFA) was then used to refine this structure. This second step was the object of a systematic bootstrap procedure, designed to minimize the risk arising from non-compliance with the multi-normality hypothesis.

Results

Table 7 shows the structure resulting from the exploratory factorial analysis. The two updated factors effectively correspond to the two dimensions of the scale. However, it was necessary to delete some items in both dimensions. Thus, terms related to price and sales force have disappeared from the "tactical" dimension. At the same time, the items related to the intensity of the battle to improve the quality of products and services were eliminated. The internal coherence is very good in both dimensions (0.70 for the strategic dimension and 0.81 for the tactical dimension). Finally, as the correlation between these two dimensions is found to be 0.45, they are close, but not identical. This two-dimensional structure was thus subjected to confirmatory factor analysis, and the two-dimensional model developed from this analysis was specified. The coefficients used to fit the model to the data are listed in The factorial structure obtained confirms the good quality of the measurement. The convergent validity of the "tactical" dimension is good (pvc=0.57). It should be noted, however, that item 62 has an insufficient factorial weight. It was nevertheless retained, because it provides dimension-specific information, and this does not prevent the attainment of a good convergent validity coefficient [START_REF] Fornell | Evaluating Structural Equation Models with Unobservable Variables and Measurement Error[END_REF]. The convergent validity of the "strategic" dimension is also good (pvc=0.60). The factorial weight of item 61 is only just acceptable. These two dimensions have good internal coherence: 0.80 for the "tactical" dimension and 0.81 for the "strategic" dimension. Finally, the computed correlation is 0.53. This coefficient is high, and indicates a high level of multi-colinearity between the two dimensions, thus suggesting a continuum between tactical and strategic decisions. From an initial set of 10 items, we retained only six. Table 10 lists the items that were discarded.

Battle to improve the quality of products Battle to improve the offer of complementary services Battle in terms of sales force Price war Table 10:Items eliminated from the initial competitive intensity scale

The discarded items can be regrouped into two subsets:  The first two items correspond to the "strategic" dimensions of the competitive battle. These items focus on the intensity of the battle to improve the quality of products and services;  The last two items correspond to the "tactical" dimension and focus on the intensity of the battle at the level of a firm's sales force and services. Finally, the "strategic" dimension of competitive intensity captures the intensity of the battle to launch new products as well as the speed of product launch and development. The "tactical" dimension measures the intensity of the competitive battle in terms of advertising, promotion and distribution. Discussion Despite the frequent use and importance of competitive intensity, this concept is rarely studied as such. No studies have looked at its internal structure. The present research proposes a two-dimensional conception of competitive intensity that observes competitive actions in the market. This two-dimensional design resulted in a proposal to measure competitive intensity. Unlike previous scales that consider competitive intensity to be one-dimensional, and do not distinguish between strategic and tactical decisions, we propose a more complete measure of competitive intensity along these two dimensions.

Theoretical Implications

In theoretical terms, and in line with the dynamic perspective of competition, this two-dimensional conceptualization of competitive intensity helps to strengthen the concept of competitive intensity, and improve the understanding of how competitive battle is applied to the market. In terms of the two dimensions we have identified, some markets are exposed to what can be termed a fundamental battle between competitors, in which they try to dominate the others, using strategic instruments requiring considerable investments, such as innovation. In other markets, competitors defend their position through the use of tactical marketing instruments that have mainly short-terms effects. In still other markets, both instruments can be used. This two-dimensional conceptualisation also seeks to assess the impact of the antecedents of competitive intensity. The antecedents of competitive intensity identified in the literature, such as strategic similarity, market concentration or 36 multi-market competition [START_REF] Baum | Competitive Dynamics of Interfirm Rivalry[END_REF]Chen, 1996;[START_REF] Gimeno | Hypercompetition in a multimarket environment: the role of strategic similarity and multimarket contact in competitive de-escalation[END_REF][START_REF] Gimeno | Reciprocal Threats in Multimarket Rivalry : Staking Out "Spheres of Influence[END_REF][START_REF] Jayachandran | The Theory of Multimarket Competition: A Synthesis and Implications for Marketing Strategy[END_REF]Peteraf, 1993;[START_REF] Ramaswamy | Competitive Marketing Behavior in Industrial Markets[END_REF] have a different influence, depending on the dimension of the competitive intensity (Bylykbashiet al., 2016). The strategic similarity between competitors thus has an influence on tactical actions only, and affects only the tactical dimension of the competitive intensity. On the other hand, it has no impact on the strategic dimension of the competitive intensity. This confirms the resource-advantage theory [START_REF] Barney | Firm resources and sustained competitive advantage[END_REF][START_REF] Wernerfelt | A resource-based view of the firm[END_REF], according to which competition is a process of battle between competitors, whose objective is to achieve a comparative advantage in resources. This comparative advantage in resources then leads to a competitive advantage and to improved performance [START_REF] Hunt | The comparative Advantage Theory of Competition[END_REF]. Competitors with superior resources, skills and abilities can more easily develop new products, and maintain for a longer period of time the competitive advantage provided by these new products [START_REF] Johnson | Stratégique[END_REF]. This two-dimensional view also provides a better understanding of the impact of competitive intensity on the products' launch strategy. Indeed, the two dimensions of competitive intensity have a distinctly different impact on launch strategy (Bylykbashiet al.;2016).

Managerial Implications

At the managerial level, this allows managers to better understand the competitive environment, which can lead to more appropriate decisions. Any error in the assessment of the state of competitive intensity can result in a waste of resources. Competitor movements do indeed generate signals for managers (Chen et al., 1992, Smith andGrimm, 1991). The decision to react or not to a competitive event is based on the information available to the manager about the competitive environment, and how he or she will interpret it [START_REF] Klemz | Managerial Aassessment of Potential Entrants : Processes and Pitfalls[END_REF]. By taking the duality within competitive intensity into account, managers can gain a better understanding of competitive battle and become more familiar with the instruments used, thus allowing them to improve operations and allocate their resources according to these two dimensions.

Limitations AndFuture Research

A first limitation is the conceptualization of the strategic dimension of competitive intensity. This dimension corresponds to an intense and fast-moving battle to launch new products on the market. However, new products vary depending on their degree of novelty. A new product can be either a real novelty [START_REF] Hoeffler | Measuring Preferences for Really New Products[END_REF], or a simple extension of the product line. We have not distinguished between new products according to their degree of novelty. Further research could refine the strategic dimension of competitive intensity by distinguishing possible differences in degree of novelty. Another limitation concerns the conceptualization of the tactical dimension, measured by the competitive conflict in terms of advertising, sales promotion and distribution. Nevertheless, in the case of some brands such as Dell or Amazon, distribution is at Vol. 5 No. 1 January, 2021ISSN 2519-1284 Acces online at www.iipccl.org 37 the heart of their strategy. In addition, for each variable in the mix, there are both strategic and tactical dimensions. Not only is it often difficult to separate them, but strategic and tactical decisions are also interdependent. Highly promoted premium brands can thus have high prices; similarly, medium-quality brands with strong advertising support can charge slightly more for their products (Faris and Rebstein, 1979); alternatively, the message in an advertising campaign can meet that of the sales team [START_REF] Urban | Design and Marketing of New Products[END_REF]. Finally, while the consideration of (strategic and tactical) duality within the concept of competitive intensity appears to be relevant, the instruments included in each dimension may be different, depending on the type of market and product: B to B, B to C, sustainable or non-sustainable, technological or non-technological [START_REF] Kotler | Marketing Management: The Millennium Edition[END_REF]. Other studies could analyse and determine the variables to be taken into account in each dimension. One final limitation has to do with the validation process for the measurement scale. Although we have verified internal consistency, scale validation was performed with just one set of collected data. It is nevertheless recommended to separate these two procedures and to use two different samples for this purpose (Gerbing and Anderson,198). It is also essential to assess the nomological validity and to retest this scale with a larger sample, since the indicators used in confirmatory analyses are sensitive to sample size [START_REF] Hu | Fit indices in covariance structure modeling: sensitivity to underparameterized model misspecification[END_REF].

  www.iipccl.org 31

  www.iipccl.org 33

Table 1 :

 1 Scales for the measurement of competitive intensity in the literature

	Vol. 5 No. 1
	January, 2021

Table 2 :

 2 Sample from the qualitative study

		Company staff	Function
	Energy management	5000 or more employees	Product manager
	Energy management	5000 or more employees	Product manager
	IT services	5000 or more employees	Product manager
	Semi-conductors	1000 to 4999 employees	Product manager
	IT services	200 to 499 employees	Product manager
	Barcode traceability system	200 to 499 employees	Product manager
	Ski equipment	0 to 49 employees	Product manager
	Construction and public works	0 to 49 employees	Product manager
	Construction and public works	0 to 49 employees	Product manager

Table 4 :

 4 Competitive intensity items found in the literature

Table 6 :

 6 Table6presents the initial 10 items of the competitive intensity scale. These items describe the intensity and speed with which marketing instruments are used in competitive battle. Initial items for the competitive intensity scale

	"You consider that: … "
	1. The rhythm of new products launched on the market was	Very fast	Fast
	globally …	Slow	Very slow
	2. The rhythm of improvement to products on the market was	Very fast	Fast
	globally …	Slow	Very slow
	3. The publicity battle was …	Very intense Weak	Intense Inexistent
	4. The sales promotion battle was …	Very intense Weak	Intense Inexistent
	5. The battle to improve the quality of products was …	Very intense Weak	Intense Inexistent
	6. The battle to launch new products was …	Very intense Weak	Intense Inexistent
	7. The battle in terms of distribution was …	Very intense Weak	Intense Inexistent
	8. The price war was …	Very intense Weak	Intense Inexistent
	9. The battle in terms of sales force (size, stimulation, canvassing,	Very intense	Intense
	clients, …) was …	Weak	Inexistent
	10. The battle to improve the offer of complementary services	Very intense	Intense
	was …	Weak	Inexistent

Table 7 :

 7 Structure derived from exploratory factorial analysis

	Tactical	Strategic

Table 8 .

 8 As shown in the table, these indexes are sound and justify further analysis.

	χ2 (ddl, p)	χ2/ddl	Γ (min -max)	Γ fitted (min -max)	RMSEA (min -max)
	17.41 (8, 0.026)	2.18	0.979 (0.944 -0.998)	0.946 (0.853 -0.996)	0.09 (0.025 -0.15)

Table 8 :

 8 Fit indicesfor the structure of the competitive intensity scaleTable9shows the results of the structure obtained from the confirmatory analysis

	Tactical	Strategic

Table 9 :

 9 Structure derived from confirmatory factor analysis

European Journal of Economics, Law and Social Sciences IIPCCL Publishing, Graz-Austria

Porter uses the term "rivalry".Although some researchers(Chen, 1996; Gimeno and Woo, 1999) use this term to express the degree of competitive battle between two competitorsonly, the terms rivalry and competitive intensity are used interchangeably.

38

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Hakim Weatherspoon

Hugo Miranda
email: hmiranda@di.fc.ul.ptiwanicki@few.vu.nlali@sics.se

Konrad Iwanicki

Ali Ghodsi

Yann Busnel
email: yann.busnel@irisa.fr

GOSSIP: Gossip Over Storage Systems Is Practical

Gossip-based mechanisms are touted for their simplicity, limited resource usage, robustness to failures, and tunable system behavior. These qualities make gossiping an ideal mechanism for storage systems that are responsible for maintaining and updating data in a mist of failures and limited resources (e.g., intermittent network connectivity, limited bandwidth, constrained communication range, or limited battery power). We focus on persistent storage systems that, unlike mere caches, are responsible for the durability and consistency of data. Examples of such systems may be encountered in many different environments, in particular: wide-area networks (limited bandwidth), wireless sensor networks (limited resources), and mobile ad hoc networks (intermittent connectivity). In this paper, we demonstrate the qualities of gossiping in these three respective environments.

INTRODUCTION

Non-traditional storage systems are pushing the boundaries into new distributed storage domains, such as the wide-area networks (WANs) [START_REF] Peterson | Experiences building planetlab[END_REF][START_REF]Global Information Grid (GIG[END_REF], wireless sensor networks (WSNs) [START_REF] Akyildiz | A survey on sensor networks[END_REF][START_REF] Mathur | Ultra-low power data storage for sensor networks[END_REF], and Mobile Ad hoc NETworks (MANETs) [START_REF] Hara | Effective replica allocation in ad hoc networks for improving data accessibility[END_REF]. These environments are often characterized by constrained resources, such as access link bandwidth in WANs, limited battery life in WSNs, and intermittent connectivity in MANETs. All of these environments suffer from some rate of node failure. We refer to the above environments as challenged networks.

Providing guarantees for durability and consistency is challenging in these new environments since node failures occur often and required resources are limited. Durability concerns data replicas vanishing from the system as a result of node failures. When the last replica disappears permanently (i.e. permanent node failure), the object is permanently lost. Therefore, to provide durability guarantees, a storage system must minimize the probability of data loss in the presence of node failures.

Consistency defines how a sequence of read and write operations (possibly performed concurrently and/or over different replicas) are handled by the system and presented to the user. The mentioned constraints in challenged networks make strong consistency models such as linearizability [START_REF] Herlihy | Linearizability: A correctness condition for concurrent objects[END_REF] or one-copy serializability [START_REF] Bernstein | Multiversion concurrency control-theory and algorithms[END_REF][START_REF] Papadimitriou | Serializability of concurrent database updates[END_REF] difficult to provide. A feasible consistency model in such challenged networks is eventual consistency [START_REF] Demers | Epidemic algorithms for replicated database maintenance[END_REF][START_REF] Terry | Managing update conflicts in bayou, a weakly connected replicated storage system[END_REF]. Eventual consistency means updates are propagated and applied at all nodes such that all replicas eventually become identical given a quiescent net-work. To achieve eventual consistency, all changes to data items must be propagated to all replicas of the item.

In this paper, we argue that gossip-based mechanisms are adequate to deal with the aforementioned storage challenges in these new environments. By gossip-based mechanisms we mean periodic pairwise exchange of bounded size messages between random nodes in the system, where the state of one (or both) changes to reflect the state of the other [START_REF] Jelasity | T-Man: Fast gossip-based construction of large-scale overlay topologies[END_REF]. Such mechanisms are touted for their simplicity, limited resource usage, robustness to failures, and tunable system behavior [START_REF] Demers | Epidemic algorithms for replicated database maintenance[END_REF]. We present characteristics for three different storage environments and describe how gossip-based mechanisms are advantageous for each. However, gossiping is not a "one-size-fits-all" mechanism. There are situations where gossip makes less sense. We present those as well.

OVERVIEW

Based on the guarantees they give on the durability of data items, distributed storage systems can be classified into two groups: caches and persistent storage systems. Caches essentially assume that each data item is soft-state, and thus, at some moment, can permanently disappear from the system, potentially without any notification. A separate data source can later restore the lost data item to the cache. In contrast, the goal of persistent storage systems is to preserve data over time within the system. If the data is lost from the latter system, it cannot be restored and is lost forever. Here, we focus on persistent storage.

Gossiping and Durability

A data item unintentionally vanishes from the system as a result of node failures. Therefore, to provide durability guarantees, a storage system must minimize the probability of data loss in the presence of node failures. This is primarily done through replication.

Replication strategies can be divided into reactive and proactive approaches. Reactive replication assumes that there exists a mechanism for monitoring the redundancy of data items. If, as a result of node failures, redundancy of some data items drops below a desired level, the system reacts by restoring lost redundancy on other nodes. Proactive replication, on the other hand, assumes that the system replicates data items in advance, in anticipation of future failures. For instance, additional redundancy may be created constantly at a low rate.

Reactive replication is quick and can provide durability at low average cost. It is therefore a perfect solution for traditional storage settings, such as storage area networks (SAN) like EMC's SAN manager or network attached storage (NAS) systems like Network Appliance's "Filer", in which either node failures occur relatively rarely or provisioning bandwidth to create new replicas when failures do occur is not a problem. As a result, employing gossiping because of its crucial ability to tolerate failures is often overkill. Moreover, gossiping is a relatively slow process that could even endanger data by not responding to failures quickly enough.

The price to pay for supporting reactive replication, however, is potentially high and bursty bandwidth utilization: each time a number of nodes fail, the system must quickly produce new copies of the lost replicas [START_REF] Blake | High availability, scalable storage, dynamic peer networks: Pick two[END_REF]. Such recovery operations create spikes in bandwidth usage when responding to failures. Unfortunately, in many modern, real-world settings addressed in this paper, provisioning bandwidth for peak usage can be expensive.

For this reason, proactively replicating data items using gossiping may be a more attainable solution. In particular, gossiping allows for constantly creating additional redundancy at low rate and thus evens out peaks in replicationrelated traffic by shifting the time at which bandwidth is used [START_REF] Sit | Proactive replication for data durability[END_REF]. Additionally, in power-constrained environments, such as wireless sensor networks and mobile ad hoc networks, predictable communication patterns, as ensured by gossiping, facilitate energy savings [START_REF] Akdere | A comparison of epidemic algorithms in wireless sensor networks[END_REF][START_REF] Luo | Pilot: Probabilistic lightweight group communication system for ad hoc networks[END_REF][START_REF] Van Renesse | Power-aware epidemics[END_REF]. However, special measures must be taken to ensure that a given proactive replication scheme guarantees durability with a desired probability.

Intuitively, the node failure rate, λ, and replica creation rate, µ, represent a balance between how fast a system loses replicas compared to how fast it can create replicas to compensate for the attrition. This ratio between replica creation rate and node failure rate determines the average replicas per object the system should expect to support [START_REF] Chun | Efficient replica maintenance for distributed storage systems[END_REF][START_REF] Dabek | A Distributed Hash Table[END_REF][START_REF] Ramabhadran | Analysis of long-running replicated systems[END_REF]. For example, if the system must handle coincidental bursts of, say, five failures, it must be able to support at least six replicas and hence the replica creation rate must be at least 6 times higher than the replica failure rate. We will refer to the ratio µ/λ as θ. More importantly, θ can be used to estimate the rate of data loss. Dabek [START_REF] Dabek | A Distributed Hash Table[END_REF] demonstrated that the rate of data loss (the probability that no replicas exists) decreases as θ increases by p[data loss] = e -θ . This model assumes that inter-arrival failure and repair times are exponentially distributed.

Gossiping and Update Propagation

Many storage systems offer users the ability to modify stored data. Concurrent modifications of replicated data items necessitate deployment of consistency enforcement algorithms. Such algorithms define and enforce contracts between the user and the storage system on how concurrent updates on a data item are reflected on its replicas.

The most natural consistency model is one-copy serializability [START_REF] Bernstein | Multiversion concurrency control-theory and algorithms[END_REF][START_REF] Papadimitriou | Serializability of concurrent database updates[END_REF]. It states that there must exist a total order on all operations such that each operation looks as if it were completed at a single node (that maintained all possible data items). In other words, it gives strong consistency guarantees.

Apart from consistency, any real fault-tolerant distributed storage system must also consider two other aspects, that is: availability and partition tolerance. Availability requires every operation to be eventually completed (for more formal definitions see [START_REF] Coan | Limitations on database availability when networks partition[END_REF][START_REF] Gilbert | Brewer's conjecture and the feasibility of consistent, available, partition-tolerant web services[END_REF]), whereas partition tolerance is the ability to complete requests in the presence of network partitions. Unfortunately, according to Brewer's conjecture [START_REF] Brewer | Towards robust distributed systems[END_REF][START_REF] Gilbert | Brewer's conjecture and the feasibility of consistent, available, partition-tolerant web services[END_REF], while it is feasible to provide any two of one-copy serializability, availability, and partition tolerance, one cannot achieve all three of them. Moreover, Coan et al. [START_REF] Coan | Limitations on database availability when networks partition[END_REF] give a low tight upper bound on the maximal possible availability of a strongly-consistent system in the presence of network partitions. Consequently, systems for which availability and partition tolerance are at stake (see the examples in the subsequent sections), must trade off one-copy serializability for a weaker consistency model.

An example of such a model is eventual consistency [START_REF] Demers | Epidemic algorithms for replicated database maintenance[END_REF]. It states that in the absence of changes, all replicas of a data item will gradually become identical. Eventual consistency can be easily ensured with gossiping. This approach has been shown to be quite useful in practice [START_REF] Demers | Epidemic algorithms for replicated database maintenance[END_REF][START_REF] Van Renesse | Astrolabe: A robust and scalable technology for distributed system monitoring, management, and data mining[END_REF]. It turns out that it is sufficient for many applications. Moreover, by allowing optimistic updates and providing applications with automated, customizable conflict resolution methods, an eventually-consistent storage system can provide high availability in the presence of network partitions [START_REF] Terry | Managing update conflicts in bayou, a weakly connected replicated storage system[END_REF].

In the following sections, we examine fault-tolerant distributed storage systems in three different settings: widearea networks, wireless sensor networks, and mobile ad hoc networks. We show how gossip-based algorithms can be employed to proactively ensure durability of data and to facilitate eventually-consistent data updates with high availability, even in the presence of network partitions.

WIDE-AREA NETWORKS

Many new distributed wide-area networks (WANs)-like PlanetLab [START_REF] Bavier | Operating system support for planetary-scale network services[END_REF], the Global Information Grid (GIG) [START_REF]Global Information Grid (GIG[END_REF], and GRID-are composed of machines from multiple autonomous organizations that are geographically dispersed. In these systems, servers cooperate to provide services such as persistent storage. Systems designed in this manner exhibit good scalability and resilience to localized failures such as power failures or local disasters.

Unfortunately, distributed systems involving multiple, independently managed servers suffer from new challenges that must be addressed to provide data durability and update propagation guarantees. First, wide-area access link bandwidth is limited and shared between nodes within the same site. As a result, the most expensive operation in the system is sending a new replica over a wide-area link. Second, such systems often exhibit high levels of churn, failure, and even deliberate disruption. In PlanetLab, for example, typically less than half of the active servers are stable (available for 30 days or more) [START_REF] Peterson | Experiences building planetlab[END_REF]. The dilemma is preventing loss of data and/or updates due to this constant rate of node churn and limited wide-area access link bandwidth.

In the next two subsections, we demonstrate how gossipbased mechanisms are used to ensure a target durability (probability of data loss) and rate of update propagation.

Ensuring Durability

Durability in distributed wide-area storage systems can be tuned via adjusting the rate of gossip. In particular, we can measure the impact that the rate of gossip has on durability via the ratio θ = µ λ where µ is the replica creation rate and λ is the node failure rate. θ ≥ 1 is required for a feasible system.

To get an idea of a real-world value of θ, we estimate λ and µ based on the historical failure record for permanent node failures on PlanetLab [START_REF] Peterson | Experiences building planetlab[END_REF]. From [START_REF] Chun | Efficient replica maintenance for distributed storage systems[END_REF], the average permanent failure inter-arrival time for the entire PlanetLab test bed was 39.85 hours. On average, there were 490 nodes in the system, so we can estimate the mean time between permanent failures for a single node as 490 • 39.85 hours or 2.23 years. Hence, λ ≈ 0.439 permanent node failures per year.

The replica creation rate µ is dependent on the number of times one node can gossip a particular replica to another node per time unit. It is limited by the achievable network throughput per node, as well as the amount of data that each node has to store. We assume that an entire nodes worth of data may be gossiped before a particular replica is gossiped again. For example, if each node stores 1TB worth of data and the access link bandwidth is 150KBps (i.e. 1.2M bps, which is typical for many wide-area settings such as PlanetLab), then the replica creation rate would be limited by 1T B/150KBps = 83 days, the amount of time to gossip a nodes worth of data. This yields µ ≈ 4.4 per year. Thus, the rate of gossip would be at most four times per year for a particular replica in this example.

Therefore, in a system with these characteristics, we can estimate the ratio between the replica creation rate and node failure rate θ = µ/λ = 4.4/0.439 ≈ 10.04. This yields an estimated rate of data loss as 1 out of 10,000 objects per year. In practice, the value of θ is somewhat lower; for example, nodes cannot make copies during downtimes or shortly after a permanent node failure. However, the fact remains that θ is higher than the minimum for a feasible system (θ ≥ 1 defines a feasible system). The system still profits from this because higher values of θ decrease the time it takes to repair an object, and thus the "window of vulnerability" during which additional failures can cause the object to be destroyed.

In general, the rate of gossip can be tuned to match a target durability (rate of data loss) provided that the ratio between the replica creation rate and node failure rate defines a feasible system.

Update Propagation

Assuming that a node storing a replica of an object can contact any other node storing another replica of this object, update propagation in wide-area networks has a wellfounded mathematical model, based on the theory of infectious diseases [START_REF] Bailey | The Mathematical Theory of Infectious Diseases and its Applications[END_REF]. For the sake of simplicity assume that an object is replicated on all n nodes. Moreover, nodes gossip in rounds, that is, every ∆T time units, and in each round a node is allowed to contact f other random nodes.

There are essentially two classes of algorithms for update propagation: "infect and die", in which a node with an updated replica tries to propagate the update for k rounds and then stops, and "infect forever", in which all updates are being propagated without any round limit. Here we focus on the latter class, as it ensures eventual consistency. Bailey [START_REF] Bailey | The Mathematical Theory of Infectious Diseases and its Applications[END_REF] proves that the ratio of the number of nodes that received the update within r rounds to the total number of nodes is equal to Additionally, Pittel [START_REF] Pittel | On spreading of a rumor[END_REF] shows the latency of update propagation in terms of the number of rounds. More specifically, the average number of rounds necessary to propagate the update among all nodes respects the following equation

1 1 + n • e -f •
log f +1 (n) + 1 f log(n) + O(1).
Thus, using gossiping, updates are spread very fast in that it takes a logarithmic number of rounds to reach every node in the system.

WIRELESS SENSOR NETWORKS

Wireless sensor networks (WSNs) observe the environment, record and possibly respond to their observations. They are composed of many small, low-cost, low-power devices that must communicate using wireless medium to store, and share the observations [START_REF] Akyildiz | A survey on sensor networks[END_REF]. In this paper, we refer to such devices as sensors.

Given the potentially large number of sensors participating in a network and their limited resources, it is crucial to deploy fully decentralized solutions and to balance the load as evenly as possible between participating sensors. In particular, since wireless communication, necessary to store, update, and retrieve data, is the most expensive operation in terms of the power consumed [START_REF] Van Renesse | Power-aware epidemics[END_REF], battery life time and small communication range represent the fundamental limitations of a sensor. Despite these limitations of individual devices, a delay-tolerant WSN must store information for long periods of time until the information can later be extracted. To this end, delay-tolerant WSNs must provide power-aware durability and update propagation mechanisms, as explained in the remainder of this section.

Ensuring Durability

Similar to wide-area networks, durability in wireless sensor networks can be tuned via adjusting the rate of gossip. Increasing the rate of gossip increases the replica creation rate, µ. However, unlike wide-area networks where the node failure rate, λ, is independent of the rate of gossip, increasing the rate of gossip in WSNs increases the node failure rate, λ, as more intensive communication drains batteries of the sensors much faster. Once the gossip rate is defined, particular value for the replica creation rate, µ, and the node failure rate, λ, can be derived. Based on these values, we can estimate the impact of gossip on durability using the ratio θ = µ λ . For example, assume a network consists of Mica mote devices (Table 1). This particular device has sufficient power to operate for 10 months if each mote uses approximately 8 mAh per day while gossiping 100 times per day. In [START_REF] Mainwaring | Wireless sensor networks for habitat monitoring[END_REF], Mica node hardware has been slightly modified, which reduces the energy consumption for similar tasks to approximately 7 mAh per day increasing node lifetime. With these characteristics, the Mica motes have sufficient power to operate for more than 10 months or 0.83 years. Hence, λ = 1.2 permanent node failures per year.

Similar to wide-area storage networks, the replica creation rate µ is dependent on the number of times one node can gossip a particular replica to another node per unit time. From the node failure rate calculation above, the node gossip rate was defined to be 100 per day. The replica creation rate for a particular replica is the gossip rate per node divided by the number of replicas per node. Hence, µ = 100 R per day where R is the number of replicas per node. Assuming R = 5000 replicas per node, the replica creation rate for a particular object stored by a particular node is µ = 100 5000 = 0.02 per day or µ = 7.3 per year.

Therefore, in a system with these characteristics, we can estimate the ratio between the replica creation rate and node failure rate θ = µ λ = 7.3 1.2 ≈ 6.1. This yields an estimated rate of data loss as 1 out of 450 objects per year. If, on the other hand, we double the rate of gossip from 100 to 200 per day, the estimated rate of data loss would remain the same. In particular, both the replica creation and node failure rate would double and cancel each other leaving θ the same.

Often, increasing the rate of gossip decreases a nodes lifetime in WSNs. To tune durability, WSNs need to find opportunities to increase the rate of gossip without increasing the frequency of communication. For example, reducing the number of objects or piggyback replication with other traffic as discussed in Section 5. In any case, setting the gossip rate needs to consider affects on both the node failure rate and replica creation rate.

Update Propagation

Update propagation is a challenging and essential task for WSNs. Similar to durability, it must take into account the communication load on each sensor. Updating object replicas has to be persistent, non-intrusive, and diffuse. Gossipbased protocols are a promising candidate to disseminate information through the network while maintaining good node load balance.

Different update propagation proposals have been considered recently. For instance, software updates is an important application. As sensors are expected to be deployed for long periods of time, they are likely to need software upgrades during their lifetime. Updating the software code automatically on a large number of sensors is a tremendous task, which is usually infeasible to perform manually in a deployed system. As another example, data updates generated by nodes need to propagated to other nodes since the time data of collection is often unknown and not predictable. These delay tolerant networks (DTN) [START_REF] Gavidia | Epidemic-style monitoring in large-scale wireless sensor networks[END_REF] continuously update stored data and need to make data available for later information collection.

In these kinds of update propagation applications, gossiping data represents an attractive solution for sharing information through the network. It permits a balance between the load of each node with an efficient speed propagation.

An analysis of gossip-based models [START_REF] Kermarrec | Probabilistic reliable dissemination in large-scale systems[END_REF] provide a proof of dissemination reliability. On a random graph, if a node's view (nodes within transmission range) is constrained to c = O(log(n)), where n is the size of the network, it assure that every nodes in the system is aware of each broadcast message with a probability of e -e -c .

In software update propagation, gossip can assure a propagation speed equivalent to the following equation [START_REF] Busnel | GCP : Gossip-based code propagation for large-scaled mobile wireless sensor network[END_REF].

ln ((ns + 2) • (n nh -2) + 4) -ln(2 • n nh ) ln(n nh ) -ln(2) × p b (1)
where

• n nh represents the average size of neighborhood (average number of nodes located in the transmission range);

• ns represents the network size in term of number of nodes;

• p b represents the period of gossip data emission.

By limiting the number of transmission of the same data (maximum t emission in the following), we can obtain the following result:

ln `ns 2 • `nnh 2 -1 ´´-ln " n nh 2 -`nnh 2 ´1-t " ln(n nh ) -ln(2) × p b (2)
If t = O(log(n)), we obtain the same propagation speed provided by Equation 1.

MOBILE AD HOC NETWORKS

Mobile Ad Hoc NETworks (MANETs) are decentralized, infrastructure-less networks composed of mobile devices with limited resources. They are of particular interest for situations where communication is required but it is too expensive or impossible to deploy infrastructure, for instance, search-and-rescue operations. In MANETs, devices communicate with each other using a wireless medium. Because wireless devices have a limited transmission range, it may not be possible for each two of them to establish a direct communication channel. The network is expected to be unstable, with nodes frequently establishing and loosing links between them due to device disconnection or movement, possibly of some of the intermediary hops. Mobility is the key difference between MANETs and WSNs 1 .

The combination of node movement and limited transmission range makes node disconnection an integral part of the MANETs networking model. Disconnection, and therefore failure, are hard to estimate as they depend of multiple factors, some of which driven by the application scenario. Examples are the size of the covered region, the number of nodes, their movement speed, their energy reserves and power consumption rate and the correlation between the movement of different nodes. This uncertainty makes, for example, strong consistency nearly impossible. Hence, replication models providing eventual consistency have been the most common approach. In addition, typical application scenarios do not consider dependencies between objects. In particular, data objects are independently generated and may possibly be related only by the queries.

Next, we illustrate how gossip can be used to overcome these challenges to provide durability and update propagation. 1 Although, WSNs can be mobile, we did not consider mobility in the Section 4, instead we consider it now in the context of MANETs.

Ensuring Durability

Durability of both the original data and updates are affected by the transient connectivity that characterizes MANETs. Further, MANET nodes are prone to permanent failures (e.g. a device can be damaged while in the field). A distributed storage system can improve the availability of this information both during the MANET lifetime (independently of network partitions) and after (thus surviving permanent failures of some nodes).

Given the limited memory of the devices, information collected while in the field may be excessively large to be stored at every node. As a result, research in MANETs focus mostly on partial replication models where no one node contains all the data, yet the system still maintains a high probability that at least one copy for each object survives the frequent failure of the nodes and network partitioning. The most popular trend is to find the most adequate number and location of replicas for different scenarios and application models. Gossip-based algorithms can be found in some of the projects in this research area. The examples presented below show that although gossip algorithms have been considered as the mechanism to support the dissemination of replicas, special care must be taken to prevent an excessive consumption of resources of the devices.

The algorithms described in [START_REF] Hara | Effective replica allocation in ad hoc networks for improving data accessibility[END_REF] have a strong resemblance with the typical gossip algorithms applied in other network settings: periodically, neighboring nodes gossip the state of their storage space and agree on a disjoint set of data objects to be replicated to improve their availability. One of the concerns is the tradeoff between the frequency of the rounds and the utility of the algorithms in face of node movement.

Data-centric storage algorithms [START_REF] Ratnasamy | GHT: a geographic hash table for data-centric storage[END_REF][START_REF] Ghose | Resilient data-centric storage in wireless sensor networks[END_REF] implement an algorithm that follows in spirit the underlying principles of gossip: messages containing data objects are periodically broadcasted by the node responsible for the primary copy to ensure its replication. A peculiarity of data-centric storage is that the node is unaware of the nodes that store a backup copy. Instead, messages are addressed to a geographical address. The gossip algorithm relies on the properties of the underlying geographical routing protocol to ensure the delivery of the messages to the correct destinations.

The algorithm described in [START_REF] Miranda | A stateless neighbour-aware cooperative caching protocol for ad-hoc networks[END_REF] uses an "on-demand" gossip model for the early dissemination of data objects, which gossips a new object as soon as it arrives. Nodes use a probabilistic algorithm to decide to store the objects. To save resources, new replicas are created in background, by piggybacking the data objects on unrelated traffic packets.

Update Propagation

The frequent disconnections in MANETs make update propagation a challenging problem.

There is a nonnegligible probability that at least one of the nodes storing a replica is not available whenever an update is triggered by some other node. In such a scenario, updates for temporarily off-line nodes must be deferred until the node becomes available.

Interestingly, the literature is vague in the distinction of new and updated data objects. The problem is trivially solved in the Data-Centric storage since it uses a primarybackup replication model but neglected in the remaining examples above, which define application models that do not consider the need for updates.

To the extent of our knowledge, this issue has not been addressed in a satisfactory manner in multi-hop ad hoc networks and deserves additional attention (see for example [START_REF] Hara | Replica allocation in ad hoc networks with periodic data update[END_REF] for preliminary work).

It is our position that gossip protocols can play a substantial role in this particular aspect. This claim is supported by noticing that updates can be rapidly propagated using any algorithm aiming at reliable message delivery in MANETs (e.g. [START_REF] Pleisch | MISTRAL: efficient flooding in mobile ad-hoc networks[END_REF][START_REF] Drabkin | RAPID: Reliable probabilistic dissemination in wireless ad-hoc networks[END_REF]).

CONCLUSION

Gossip is a mechanism that performs well in distributed storage settings where resources are limited and failures need to be tolerated while reducing the risk of data and update loss. We provide three case studies: wide-area networks with limited access link bandwidth, wireless sensor networks with limited battery life and communication range, and mobile ad hoc networks with limited connectivity. In these environments, we demonstrate how to tune the rate of gossip to achieve desirable durability levels (rate of data loss) and rate of update propagation. Update propagation is used to ensure eventual consistency. Outside of these environments or others like them, however, gossip may not be a good mechanism if node failure is a rare occurrence or new replicas can readily be created since resources such as bandwidth or battery life are not limited.

Table 1 :

 1 r . In other words, this value increases exponentially fast on average, by a factor of e f in each round. Typical power requirement for various operations of a Mica mote.

	Operation	nAh
	Transmitting a packet	20.000
	Receiving a packet	8.000
	Radio listening for 1 millisecond	1.250
	Operating sensor for 1 sample (analog) 1.080
	Operating sensor for 1 sample (digital)	0.347
	Reading a sample from the ADC	0.011
	Flash Read Data	1.111
	Flash Write/Erase Data	83.333