Antoine Gardarin
email: antoine.gardarin@inrae.fr

Muriel Valantin-Morison

Which pitfall traps and sampling effort to choose to evaluate cropping system effects on spider and carabid assemblages?

Keywords: Activity-density, CWM body size, Preserving fluid, Taxonomic richness, Trap diameter

In arable agroecosystems, arthropod communities often have a reduced abundance and diversity, which represents a challenge for sampling techniques needed to detect small differences among these simplified communities. We evaluated the suitability of pitfall traps for comparing the effects of cropping systems on arthropod communities. In a field experiment, we compared the effects of two pitfall trap diameters, the type of preserving fluid and the sampling effort on three metrics (activity-density, taxonomic richness and community weighted mean [CWM] of body size) for carabids and spiders. Trap size affected the observed composition of communities, with large traps yielding a higher proportion of spiders, and a higher richness and CWM body size for both taxa. The type of preserving fluid had a weaker effect. Simulations with various sampling efforts showed that only very different communities could be distinguished with less than ten traps per field or less than 30 field replicates. Fewer traps were required to find differences between cropping systems for body size than for other metrics. Carabid activity-density and body size, and spider genus richness, were the variables better distinguishing between cropping systems with the smallest sampling effort. A high sampling effort was required for comparing activity-density and richness across cropping systems. Selection of the most appropriate trap design, metrics and crops are the main factors for optimizing the trade-off between sampling effort and the ability to detect arthropod community responses to habitat management.

Introduction

At a time when agriculture is facing many challenges (biodiversity loss, climate change and dependence on synthetic inputs), innovative sustainable cropping systems targeting multiple issues must be designed and assessed [START_REF] Foley | Solutions for a cultivated planet[END_REF]. Agricultural techniques that enhance the biodiversity of soil organisms, such as ground-dwelling arthropods, not only promote conservation biological control [START_REF] Thérond | A new analytical framework of farming system and agriculture model diversities. A review[END_REF]), but also support higher trophic levels. Ground-dwelling arthropods have important roles in the dynamics of soil functioning and associated ecosystem services [START_REF] González | Distribution of ecosystem services within oilseed rape fields: effects of field defects on pest and weed seed predation rates[END_REF]. In agroecosystems, carabids and spiders are important predators that regulate phytophagous insect and weed populations [START_REF] Kromp | Carabid beetles in sustainable agriculture: a review on pest control efficacy, impacts and enhancement[END_REF][START_REF] Marc | Spiders (Araneae) useful for pest limitation and bioindication[END_REF]. The impact of these organisms depends on the density, the richness and functional composition of their communities [START_REF] Rusch | Predator body sizes and habitat preferences predict predation rates in an agroecosystem[END_REF][START_REF] Jonsson | Relationships between natural enemy diversity and biological control[END_REF]. Assessing arthropod communities under different cropping systems can help reveal whether a cropping system preserves soil biodiversity, its functioning and the associated services.

Pitfall traps are widely used to sample ground-dwelling arthropod assemblages [START_REF] Woodcock | Pitfall trapping in ecological studies[END_REF]. The design of pitfall traps varies considerably between studies, and a number of features, including the trap diameter and the type of preserving fluid, have been shown to have a significant impact on capture rates (Knapp andRuzicka 2012, Brown and[START_REF] Brown | A review of extensive variation in the design of pitfall traps and a proposal for a standard pitfall trap design for monitoring ground-active arthropod biodiversity[END_REF]. Several methodological studies have been performed [START_REF] Work | Pitfall trap size and capture of three taxa of litter-dwelling arthropods: Implications for biodiversity studies[END_REF][START_REF] Lange | Effect of pitfall trap type and diameter on vertebrate by-catches and ground beetle (Coleoptera: Carabidae) and spider (Araneae) sampling[END_REF][START_REF] Corti | A comparison of pitfall-trap and quadrat methods for sampling ground-dwelling invertebrates in dry riverbeds[END_REF]) in natural or seminatural habitats, such as forests, grasslands and riverbeds, but less frequently in agroecosystems (Holland andSmith 1999, Lövei and[START_REF] Lövei | Can carabidologists spot a pitfall? The non-equivalence of two components of sampling effort in pitfall-trapped ground beetles (Carabidae)[END_REF]. In natural ecosystems, the vegetation has a different architecture than in agroecosystems (litter often buried by tillage, bare soil between rows, and less diverse vegetation), which has known effects on beetle communities [START_REF] Ng | Disentangling the effects of farmland use, habitat edges, and vegetation structure on ground beetle morphological traits[END_REF]. It remains thus unclear to what extent the results of methodological studies realized in natural ecosystems can be generalized to characterize the simplified communities of agroecosystems.

First, trap diameter varies considerably between studies [START_REF] Brown | A review of extensive variation in the design of pitfall traps and a proposal for a standard pitfall trap design for monitoring ground-active arthropod biodiversity[END_REF]. Largediameter pitfall traps collect more individuals of all taxa than smaller traps, but they also collect more individual spiders (Lycosidae), more spider species and fewer small carabid individuals than expected when the catch rates are corrected for trap circumference [START_REF] Work | Pitfall trap size and capture of three taxa of litter-dwelling arthropods: Implications for biodiversity studies[END_REF][START_REF] Lange | Effect of pitfall trap type and diameter on vertebrate by-catches and ground beetle (Coleoptera: Carabidae) and spider (Araneae) sampling[END_REF]. Indeed, capture rates depend on the mobility and behavior of the organisms. In arable fields, where the architecture of the surface vegetation is different than in natural habitats, ground-dwelling arthropods are likely to be more mobile, potentially reducing the effect of trap diameter on capture rates [START_REF] Halsall | The efficiency of pitfall trapping for polyphagous predatory Carabidae[END_REF].

Second, many types of preserving fluids are available, and the pros and cons of each have been hotly debated (Schmidt et al. 2006, Brown and[START_REF] Brown | A review of extensive variation in the design of pitfall traps and a proposal for a standard pitfall trap design for monitoring ground-active arthropod biodiversity[END_REF]. Ethylene glycol and formalin are the most widely used [START_REF] Work | Pitfall trap size and capture of three taxa of litter-dwelling arthropods: Implications for biodiversity studies[END_REF][START_REF] Lange | Effect of pitfall trap type and diameter on vertebrate by-catches and ground beetle (Coleoptera: Carabidae) and spider (Araneae) sampling[END_REF], as they are highly effective due to their capture efficiency and their ability to preserve dead individuals [START_REF] Jud | Fluid type, dilution, and bitter agent influence spider preservation in pitfall traps[END_REF]. However, both are toxic. Propylene glycol, which has been developed more recently, is both nontoxic and very efficient for collecting carabids individuals and is suitable for estimating their community richness (Knapp andRuzicka 2012, Knapp et al. 2016). Salt water and vinegar are other possible cheap alternatives, and water offers the further advantage allowing use of the material for DNA analyses if the samples are collected before they start to decay and stored in ethanol afterwards. Water and vinegar have been evaluated for preservation efficacy; both have lower preservation efficiency than ethylene glycol or formalin, but their capture efficiency has rarely been assessed. Acetic acid (vinegar) is commonly used by beetle collectors as it may be an attractant for large carabids [START_REF] Scheller | Pitfall trapping as the basis for studying ground beetle (Carabidae) predation in spring barley[END_REF][START_REF] Woodcock | Pitfall trapping in ecological studies[END_REF][START_REF] Mccravy | Effects of pitfall trap preservative on collections of carabid beetles (Coleoptera: Carabidae)[END_REF]. Although not scientifically proven, it can be assumed that vinegar attracts at least certain species and therefore potentially affects the captured assemblages. It has also been suggested that acetic acid (vinegar) may act as an attractant and that the low density of salt water may enhance the ability of arthropods to escape. However, the effect of this factor on capture efficiency remains unclear [START_REF] Koivula | Pitfall trap efficiency: do trap size, collecting fluid and vegetation structure matter?[END_REF].

Third, the number of traps and the spatial design, which account for spatial heterogeneity [START_REF] Sereda | Assessing spider diversity on the forest floor: Expert knowledge beats systematic design[END_REF], are key points in a sampling strategy. The use of 20 to 70 traps has been recommended for the determination of carabid species richness at a given site [START_REF] Woodcock | Pitfall trapping in ecological studies[END_REF]. This sampling effort is often impracticable, in terms of working time both to set up and collect the traps and to identify the captured arthropods, when it has to be replicated over a network of multiple sites to account for factors such as landscape effects.

Arable fields are generally characterized by the presence of depleted arthropod communities with low diversity [START_REF] Geiger | Persistent negative effects of pesticides on biodiversity and biological control potential on European farmland[END_REF][START_REF] Postma-Blaauw | Soil biota community structure and abundance under agricultural intensification and extensification[END_REF], in which carabids and spiders have a highly heterogeneous spatial distribution (Holland et al. 1999). A large sampling effort is therefore likely to be required for accurate comparisons of the activity-density and richness values between fields managed with different cropping systems. This can be problematic in terms of feasibility. Studies investigating the functioning of these communities also require characterization of the functional composition of the arthropod community, for instance in terms of diet or body size [START_REF] Rudolf | Seasonal shifts in predator body size diversity and trophic interactions in size-structured predator-prey systems[END_REF][START_REF] Rusch | Predator body sizes and habitat preferences predict predation rates in an agroecosystem[END_REF]. Such metrics describing the functional composition of arthropod communities have never been evaluated in methodological studies comparing pitfall trap designs, although it is known that pitfall traps tend to collect large arthropod individuals [START_REF] Hancock | Pitfall trapping bias and arthropod body mass[END_REF]. Community weighted means (CWM) of trait values are generally determined by the identity and proportion of the dominant species, with rare species making only minor contributions. A smaller sampling effort should therefore be required for the estimation of this metric than for species richness.

In this study, we aimed to test the influence of different sampling parameters on the observed differences among arthropod communities between several cropping systems. This included comparing pitfall trap characteristics, the associated preserving fluid and the sampling effort. We then used field data from three cropping systems for a simulation study in which we varied the number of pitfall traps per field. Simulation studies, which are based on artificial communities generated from preliminary data, are powerful for estimating the power and sensitivity of different sampling efforts in different scenarios [START_REF] Arnold | Simulation methods to estimate design power: an overview for applied research[END_REF][START_REF] Baumgardt | Development of Multispecies, Long-Term Monitoring Programs for Resource Management[END_REF]. Here, we calculated the minimum sampling effort required to differentiate between the effects of contrasting cropping systems on the three metrics of carabid and spider communities that were described above.

2.Materials and methods

Experimental design

This experiment was performed at a long-term experimental site at Grignon, France (N 48.8416, E 1.9542), where cropping systems with innovative objectives and technique combinations have been implemented since 2008 (for more information, see Colnenne-David andDoré 2015, Colnenne-David et al. 2017). The experiment is located is the middle of a plateau, with a deep homogeneous loamy clay soil, within a larger cropped field and without any particular landscape element in the immediate vicinity.

We studied three cropping systems within this existing experimental design. The first was a productive high-environmental performance cropping system (PHEP), designed to meet high targets for both production and environmental criteria. Pesticide applications were allowed but the treatment frequency index and ploughing frequency were halved in comparison with conventional cropping systems. This system was used as a reference here, although its environmental objectives were higher than those of the conventional cropping systems used in the vicinity. The other systems were designed to meet additional environmental targets. The second cropping system was a no-pesticide cropping system (No-Pest), in which no pesticide use was tolerated, even pesticides authorized in organic agriculture. Chemical fertilizers were, however, allowed. Ploughing occurred three times over the six-year rotation of this system. The third cropping system was a low-greenhouse gas emission cropping system (L-GHG), designed to reduce greenhouse gas emissions by 50% relative to the PHEP system. These objectives were achieved through the maintenance of a continuous soil cover and the elimination of soil tillage. The targeted level of pesticide used was the same as in the PHEP system. Each cropping system was replicated on three 0.42 ha (65 m × 65 m) fields, but the replicates did not always contain the same crop simultaneously (the crop rotation was the same but the crops were staggered in time, [START_REF] Colnenne-David | Ambitious environmental and economic goals for the future of agriculture are unequally achieved by innovative cropping systems[END_REF]).

Arthropod sampling with different kinds of pitfall traps

In 2014 and 2015, we sampled ground-dwelling arthropods (1) in a winter wheat or winter barley field for each of the three cropping systems (3 fields), and (2) in a winter oilseed rape field for the PHEP and L-GHG cropping systems (2 fields). This resulted in the sampling of five fields corresponding to five "cropping system × crop" combinations each year, with five different fields each year. The dataset thus comprises two replicates (i.e. two years) for each "cropping system × crop" combination (Fig. 1), resulting in 10 fields in total. Winter wheat and winter barley were grouped under "winter cereals" in all analyses as these crops are very close.

Arthropods were sampled with pitfall traps placed in April (15 th April 2014 and 22 nd April 2015), May (6 th May 2014 and 15 th May 2015) and June (3 rd June 2014 and 12 th June 2015). These dates corresponded to 800, 1100 and 1500 degree-days, calculated each year as the daily sum of positive mean air temperatures from January 1 onwards, in order to account for the different climatic conditions across years [START_REF] Ricci | Local pesticide use intensity conditions landscape effects on biological pest control[END_REF]. The pitfall traps consisted of transparent plastic containers, filled with a preserving fluid and inserted into the soil such that their rim was flush with the soil surface. They were protected from the rain by inverted opaque plastic flower-pot saucers (14 cm in diameter) supported about 2 cm above the soil surface with two nails (Fig. 1 A). These roofs likely did not cause any additional shade since the traps were set in a dense crop canopy that already covered the soil.

A minimal distance of 15 m was kept between each sampling station (location of each individual trap) to minimize interferences between traps [START_REF] Digweed | Digging out the ''diggingin effect'' of pitfall traps: Influences depletion and disturbance on catches of ground beetles (Coleoptera: Carabidae)[END_REF] and to avoid depopulating the fields with a too high number of traps. We combined an incomplete factorial design with two sampling designs and different trap numbers during three periods in the spring (Fig. 1 B).

The sampling scheme was designed to meet our two objectives, i.e. comparing pitfall trap characteristics (size and preserving fluid) and comparing the sampling effort. In each field (one field for each crop × cropping system combination, five fields in total per year), we placed three types of pitfall traps: (1) eight large traps (9.5 cm diameter, 7 cm high) filled with water, salt (50 g/l) and unscented detergent to break surface tension (20 ml/l); (2) four small traps (5.5 cm diameter, 7 cm high) filled with the water, salt and detergent solution; (3) four small traps (5.5 cm in diameter, 7.5 cm high) filled with vinegar (8% acetic acid).

Large traps were also used for the sampling effort study. They were eight within each field in order to have a wide range of trap number per field and to analyze how this could affect the comparison of community metrics between cropping systems. To compare the effect of type of trap, there were only four traps per field to avoid depleting arthropod population in relatively small fields. Pitfall traps were filled to two-thirds of their volume with the preserving fluid. In April, only the eight large traps with the salt solution were placed in the field, whereas all three types of trap were placed in the field in May and June (Fig. 1 B). We chose here to compare the effect of type of preserving fluid on the months where the arthropod activity-density was the highest.

The sampling stations were 12 m away from the edge of the fields, which were surrounded by 5m wide paths with bare ground. In total, we placed each year 8 traps × 5 "cropping system-crop" combinations in April and 16 traps × 5 "cropping system-crop" combinations per sampling date in May and June (Fig. 1 B). Traps were left for one week and the arthropods trapped were then preserved in ethanol (70%) for later identification.

Field data analyses

Carabids were identified to species level, except for Amara spp. (Bonelli, 1810), which were determined to genus level because of identification uncertainties [START_REF] Roger | Clé de détermination des carabidés des paysages agricoles du nord-ouest de la France[END_REF]) Adult spiders were identified to genus level [START_REF] Roberts | The Spiders of Great Britain and Ireland[END_REF][START_REF] Roberts | Araignées de France et d'Europe[END_REF]. Since the aim of the study was not to analyze the temporal dynamics of arthropods, we pooled, for each trap, the data from the two sampling dates (May and June) in the same year.

Statistical analyses were performed with R software, version 3.1.3 (R Development Core Team, 2015). We first analyzed the effect of trap size and type of preserving fluid on the activity-density and species (carabid) or genera (spider) richness values obtained. CWM body sizes were calculated as the mean body length weighted by the relative activity-density of each species (carabids) or genus (spiders) using the FD package [START_REF] Laliberté | FD: measuring functional diversity from multiple traits, and other tools for functional ecology[END_REF]. Body length values where obtained from the BETSI database [START_REF] Pey | A thesaurus for soil Invertebrate trait-based approaches[END_REF]. For spiders, species data was not be used since they were identified at genus level only. Consistent with phylogenetic studies showing that spider body size is a conserved trait [START_REF] Entling | Body sizeclimate relationships of European spiders[END_REF][START_REF] Gonçalves-Souza | Disentangling the phylogenetic and ecological components of spider phenotypic variation[END_REF], we assumed that there was not a wide variation in body size within spider genus and we averaged body size values for all the species available in the database at genus level before calculating CWM of spider body size. Spider body size was averaged over males and females and we did not account for the sex of trapped individuals (therefore assuming a sex ratio of 1).

We investigated the effects of trap type on the six response variables (activity-density, richness and CWM body size for carabids and spiders). We used generalized linear mixed models (lme4 package) with a Poisson error distribution for activity-density and richness or linear mixed models (lme4 package) for CWM body size and log-or square root-transformed variables when necessary to reduce the over-dispersion (computed according to Bolker, 2020). Cropping system, crop type and their interaction were introduced as fixed-effect factors. A random field effect was introduced to account for the variability between fields. A random station effect, nested within the field effect, was used to take into account the location of the pitfall trap within the field. The distribution of residuals was checked with the DHARMa package [START_REF] Hartig | DHARMa: residual diagnostics for hierarchical (multi-Level / mixed) regression models[END_REF]. The significance of the fixed effects was tested with type II analyses of deviance with Wald chi-square tests (Anova function from the car package, Fox and Weisberg 2019). In case of a significant effect, post-hoc Tukey tests were performed for multiple comparisons (multcomp package, [START_REF] Hothorn | Simultaneous inference in general parametric models[END_REF].

In order to analyse the patterns of assemblage composition according to the type of traps, a nonmetric multidimensional scaling (NMDS) ordination was performed using the Bray-Curtis similarity index (vegan package, Oksanen 2013). A three-dimensional solution was selected because it consistently maintained a low stress (<0.2) across multiple runs. To identify correlations between the type of traps and NMDS axes, we tested separately the effect of trap size and of preserving fluid (on the subset of small traps) using the 'envfit' function (package vegan). This function tests for significance using a permutation test and calculate r 2 values for the correlation between trap features and the NMDs axes. To determine the association between some taxa and the type of traps, we also calculated the indicator value IndVal using the indicspecies package [START_REF] Cáceres | Associations between species and groups of sites: indices and statistical inference[END_REF]. The significance of indicator values was tested using 1000 permutation tests and Sidak's correction for multiple testing.

Simulations

Estimation of the cropping system, crop type, field and station effects

We investigated the sampling effort required to distinguish carabid and spider communities between contrasting cropping systems by performing a simulation study. Using the field data, we first developed statistical models relating the activity-density, richness and CWM body size of carabids and spiders to the kind of cropping system. As trap type affected several of these metrics, we retained only the data for large pitfall traps filled with salt solution for which we had the largest dataset (eight traps per field and per sampling date). For each trap, we pooled the data for the three sampling dates (April, May and June) in each year. Effects of cropping system, crop type and their interaction were evaluated using the same statistical approach as described in the section 2.4.1 using generalized linear mixed models or linear mixed models, including a random field effect and a random station effect.

We then used the statistical models obtained to predict three community metrics: activity-density, richness and CWM body size, for two taxonomic groups (carabids and spiders), and two crops (cereals and oilseed rape), giving 12 response variables.

Simulation of a range of trap numbers crossed with a range of cropping system effects

We first investigated the effect of the number of traps, by generating a dataset for each response variable for a number of pitfall traps ranging from 2 to 40 per field, for one or three field replicates. This sampling effort encompasses and extends beyond the most common practices in ecological and agronomic studies (e.g., [START_REF] Woodcock | Pitfall trapping in ecological studies[END_REF][START_REF] Eyre | Ground beetles (Coleoptera, Carabidae) as indicators change and pattern in the agroecosystem: longer surveys improve understanding[END_REF][START_REF] Engel | Pitfall trap sampling bias depends on body mass, temperature, and trap number: insights from an individual-based model[END_REF]. The station effect associated with each trap and the field effect were randomly drawn from normal distributions with a variance corresponding to the random effects estimated in the descriptive statistical analyses (section 2.4.2). Comparisons of cropping system effects were carried out for pairs of systems. The PHEP system was always used as the reference, and the positive or negative effects on arthropod communities relative to this reference were determined for each of the innovative cropping system. We simulated a range of cropping systems via their effect on activity-density, richness and CWM body size values. We varied these metrics from almost -100% to +150% relative to the reference cropping system. The range of positive effects was consistent with our observations and with the literature [START_REF] Rusch | Management intensity at field and landscape levels affects the structure of generalist predator communities[END_REF][START_REF] Henneron | Fourteen years of evidence for positive effects of conservation agriculture and organic farming on soil life[END_REF][START_REF] Djoudi | Farming system and landscape characteristics differentially affect two dominant taxa of predatory arthropods[END_REF], while negative effects were tested for exploration purposes. We then adapted this simulation plan for analysis of the effect of the number of field replicates (see additional analyses in supporting information).

Calculation of the minimum sampling effort to detect a difference between the two cropping systems

In each tested situation (i.e., each combination of cropping system effect in a given crop, of sampling effort, for each response variable and each taxonomic group), we checked if the response variable (metrics of arthropod community) was significantly different (P < 0.05) between the simulated and the reference cropping system. Data for each situation were generated 1000 times to perform as many comparisons. We recorded the number of cases in which there was a significant difference between the two cropping systems with the metrics in question. Significant differences were assessed using generalized linear mixed models for the activity-density and richness variables, with a Poisson error distribution and a log-link function, and a linear mixed model for CWM body size. These models included random effects for trap location and field. This resulted in a total of 29,232,000 comparisons.

We then determined the minimum number of traps and field replicates required to obtain a significant difference between the community associated with the reference system and the community associated with the simulated cropping system in 95% of simulations.

Results

In total, 2885 individual carabids and 9525 individual spiders were collected over the five cropcropping system combinations, two experimental years and three sampling dates per year.

Effect of trap size and type of preserving fluid on the trapped carabid and spider communities

Activity-density was much lower in small traps (5.5 cm diameter) than in large traps (9.5 cm diameter, Fig. 2,Table A.1 in Supplementary materials). Average activity-densities were halved for carabids and divided by three for spiders when comparing large and small traps. In addition, activity-density for spiders was slightly lower in traps filled with vinegar than in traps filled with salt water. For salt-water traps, carabid and spider richness were higher for large than for small traps. Within small traps, richness was not affected by type of preserving fluid (Fig. 2,Table A.1). CWM body size was lower in small salt-water traps than in large salt-water traps, for both carabids and spiders. CWM body size in small vinegar-filled traps was not significantly different from that for the other two types of trap (Fig. 2,Table A.1).

The biplot derived from the NMDS tended to slightly discriminate communities sampled in large vs. small traps along the first axis (Fig. 3). The permutation test indicated that trap size was significantly related to NMDS axes, but this explained a very small fraction of the variance (P = 1.0•10 -3 , r 2 = 0.16). According to the IndVal calculations, large traps were associated with several spider genera, such as Oedothorax, Tenuiphantes, Erigone, Diplocephalus and Pardosa, but also several carabids, Pterostichus melanarius (Illiger, 1798) and Anchomenus dorsalis (Pontoppidan, 1763), all of them being significant indicator species of large traps.

The NMDS and permutation tests did not distinguish the traps according to the types of preserving fluid (P = 0.67), although Notiophilus biguttatus (Fabricius, 1979) was significantly kept by IndVal as indicator of traps filled with vinegar.

Fig. 2 Effect of the three types of pitfall trap on the activity-density, richness and CWM body size values obtained for carabids and spiders. The letters above the boxplots indicate significant differences between trap types in post-hoc Tukey tests (P < 0.05). Carabid activity-density

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Type of pitfall trap

Spider activity-density

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Type of pitfall trap

Spider genus richness

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5.0 7.5 9.5 cm salt water 5.5 cm salt water 5.5 cm vinegar

Type of pitfall trap

Carabid species richness

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Differences in carabid and spiders communities between cropping systems

The carabid and spider communities caught in the traps were generally affected by the nature of the crop or by a crop×cropping system interaction (Table 1, Fig. A.1), depending on the response variable. In addition to the effects of crop and cropping system, the statistical models summarized in Table 1 provided estimates of the random effects of field and sampling station.

Averaged over the six statistical models (Table 1), marginal coefficients of determination, accounting for fixed crop and cropping system effects, equalled 43.5%. The conditional coefficients, accounting also for field and station random effects, equalled 68.2%. This goodness of fit was considered acceptable in order to use the models for simulating a wider sampling effort with different values of activity-density, richness and CWM and to generate a variability comparable with that observed in the field.

Effect of sampling effort on the ability of activity-density, richness and CWM body size estimates to distinguish between contrasting simulated communities

The relationships between the arthropod metrics, when the differences were expressed in proportions, and the minimum sampling effort required to detect these differences were approximately the same for all three metrics (Fig. 4).

A variation of carabid or spider activity-density of less than 30% (i.e., 5 carabid or about 20 spider individuals) between a simulated and the reference PHEP system could not be detected if there were fewer than 40 traps per field (Fig. 4 andA.2). With three field replicates, five to ten traps were required to detect a variation of 50% in activity-density, corresponding to a difference of about 10 carabids or 30 to 50 individual spiders.

A minimum of three to five traps per field for carabids and five to 15 traps per field for spiders was required to differentiate between two cropping systems differing by five species or genera.

The sampling effort increased to more than 20 traps per field for the detection of a difference in richness below two species or two genera. For CWM body size, the sampling effort required decreased sharply, from 30 to less than five traps, for a difference between two simulated cropping systems of 1 to 2 mm in carabids and 0.3 to 0.7 mm in spiders (Fig. 3).

We then represented the observed effects of the studied cropping systems on these sampling effort curves (see vertical dashed lines on Fig. 4 andA.2). In general, the observed effects of the No-Pest cropping system relative to the PHEP system were so small that more than 30 or 40 traps per field, with three field replicates, would have been required to detect a significant difference for the three metrics (Fig. 3). In the L-GHG system, particularly for oilseed rape, the differences in activity-densities and in CWM body size were slightly larger and easier to detect.

Fig. 4 Minimum sampling effort (number of traps) required to differentiate two cropping systems as a function of the simulated proportional difference in the response variables between the two systems, the productive one being taken as a reference (vertical full black line). The vertical dashed lines indicate the observed differences in the cropping system experiment (section 3.2). The response variables were carabid and spider activity-density, richness and CWM body size (mm). Simulations were carried out with one (blue circles) or three (green triangles) field replicates.

Table 1 Effects of the crop and cropping system on carabid and spider activity-densities, richness and CWM body size. These results were obtained with data from for large pitfall traps filled with salt water only, summed over the three sampling dates (df: degrees of freedom).

Discussion

We evaluated the extent to which pitfall traps were appropriate for studies characterizing the effects of arable cropping systems on the composition and structure of spider and carabid communities. We first compared the effects of pitfall trap size and type of preserving fluid on carabid and spider communities, which are the main sources of variation in pitfall trap design.

As expected, activity-density increased with trap size. Larger traps cover more ground, resulting in a higher probability to catch randomly moving individuals. Increasing the trap diameter by a factor of 1.7 (from 5.5 to 9.5 cm) resulted in a similar increase in the number of carabids caught, but a tripling of the numbers of spiders caught, consistent with previous observations [START_REF] Work | Pitfall trap size and capture of three taxa of litter-dwelling arthropods: Implications for biodiversity studies[END_REF][START_REF] Lange | Effect of pitfall trap type and diameter on vertebrate by-catches and ground beetle (Coleoptera: Carabidae) and spider (Araneae) sampling[END_REF]. The effect of trap size has already been shown to differ between the species caught, as a function of their mobility (often related to their size), and the community composition results were affected by trap size. Genera from the Linyphiidae family were overrepresented in the large traps. This increase in the number of catches was proportional to trap perimeter increase for carabids (which nearly doubled, like diameter), and to trap surface increase (which was tripled in large vs small traps, 70.8 vs 23.7 cm 2 ) for spiders. A likely explanation is the contrasting behaviour when they encounter the rim of the trap between carabids and wandering spiders on the one hand, and Linyphiidae spiders on the other. Linyphiidae spiders can enter and explore the trap without necessarily falling into the fluid [START_REF] Topping | Behavioural responses of three linyphiid spiders to pitfall traps[END_REF].

Large traps also captured larger numbers of carabid species and spider genera. This may be because the large traps are better able to catch species with behaviours enabling them to avoid or escape from traps, as already reported for Linyphiidae spiders [START_REF] Topping | Behavioural responses of three linyphiid spiders to pitfall traps[END_REF]) and carabids [START_REF] Halsall | The efficiency of pitfall trapping for polyphagous predatory Carabidae[END_REF]. In terms of body size, CWM body size increased with trap size, for both carabids and spiders, perhaps because large species were better able to detect, avoid or escape from small traps.

For a fixed trap size, the type of preserving fluid had no effect on the variables considered, except for spider activity-density, for which vinegar-filled traps had a slightly lower trapping efficiency, suggesting a possible deterring effect. This had no significant effect on community taxonomic richness or functional composition, which was confirmed by the multivariate analysis on community composition. Despite initial expectations [START_REF] Mccravy | Effects of pitfall trap preservative on collections of carabid beetles (Coleoptera: Carabidae)[END_REF], there was no attractive effect of vinegar toward carabids and spiders. Overall, we can consider that traps filled with salt water or vinegar perform equally in terms of taxonomic or functional composition of the sampled communities.

These results illustrate how estimates of community composition and structure given by pitfall traps can be affected by the activity, behaviour and size of the arthropods studied [START_REF] Hancock | Pitfall trapping bias and arthropod body mass[END_REF]). These limitations have already been reported for activity-density and richness [START_REF] Topping | Limitations to the use of pitfall traps in ecologicalstudies exemplified by a study of species in a field of winter-wheat[END_REF]), but we also demonstrate here that functional characterization (here CWM body size, one of the most frequently used functional descriptors) is also affected. The use of functional indicators, such as the CWM of traits, to predict the role of arthropods in ecosystem functioning, in terms of predation for example, may therefore be risky. The correction of these sampling biases by body mass, as recommended by [START_REF] Engel | Pitfall trap sampling bias depends on body mass, temperature, and trap number: insights from an individual-based model[END_REF], is required to obtain a reliable view of community taxonomic and functional composition and structure.

Complementary sampling techniques can also be useful to increase completeness of recorded assemblages or to reduce sampling effort [START_REF] Knapp | Incomplete species lists produced by pitfall trapping: How many carabid species and which functional traits are missing?[END_REF].

When addressing cropping system comparisons, the observed differences in activity-densities and richness were not specific to our case study and are similar to those already reported in other long-term cropping system experiments comparing conventional, organic and conservation agriculture cropping systems [START_REF] Rusch | Management intensity at field and landscape levels affects the structure of generalist predator communities[END_REF][START_REF] Henneron | Fourteen years of evidence for positive effects of conservation agriculture and organic farming on soil life[END_REF][START_REF] Djoudi | Farming system and landscape characteristics differentially affect two dominant taxa of predatory arthropods[END_REF]. We then developed a simulation procedure to investigate the effect of the numbers of traps and field replicates on the ability to detect cropping system effects on carabid and spider communities, based on three metrics: activity-density, richness and CWM body size. The dataset generated took into account the important variability caused by the trap location and field effects. This simulation approach also made it possible to analyse the effect of sampling effort when comparing fields with more marked differences in community metrics than those observed.

Only very different communities could be significantly distinguished with a reasonable number of traps and field replicates. Indeed, a sampling design with ten pitfall traps per field and three field replicates was able to detect a 100% increase in carabid or spider activity-density between two cropping systems, but not smaller increases. Five traps were sufficient to distinguish between communities differing by 20 or 30% in CWM body size (for three and one field replicates, respectively), but the required sampling effort increased sharply for differences below this threshold.

The relationships between the difference in arthropod metrics between cropping systems and the minimum sampling effort required to detect this difference were similar for activity-density and richness, contrary to the findings of [START_REF] Perner | Sample size and quality of indication -a case study using ground-dwelling arthropods as indicators in agricultural ecosystems[END_REF], who reported that the required sample size for estimating richness was smaller than that for abundance parameters. A smaller number of traps was required to find differences in CWM body size between cropping systems. This finding highlights the suitability of this metric for analysing the response of arthropod communities to different management techniques. The results were also similar between the two taxa, as reported by [START_REF] Perner | Sample size and quality of indication -a case study using ground-dwelling arthropods as indicators in agricultural ecosystems[END_REF]. This finding suggests that these metrics and taxa are, a priori, equally suitable for use in studies aiming to detect cropping system effects. However, they displayed very different patterns of response to the three cropping systems studied here. In this case, carabid activitydensity, carabid CWM body size and spider genus richness were the variables that allowed distinguishing between cropping systems with the smallest sampling effort, whereas a much greater sampling effort was required for carabid richness. The sampling effort could be reduced by increasing the number of field replicates, but not equally for all metrics and taxa (Appendix B in Supplementary materials). This sample size reduction was the strongest for CWM body size and for all metrics in oilseed rape crops. In general, however, several metrics are sought simultaneously and sampling designs would need to be adjusted to the factor that requires the highest sampling effort. It should be kept in mind, however, that identifying spiders at genus level only did not allow us to directly compare the results on taxonomic richness for the two taxa.

Conclusion

The effects of three innovative contrasting cropping systems on arthropod communities were difficult to differentiate from other sources of variability within and between fields and years, although they were of a similar amplitude to those already reported for organic or conservation agriculture. Large trap size increased the sampling effort and increased the trapping of large species, whereas the type of preserving fluid (salt water vs. vinegar) had only a limited impact on the communities sampled. As expected, a high sampling effort was generally required for the comparison of activity-density and richness values across fields managed with different cropping systems. Also consistent with our initial expectations, a smaller sampling effort was generally required for the comparison of functional composition between two communities, than for comparisons of taxonomic richness, because this metric is less sensitive to rare taxa or to the number of individuals trapped. Finally, we found that the minimum sampling effort was much smaller for comparisons of the effects of cropping system in oilseed rape crops than in cereals. Selection of the most appropriate trap design, metrics and crops for study therefore appeared to be the main levers for optimizing the trade-off between sampling effort and the ability to detect arthropod community responses to habitat management.

Fig. 1

 1 Fig. 1 A: Pitfall trap in a cereal field; B: Schematic representation of the sampling design. Data were pooled over months prior to analysis.

Fig. 3

 3 Fig. 3 Biplot representation of the NMDS ordination of the communities of carabid species and spider genera in the three types of pitfall traps (squares = large traps with water; circles = small traps with water; triangles = small traps with vinegar). Traps (individuals, left) were described by the activity-density of the species (variables, right) they contained. Ellipses are 95% confidence intervals around the centroid position (stars).

Acknowledgments

We thank Caroline Colnenne-David and Gilles Grandeau for their collaboration for the cropping system experiment "Systèmes intégrés sous contraintes", Dominique le Floch, Thomas Bréquigny and Yoann Penel for their participation in field sampling, Jean-David Chapelin-Viscardi and Alexis Saintilan for assistance with arthropod identification and David Makowski for his valuable advice concerning statistical analyses. This work was supported by the French "Pour et sur le plan Écophyto 2018" research program.

Authors' contributions

AG and MVM conceived ideas and designed the methodology; AG collected and analyzed the data and led the writing of the manuscript. All authors provided critical input concerning the draft versions of the manuscript and approved the final version for publication.


Yanjun Li
email: yanjun.li@loria.fr

Chung Shue Chen

Ye-Qiong Song
email: song@loria.fr

Real-Time Routing Protocols for Wireless Sensor Networks

Developing real-time routing protocols under energy constraint is one of the key points for providing end-to-end delay guarantee in multi-hop wireless sensor networks. In this paper, we give, at first, an overview of the existing real-time routing protocols and point out some potential approaches to improve them. To enhance existing protocols, one way is to make routing decision based on multi-hop rather than 1-hop neighborhood information. We study the asymptotic performance of a generic routing metric as the quantity of information a priori increases and propose then a 2-hop neighborhood information based real-time routing protocol. As an example, the approach of mapping packet deadline to a velocity is adopted as in SPEED; however, our routing decision is made based on the 2-hop velocity. An energy efficient probabilistic drop is proposed to improve energy utilization efficiency. When packet deadline requirement is not stringent, a design is integrated to release nodes from heavy consumption. Energy balance over nodes is thus improved. Simulation results show that, compared with protocol SPEED that only utilizes 1-hop information, the proposed scheme leads to lower deadline miss ratio and higher energy efficiency.

Introduction

For emerging applications of wireless sensor networks (WSN) in surveillance, industrial control, medical care and inventory tracking systems, real-time quality-ofservice (QoS) is desired as these applications are often in nature time sensitive. Different from existing best-effort service which may not have stringent packet timeliness requirement and can tolerate a significant amount of packet loss, these real-time (RT) applications are much more demanding. Out-of-date data are often irrelevant and may even lead to negative impacts to the system control and performance [START_REF] Stankovic | Real-time communication and coordination in embedded sensor networks[END_REF][START_REF] Li | Real-time QoS support in wireless sensor networks: a survey[END_REF]. QoS and timeliness guarantee in WSN is therefor favorable in newly required RT service.

Supporting real-time QoS in WSN can be addressed from different layers and domains [START_REF] Li | Real-time QoS support in wireless sensor networks: a survey[END_REF]. For example, the medium access control (MAC) is capable of supporting channel access delay guarantee but in single-hop manner, while a routing protocol can help to provide endto-end or multi-hop transmission guarantee in network layer. Cross-layer optimization has a potential of some further improvements. Recently, in-network data aggregation strategy has attracted more and more attentions in complementing routing protocols for reducing data redundancy and alleviating network congestion. Meanwhile, proper middleware design will help to bridge application and lower layers efficiently so as to support system abstraction and mutual coordinations. In this paper, we will focus on routing protocol which has always played a very significant role in supporting end-to-end QoS.

Considering system simplicity, most existing routing protocols utilize 1-hop neighborhood information. It is potential that multi-hop information may lead to improved performance in issues such as routing, message broadcasting, and channel access scheduling [START_REF] Stojmenovic | Loop-free hybrid singlepath/flooding routing algorithm with guranteed delivery for wireless networks[END_REF][START_REF] Lou | On reducing broadcast redundancy in ad hoc wireless networks[END_REF][START_REF] Bao | Channel access scheduling in ad hoc networks with unidirectional links[END_REF]. It is very likely that a system can perform better if more information is available and effectively utilized. Here, we first study the asymptotic performance of a generic routing decision when the quantity of information a priori increases. Based on the preliminary results, a 2-hop information based RT routing protocol is proposed and its improvement is shown over 1-hop protocol such as SPEED [START_REF] He | SPEED: a stateless protocol for real-time communication in sensor networks[END_REF]. The choice of two hops is a tradeoff between performance improvement and complexity. The following work will focus on how to use or integrate the 2-hop information effectively so as to improve both energy and real-time performance.

The rest of the paper is organized as follows. Section 2 discusses related routing protocols in WSN. Section 3 studies a generic routing metric and shows its performance as information a priori increases. Section 4 presents the design of a 2-hop information based routing protocol. Simulation and comparison are reported. Meanwhile, potential enhancement is addressed. Finally, Section 5 concludes the paper.

An overview of RT routing protocols

Real-time service has been considered in some existing WSN protocols. Akkaya and Younis [START_REF] Akkaya | An energy-aware QoS routing protocol for wireless sensor networks[END_REF] have proposed an energy-aware QoS routing protocol which finds energyefficient path and by which the end-to-end delay requirement can be met. It is suggested to have a classifier in each node to check incoming packet type and divert traffics into different RT and non-RT priority queues. The delay requirement is converted into bandwidth requirement. By using an extended version of Dijkstra's algorithm, the protocol finds a list of least cost paths and picks a path from the list which can meet the delay requirement.

In [START_REF] Ergen | Energy efficient routing with latency guarantee for sensor networks[END_REF], Ergen et al. present an energy efficient routing method with delay guarantee for WSN. They first exclude the delay constraint and formulate the lifetime maximization as a linear programming (LP) problem aiming to determine optimal routing path and maximize the minimum lifetime of nodes. The result of LP is first implemented in a centralized way and then approximated by a distributed iterative algorithm. Then, delay guarantee is included by limiting the length of node-to-sink routing path.

In [START_REF] Boughanmi | A new routing metric for satisfying both energy and delay constraints in wireless sensor networks[END_REF], Boughanmi and Song have proposed a routing metric for evaluating path efficiency. It is defined by the ratio of energy efficiency to end-to-end delay, where the energy efficiency is specified by considering link failure and packet retransmission. The end-to-end delay is defined by the hop count between source and sink, collected by routing response messages in initialization phase. The new routing metric is applied in AODV routing protocol with IEEE 802.15.4 [10] MAC sublayer. Result shows that it can improve the network lifetime and end-to-end delivery ratio when compared to traditional AODV and the metric in [START_REF] Ergen | Energy efficient routing with latency guarantee for sensor networks[END_REF].

Pothuri et al. [START_REF] Pothuri | Delayconstrained energy efficient routing in wireless sensor networks through topology control[END_REF] design a heuristic solution to find energy-efficient path for delay-constrained data in WSN. A set of paths between source and sink nodes are identified and indexed in the increasing order of their energy consumption. End-to-end delay is estimated along each of the ordered paths and the one with the lowest index that satisfies the delay constraint is selected. Their proposed framework achieves a good balance between latency and energy consumption. However, the solution is based on the assumption that nodes are equipped with two radios: a low-power radio for short-range and a high-power radio for long-range communication such that each node can reach the sink directly using its long-range radio.

ZigBee alliance [START_REF] Alliance | [END_REF] defines the network and application layers on the top of physical and MAC layer standardized by IEEE 802.15.4. The network layer uses a modified AODV by default and hierarchical tree routing (HTR) as last resort. In [START_REF] Nefzi | Performance analysis and improvement of Zigbee routing protocol[END_REF], Nefzi and Song have analyzed and compared the performance of AODV and HTR in terms of end-to-end delay and energy consumption. It is found that the network with HTR has smaller average end-to-end delay and longer lifetime than that with AODV. However, AODV does better in end-to-end delay in the worst case performance. Besides, the energy consumption of AODV is more uniformly distributed. An improvement is made by using a neighborhood table in routing decision in order to improve the worse-case delay in HTR by shortening the worst-case routing path. To some extent, end-to-end hop number implies end-to-end delay. Thus, HTR is suitable in guaranteeing the delay time by simply measuring the hop count from source to sink.

In addition, several RT routing protocols use velocity assignment policy, including SPEED [START_REF] He | SPEED: a stateless protocol for real-time communication in sensor networks[END_REF]. The packet deadline is mapped to a velocity in terms of the distance to destination. A packet is forwarded by a node if it can meet the required velocity. When there is no neighbor node which can meet the requirement, the packet is dropped probabilistically while regulating the workload. Back-pressure packet re-routing in large-delay link is carried out to switch and reduce packets directed to a congested region. In [START_REF] Felemban | MMSPEED: Multipath multi-SPEED protocol for QoS guarantee of Reliability and timeliness in wireless sensor network[END_REF], MM-SPEED extends SPEED. It provides multiple delivery velocities for packets with different deadline requirements for supporting different QoS. RPAR [START_REF] Chipara | Real-time power-aware routing in sensor network[END_REF] offers another improved version of SPEED. The required velocity is based on the progress towards the destination and the packet's remaining time before the deadline. A node will dynamically adjust its transmission power to meet the required velocity in the most energyefficient way. If no node can meet the velocity, the transmission power will be adjusted to attempt a new discovery. It is worth noting that all the above protocols are based on 1-hop neighborhood information.

In our proposed scheme to be described in Section 4, we also adopt the approach of mapping packet deadline to a velocity. The concept has been shown effective in [START_REF] He | SPEED: a stateless protocol for real-time communication in sensor networks[END_REF][START_REF] Felemban | MMSPEED: Multipath multi-SPEED protocol for QoS guarantee of Reliability and timeliness in wireless sensor network[END_REF][START_REF] Chipara | Real-time power-aware routing in sensor network[END_REF]. However, our routing decision is made based on 2-hop neighborhood information and the corresponding metrics. It is therefore named as Two-Hop SPEED (TH-SPEED) here. For computing 2-hop neighborhood information in wireless ad hoc and sensor networks, some distributed algorithms and efficient information exchange schemes are reported in [START_REF] Calinescu | Computing 2-hop neighborhoods in ad hoc wireless networks[END_REF][START_REF] Rajendran | Energy-Efficient, Collision-Free Medium Access Control for Wireless Sensor Networks[END_REF]. For a network of n nodes, the complexity analysis presented in [START_REF] Calinescu | Computing 2-hop neighborhoods in ad hoc wireless networks[END_REF] has shown that every node can obtain the knowledge of 2-hop neighborhood by a total of O(n) messages, while each message has O(log n) bits.

Multi-hop information based routing and metric: a case study

In this section, we report the performance comparison of a 1-hop, 2-hop, and 3-hop neighborhood information based routing metric, aiming to have a general idea of how much the performance can be improved provided that one can have more routing information a priori. The new routing metric considers both the advance in distance and link quality, incorporated in the routing decision at each hop. The performance based on 1-hop information is compared to those with multi-hop information.

Analytical link model

In the study, we adopt the lossy WSN link layer model derived in [START_REF] Zuniga | Analyzing the transitional region in low power wireless links[END_REF], which is built on aggregate statistical mea-sures for realistic time-varying channels. The packet reception rate (PRR), 0 ≤ p ≤ 1, of a wireless link is modeled as:

p(d) = 1 - 1 2 exp - γ(d) 2 1 0.64 8f (1)
where d is the transmitter-receiver distance, γ(d) is the signal-to-noise ratio (SNR), and f is the frame size 1 , with respect to Mica2 Motes [START_REF] Crossbow | Mica2 Motes datasheet[END_REF] in standard non-coherent FSK. This model takes into account both distancedependent path loss and log-normal shadowing in characterizing the wireless link. For transmitting power P t , γ(d) dB = P t dB -P L(d) dB -P n dB [START_REF] Li | Real-time QoS support in wireless sensor networks: a survey[END_REF] where P t dB is set to 0 dBm while the noise floor P n dB is at -115 dBm in reference to Mica2 radios. The path loss P L(d) dB will adopt the following commonly used model, e.g. [START_REF] Zuniga | Analyzing the transitional region in low power wireless links[END_REF], with respect to the channel statistics in [START_REF] Sohrabi | Near ground wideband channel measurement in 800-1000 MHz[END_REF]:

P L(d) dB = P L(d 0 ) dB -10n log 10 (d/d 0 ) + X σ dB (3)
where n denotes the path loss exponent, d 0 is the reference distance (at 1 meter), while X σ has a log-normal distribution with zero mean and variance σ2 . In reference to [START_REF] Zuniga | Analyzing the transitional region in low power wireless links[END_REF][START_REF] Seada | Energy-efficient forwarding strategies for geographic routing in lossy wireless sensor networks[END_REF], we adopt the "sandy flat beach" model [START_REF] Sohrabi | Near ground wideband channel measurement in 800-1000 MHz[END_REF] to simulate common WSN application environment. Performance in other environment models is also evaluated. Results have shown similar tendency and support same conclusion. Due to the scope of this paper, we only present those obtained from the sandy flat beach model with n = 4, σ = 4, and P L(d 0 ) = -40.8 dBm. Following [START_REF] Zuniga | Analyzing the transitional region in low power wireless links[END_REF], the frame size f is set as 50 bytes.

Forwarding metric analysis

As reported in [START_REF] Seada | Energy-efficient forwarding strategies for geographic routing in lossy wireless sensor networks[END_REF], the product of PRR and the distance progress towards destination is a more effective forwarding decision metric than a purely distance based routing algorithm in systems of time-varying links. For instance, packet loss also occurs in forwarding between nodes in short distance due to the fact of link uncertainty while 0 < p(d) < 1. Instead of simply taking the product of PRR and the distance progress as decision metric, we consider the following new metric. Some technical definition are required in advance.

For each node i, N(i) is used to denote the set of its direct neighbors. F(i) is used to denote the set of node i's potential forwarders which will make a progress towards the destination. In other words,

F(i) {j|d(i, D) -d(j, D) > 0, j ∈ N(i)}. (4)
Moreover, F 2 (i) is used to denote the set of forwarding nodes in 2-hop. Consequently,

F 2 (i) {k|d(j, D) -d(k, D) > 0, j ∈ F(i), k ∈ N(j)}.
(5) Remarks:

1 It includes preamble, packet payload and CRC.

1. The distance d i,j between pair nodes i and j is assumed measurable.

2. The PRR, p(d i,j ), of each distance d i,j is modeled and given by [START_REF] Stankovic | Real-time communication and coordination in embedded sensor networks[END_REF]. The PRR statistics are assumed known, including path loss exponent n, log-normal shadowing standard deviation σ, and the path loss reference P L(d 0 ).

3. The progress from node i to its candidate forwarder j is identified by its expected distance, d j,D , to the destination node (says, D), when chosen:

d j,D ∆ =p(d i,j )d j,D + (1 -p(d i,j ))d i,D . (6)
This can also be interpreted as the expected position after 1-hop routing despite the fact that a packet cannot be buffered at the expected point. However, d j,D can serve as a metric for choosing the suitable one.

4. The node among F(i) with smallest d j,D is selected as the packet forwarder, denoted by j * .

5. The packet is forwarded to node j * . However, this does not mean the transmission is surely successful since the PRR between nodes i and j * could be smaller than 1. In general, 0 < p(d i,j * ) < 1. Thus, it has a success rate of p(d i,j * ) when sending a packet from i and j * in the coming forwarding. If a transmission fails due to this link uncertainty, the buffered packet at current node i will initiate a new forwarder selection based on new or updated network topology and link reliability. One may consider it as an ARQ retransmission with possibly updated PRR and links.

Consider a 2-hop information based routing 2 , similarly to [START_REF] He | SPEED: a stateless protocol for real-time communication in sensor networks[END_REF], we select the one among j with smallest d

(2) j,D defined below as the next-hop forwarder. The following metric is to identify the best potential candidate with expected progress in 2 hops:

d (2) j,D ∆ = p(d i,j )p(d j,k )d k,D + (p(d i,j )p(d j,k ) + p(d i,j )p(d j,k ))d j,D + p(d i,j )p(d j,k )d i,D (7)
where p(•) ∆ =1 -p(•) for notational convenience. Iteratively, consider 3-hop information based routing. Says, a neighbor node of k is node l. Similarly to ( 6) and ( 7), we define the best candidate of next-hop forwarder by its expected progress in 3-hop neighborhood with respect to the following metric:

d (3) j,D ∆ = p(d i,j )p(d j,k )p(d k,l )d l,D + (p(d i,j )p(d j,k )p(d k,l ) + p(d i,j )p(d j,k )p(d k,l ) +p(d i,j )p(d j,k )p(d k,l ))d k,D + (p(d i,j )p(d j,k )p(d k,l ) + p(d i,j )p(d j,k )p(d k,l ) +p(d i,j )p(d j,k )p(d k,l ))d j,D + p(d i,j )p(d j,k )p(d k,l )d i,D . (8)

Simulation and performance

Nodes are uniformly distributed in a geographical area of (200m × 200m). The source and destination nodes are located at (30m, 30m) and (170m, 170m) respectively. Following ( 1)-( 3), given distance d between a pair of nodes, the corresponding PRR, p(d), is drawn with respect to the log-normal shadowing each time during packet routing. The simulation model can be interpreted as in timevarying wireless links with dynamic network topology and connectivity 3 .

In the performance evaluation, the number of hops required in routing from source to destination is highly concerned. It implies the routing delay. Here, we do not take into account MAC layer delay. This will help to identify the performance only due to routing issues and isolate from impacts of other factors. A more complete study of a 2-hop based routing including MAC and WSN experimental link model will be presented later in Section 4. Meanwhile, we also look at the reachability of routing that is defined by the percentage of runs in which packets from source can reach the destination. If a packet is always delayed at a specific node or possibly looped in an isolated region and thus cannot go to the destination after a large number of hops, it will be considered as unreachable, i.e. routing failure.

Here, simulation results are obtained by 3000 runs each. Fig. 1 and Fig. 2 show the reachability and average number of hops required from end-to-end respectively. In Fig. 1, reachability generally increase as node density increases as expected. Besides, enhancement is observed generally from the k-hop to k + 1-hop based routings when more neighborhood information is allowed. 3 A connectivity is often defined [START_REF] Zuniga | Analyzing the transitional region in low power wireless links[END_REF] by PRR great than or equal to 0.9, while the transitional region is in PRR values between 0.1 and 0.9. Note that the gain since from 2-hop to 3-hop is relatively marginal, while that from 1-hop to 2-hop based routing is more attractive. It should be noted that when the number of nodes in the WSN is large, the improvement of reachability from k-hop to k +1-hop based routing is small. This is due to the fact that, as pairs of nodes are getting closer and closer, the PRR will be high for most cases. Thus, even if we just follow the 1-hop information, a packet can easily reach the destination by a simple path searching. This can also be observed in Fig. 2 that the gap in-between the four curves of average number of hops required is getting smaller. However, the difference from 1-hop to 2-hop based routing is still quite significant, particularly when the number of nodes is relatively small.

Note that the ∞-hop result is provided as a benchmark, which refers to an ideal and optimistic performance. In Fig. 2, the average number of hops required is taken from runs in which a packet is routed from source to destination. It indicates the statistical result of successful forwarding. As shown in Fig. 2, as the number of nodes in the WSN increases, statistically the number of hops required will decrease since now more and better forwarding options are likely available. This helps a better progress and reduces the number of hops experienced.

TH-SPEED: another case study 4.1. Algorithm design

Referring to the study above, we may have a general idea that 2-hop information based routing better improves the routing path decision. This is the motivation of TH-SPEED design. TH-SPEED primarily aims at lowering packet deadline miss ratio for demanding real-time WSN. However, it also considers energy utilization effi-ciency which has not been addressed in SPEED and MM-SPEED. Similarly to SPEED, we assume each node is aware of its geographic location possibly by some localization techniques [START_REF] Doherty | Convex position estimation in wireless sensor networks[END_REF], or just using the mechanism specified in the IEEE 802.15.4a amendment [START_REF]Wireless Medium Access Control (MAC) and Physical Layer (PHY) Specifications for Low-Rate Wireless Personal Area Networks (LR-WPANs)[END_REF]. Suppose location information can be further exchanged among 2-hop neighbors [START_REF] Rajendran | Energy-Efficient, Collision-Free Medium Access Control for Wireless Sensor Networks[END_REF][START_REF] Bao | Transmission scheduling in ad hoc networks with directional antennas[END_REF]. Therefore, each node is aware of its immediate and 2-hop neighbors, and their locations. To estimate the packet delivery speed to next hop, we adopt the velocity concept used in SPEED.

TH-SPEED has four core components: (i) 2-hop velocity based forwarding strategy, (ii) delay estimator, (iii) energy-efficient probabilistic drop, and (iv) optional residual energy cost function for node energy consumption balancing. Basically, our protocol uses a 2-hop packet delay estimation to compare with the required velocity and thus decides which node should be the forwarder. If there is no suitable one, the packet will be dropped by in a probabilistic mechanism. By the 2-hop information, holes or congestions in the network could be predicted at an early time. Meanwhile, a more promising path can be identified after considering more possibilities. The cost is that TH-SPEED requires more neighborhood information for a better decision. Besides, some more computations are conducted in decision making. We assume the increment is affordable and will discuss in Section 4.3 one possible solution to reduce the overhead.

Two-hop velocity based forwarding

To begin with, some technical definitions are required. The source and destination nodes are labeled by S and D respectively. End-to-end packet delivery velocity for a required deadline, t set , is defined as:

S set = d(S, D)/t set . (9)
In SPEED, the core stateless non-deterministic geographic forwarding (SNGF) works as follows. Upon receiving a packet, node i calculates the velocity provided by each of the forwarding nodes in F(i) expressible as:

S j i = d(i, D) -d(j, D) Delay j i ( 10
)
where j ∈ F(i) and Delay j i denotes the estimated hop delay between nodes i and j. If there exists j such that S j i > S set , the one with largest velocity is selected.

In the proposed TH-SPEED, similarly, by 2-hop information, node i will calculate the velocity provided by each of the 2-hop forwarding node pairs, {F(i), F 2 (i)}. That is,

S j→k i = d(i, D) -d(k, D) Delay j i + Delay k j ( 11
)
where j ∈ F(i) and k ∈ F(j). If there exists node pairs {j, k} such that S j→k i > S set , the one that can provide the largest velocity is preferred. Therefore, node j, the parent of node k, will be chosen as the immediate forwarder. Then, node j will relay the packet and takes the role of node i. The mechanism continues and repeats at node j with its 2-hop neighborhood so as to find the next forwarding node iteratively. Fig. 3 gives an example. Suppose a packet is to be sent from S to D. Here, {A, B, C} ∈ F(S), {E, F } ∈ F(A), {G, H} ∈ F(B), {I} ∈ F(C), {J} ∈ F(F ) and {K} ∈ F(G). Let the end-to-end deadline be 0.65s. Following [START_REF] Boughanmi | A new routing metric for satisfying both energy and delay constraints in wireless sensor networks[END_REF] and the numerical values given in Fig. 3,

S set = 100m/0.65s = 154 m/s.
According to SPEED, by (10), Thus, node A will be chosen as the forwarder since it can provide the largest velocity higher than S set . Iteratively, node A will choose node F as its forwarder since S E A = (80m-78m)/0.06s = 33.3 m/s, while S F A = (80m-65m)/0.08s = 187.5 m/s.

However, according to TH-SPEED, node S will search among its 2-hop neighborhood and calculate the velocity provided by each 2-hop pair. Following [START_REF] Pothuri | Delayconstrained energy efficient routing in wireless sensor networks through topology control[END_REF], node pair {B, G} can provide velocity: = 169.2 m/s respectively. Therefore, node B will be chosen as the immediate forwarder. By TH-SPEED, it is expected that the sender will have a forwarding node pair that can provide the largest velocity in 2-hop neighborhood. However, by SPEED, it is only one-hop optimized. Besides, if there is a topology hole after the first forwarding node, SPEED can get a problem. However, by TH-SPEED, this can be alleviated.

Inherently, TH-SPEED has 1-hop more prediction capability as using a "telescope" while finding the path. General speaking, even if the starting choice is not the globally optimized one, it may have a better chance to gradually be corrected due to the deeper sight of view when compared with SPEED.

Delay estimator

In [START_REF] Pothuri | Delayconstrained energy efficient routing in wireless sensor networks through topology control[END_REF], it is observable that the delay estimation from a sender to its available forwarders has played a significant role in the velocity metric. The delay of a packet from node i to its forwarder j is comprised of the MAC delay, transmission time (including acknowledgement time) and the transmission count 4 , denoted by Delay M AC , Delay tran and C j i respectively.

Delay j i = (Delay M AC + Delay tran ) × C j i . (12)
The transmission time of a packet and its acknowledgement can be considered as constant determined by the packet size and network bandwidth. That is,

Delay tran = packet size + ack size bandwidth . (13)
Our delay estimator follows the classical method used for round trip time (RTT) estimation in TCP protocol [START_REF] Jacobson | Congestion avoidance and control[END_REF], via the following updating equation:

R ← αR + (1 -α)M ( 14
)
where R is the average RTT estimate, M is the RTT measurement from the most recently received packet, and α is filter gain. It is shown efficient in [START_REF] Jacobson | Congestion avoidance and control[END_REF] and [START_REF] Chipara | Real-time power-aware routing in sensor network[END_REF]. Following the same concept, we estimate Delay j i by the joint consideration of the history average delay and the most recent value from the former transmission. However, if the packet fails to be transmitted after exceeding the maximum number of retransmissions according to ARQ mechanism, the measurement M j i for node pair (i, j) in current time will be set to a large value to avoid selecting the path for a certain number of rounds. Estimate of Delay j i at time t can thus be expressed as:

Delay j i (t) = α t -1 t-1 k=1 Delay j i (k) + (1 -α)M j i (t -1). (15)
The link delay of a packet is measured by the sender, which will stamp the time a packet is sent out and compare it with the time an ACK is received. Assume that 4 ARQ is adopted thus if the packet fails to be transmitted due to collision or bad links, retransmission will be initiated. the ACK is transmitted in a parallel channel without collision and loss, the single-hop delay can be approximated by the RRT since the propagation time of ACK is negligible. To update the link delay information to corresponding nodes in the routing path, after receiving the ACK with delay information from its forwarder, a node will multicast a feedback packet, which contains the updated delay of the forwarding link, to its parent nodes. Fig. 4 shows an example of the link delay update after node G is chosen as the forwarder of node E. Delay G E is updated at E after receiving ACK from G and then feedback to A, B and C. Accordingly, the delay field EG in their records, e.g. a 2-hop delay table, will be updated to [START_REF] Chipara | Real-time power-aware routing in sensor network[END_REF] with the new information.

Energy-efficient probabilistic drop

A policy of energy-efficient probabilistic drop is taken when no node in the 2-hop forwarding set can provide the required velocity. The packet drop probability is proportional to its distance apart from the destination. That is, a node closer to the source will have a higher probability to drop the packet than the node closer to the destination when there is no forwarder which can meet the required velocity. Since a packet near the destination has already traveled a long way and a lot of nodes have consumed energy to forward it. It is worthwhile to try the best to see whether we can finally deliver it successfully. Although the current hop may not be able to meet the required velocity, it is possible to meet the end-to-end requirement finally if the coming hops have relatively short delays. However, if the node near the source cannot meet the velocity, from the point of view of energy utilization efficiency, it will be more efficient to drop earlier and look for a better chance in the coming retransmission.

Details of the probabilistic drop policy are described below. Suppose node i searches among its 2-hop neighborhood and cannot find a forwarder that can maintain the required velocity, it will drop the packet by a probability equal to d(i,D) d(S,D) , where d(i, D) is the distance from node i to destination and d(S, D) is the distance between the source and destination respectively.

We will show in Section 4.2 the consequent difference of the energy-efficient probabilistic drop with respect to two other methods: (i) all packets will be forwarded via the nodes which provide the largest velocity even when they cannot meet S set , and (ii) once there is no node that can provide the required velocity, the packet will be dropped immediately. The policy of energy-efficient probabilistic drop has outperformed the other two under a joint consideration of deadline miss ratio and energy efficiency.

Energy balancing

In SPEED, no strategy for energy balance is considered. Some nodes will frequently be chosen as forwarders due to their significant positions in the geographical area. This can be observed from the simulation result reported in Section 4.2. If a tradeoff between packet delay and node energy consumption balance is allowed or the deadline requirement is not very stringent, it may not be necessary to always choose the node that can provide the largest velocity as forwarder. Instead, we choose the one which has the largest joint metric, ve, defined in terms of the velocity and residual energy below. Provided that the velocity is still higher than S set , a certain amount of the expected velocity is sacrificed to have energy consumption balance by looking at the residual energy and velocity together:

ve j→k i = c v × S j→k i Sset + c e × residual energyj initial energyj c v + c e (16)
where c v and c e are the weights of velocity and energy respectively. A larger c v value tends to prefer nodes which can provide greater velocity and thus less delay. However, it may lead to concentrative energy consumption. A larger c e will direct traffics to more nodes and consequently lead to a better load balancing but possibly increased packet delay. The tradeoff between c v and c e depends on the link quality and traffic distribution. We will leave the investigation as future work and currently set c v = c e = 1.

Performance evaluation

The effectiveness of TH-SPEED is evaluated in the following simulation studies. To be close to practical WSN and realistic implementation, we set the MAC layer, link quality model and energy consumption parameters based on Mica2 Motes. Here, we will focus on the conventional many-to-one traffic model commonly adopted in environmental monitoring WSN. A number of 200 nodes are randomly distributed in a 200m × 200m area. For comparison, results from a number of 400 nodes will be discussed as well. To simulate multi-hop transmissions with a large enough number of hop counts, we locate the sources in the left lower area of the region and uniformly distributed within a circle of radius 30m centered at (30m, 30m), while the sink is fixed at position (200m, 200m).

MAC setting

Following the default CSMA scheme in Mica2 Motes, to initiate a packet transmission, a sensor node will generate a random initial backoff time uniformly distributed in the range of [15, 68.3] ms and start a timer. Upon timer expiration, the channel is sensed. If it is found idle, a packet is transmitted. If the channel is busy, the sensor node will generate a further random time because of the congestion. The time is uniformly distributed in the range of [12.08, 193.3] ms. The backoff timer starts again. To improve delivery reliability, ARQ is employed here. If the total number of transmission count and MAC backoff count is great than 7, the packet is dropped.

Experimental link model

Here, we adopt the link model from an experiment based on Mica2 Motes. A sequence of sensor nodes are deployed linearly in spacing of 0.5 m from one another. The packet loss rate between pairs of nodes at different distance is measured. At any time, there is always one transmitter and the remaining nodes will count the number of packets successfully received. Each node is scheduled to transmit 80 packets at 10 packets/s in one around and finally the average reception rate is counted. Nodes are deployed on the ground of an open tennis court. The transmission power is set at 0 dBm. Fig. 5 shows the result of scatter diagram and how link quality varies with distance. The study in [START_REF] Woo | Taming the underlying challenges of reliable multihop routing in sensor networks[END_REF] has shown similar pattern.

By Fig. 5 and collected statistics, the link quality can be described as a piecewise function of distance d and modeled by a random variable r(d, µ, σ 2 ) in normal distribution with mean µ and variance σ 2 in the range of respective distance [START_REF] Li | Analyzing and Modeling of the Wireless Link for Sensor Networks[END_REF]. Table 1 shows the model parameters. For our simulation, a random number x is generated each time and then compared to r(d, µ, σ). If x < r(d, µ, σ 2 ), the packet is supposed successfully transmitted. Otherwise, it is considered lost and retransmission will be initiated. Therefore, a bad link will generally lead to a greater delay with more retransmissions.

Energy consumption model

Table 2 shows the energy model based on Mica2 Motes [START_REF] Shnayder | Simulating the power consumption of largescale sensor network applications[END_REF]. When the node is sending a packet, the CPU is in active state and the current consumption equals to 8.0 + 8.5 = 16.5 mA with a time duration of 0.5 ms. When receiving a packet, the CPU is in active state and the current consumption is 8.0 + 7.0 = 15.0 mA with a duration of 0.5 ms. When the node is just listening, the current consumption is only counted by the CPU's consumption, i.e. 8.0 mA. In sleeping mode, the CPU is in idle state and the current consumption is only 3.2 mA. Initial energy in each node is assumed the same. The voltage supply is by default 3V and constant.

Simulation and performance

In supporting real-time QoS, we are particularly interested in the packet delay performance and their deadline miss ratio. Note that the following definitions are all in end-to-end sense.

(i) Deadline miss ratio (DMR) is defined by the number of packets which miss their deadlines over the number of initiated packets.

(ii) Energy consumed per packet (ECP) is defined by the total energy consumed divided by the number of packets successfully transmitted.

(iii) Packet average and worst-case delays are defined by the mean of packet delay and the largest value experienced by the successfully transmitted packets.

First, we will show the effectiveness of energy-efficient probabilistic drop strategy employed in a comparison to the two other approaches previously mentioned: (i) all packets will be forwarded via nodes with largest velocity even when they cannot meet the required velocity, namely as best-effort forwarding, thus no packet will be dropped, and (ii) once there is no node that can provide the required velocity, the packet will be dropped immediately, namely as hard-decision drop.

The comparison of their DMRs under a same network topology with 200 nodes and 25 sources is given in Fig. 6. Best-effort forwarding has a slightly lower DMR when the deadline is relatively tight. However, when the deadline is increased and greater than 700 ms, the performance of best-effort forwarding is worse than that in the probabilistic drop because packet congestion occurs and the besteffort forwarding does not drop packets. Consequently, it suffers higher loss. Hard decision drop has a much higher DMR than the other two when the deadline is small since it is incapable of taking the benefit of statistical diversity gain during the multi-hop propagation, for example, in the best-effort forwarding.

As energy utilization efficiency is also one of the major concerns, we compare that in the three strategies. Fig. 7 shows their energy consumed per successfully transmitted packet. It is observed that Fig. 7 has quite similar characteristics and tendency as those shown in Fig. 6. The besteffort forwarding has a slightly lower energy consumption than the probabilistic drop scheme when the deadline is very tight. However, since deadline greater than 700 ms, probabilistic drop is generally much more energy-efficient via dropping packets with a consideration of the routing progress. On the other hand, hard decision may underestimate the capability of meeting the deadline later even when the packet has propagated to a location close to the destination and thus lead to a certain level of energy inefficiency. Despite the probabilistic drop scheme is not always the best among the three, by comparing their DMRs and energy consumption, it can reach an overall better performance and is more adoptable.

In the following, a detailed performance study of TH-SPEED is conducted and compared with SPEED. Fig. 8 shows the DMR of TH-SPEED in a WSN of 200 nodes, in which there are 10 source nodes. The result is plotted against different deadline requirements from 600 ms to 3000 ms. As expected, the DMR decreases as the deadline increases. It is observable that under TH-SPEED, when the deadline is large enough, the DMR converges to zero. In comparison, as shown in Fig. 8, SPEED has a much higher DMR generally. Besides, even when the deadline is up to 3000 ms, SPEED has only tended to a DMR level of 0.1. Comparatively, the DMR in TH-SPEED drops much faster than that in SPEED. The result has clearly indicated the effectiveness of TH-SPEED with the proposed 2-hop based routing strategy.

The energy efficiency of TH-SPEED is compared to SPEED in Fig. 9. As expected, the energy consumed per successfully transmitted packet decreases as the deadline increases since more packet can be finally forwarded to the destination due to a longer allowable time for the packet delivery. Compared to SPEED, TH-SPEED has consumed less energy. In other words, it has a higher energy efficiency. One of the major reasons is that TH-SPEED can achieve a lower DMR. It is observable that Fig. 9 has similar tendency and convergence characteristics as those in Fig. 8. Generally, TH-SPEED outperforms SPEED and can converge to a lower energy consumption level as deadline increases.

Fig. 10 shows the packet end-to-end average and worstcase delays respectively. It is observed that TH-SPEED and SPEED have quite close performance. Generally speaking, when there are several routing paths with delays which can satisfy the required velocity, TH-SPEED will have a better chance to go into a shorter path and have lower end-to-end delay due to the 2-hop routing optimal selection 5 . As shown in Fig. 8, it is able to successfully deliver more packets from end to end. However, note that they will include some packets from relatively bad network topology scenarios or large routing delay situations in which SPEED may have already dropped the packets. Therefore, it is possible that the worst-case or average delay in TH-SPEED may be higher than those in SPEED by the measurements. This phenomenon is observable in Fig. 10. However, more importantly, the worst-case delay is always bounded by the deadline requirement.

Furthermore, the number of nodes is increased from 200 to 400 in the same area and with same number of source nodes. While comparing TH-SPEED and SPEED in DMR, ECP and packet delay in 400 nodes, simulation results obtained show that the performance tendency and characteristics are very similar to those in Fig. 8, Fig. 9 and Fig. 10 respectively. Due to a lack of space, we will present elsewhere. However, it is worth noting that, in both network sizes, TH-SPEED outperforms SPEED in DMR and also energy utilization efficiency indicated by Fig. 8 and Fig. 9. Meanwhile, their packet average and worst-case delays have very similar performance.

Moreover, we investigate the performance of TH-SPEED under different workload. Fig. 11 shows the DMR as the number of sources is increased from 2 to 20, while the deadline requirement is fixed at 800 ms. In both SPEED and TH-SPEED, it is observed that the DMR increases as the number of sources increases and so is the energy consumption as indicated in Fig. 12 respectively. The increase in DMR is resulted by the increased channel busy probability, packet collisions at MAC and network congestion by the increased number of sources and consequent traffics. However, compared to SPEED, TH-SPEED has a lower DMR and energy consumption as shown in Fig. 11 and Fig. 12 respectively. This reflects the general improvement by TH-SPEED. The packet average and worst-case delay performance in both schemes is approximately at the same level. Plots are omitted due to the similarity.

Last, we study the performance of the residual energy cost function, which is an optional add-on for node energy consumption balance in case packet deadline requirement can be relaxed and a relatively large value is allowed. The motivation is that if there are several nodes who can serve as forwarding nodes and provide a velocity greater than the required velocity, instead of simply choosing the one that has the largest velocity, we can take into account the residual energy of nodes for a better balancing. Among those who can meet the velocity requirement, a node with higher residual energy will be favorable.

Fig. 13 shows the node distribution and their locations in this study. There are totally 200 nodes including 4 source nodes. The sources are located in the lower left area inside the circle, while the sink is fixed at the upper right point. The deadline is set to a large value of 3000 ms. Fig. 14 and Fig. 15 show the node energy consumption distribution in SPEED and TH-SPEED respectively after 200 runs. Nodes that have consumed much more energy than the other are highlighted in solid and dashed rectangles referring to SPEED and TH-SPEED respectively.

As observed in SPEED, some nodes along the path from sources to sink are frequently chosen as forwarders and consume much more energy than the other, while in TH-SPEED only nodes close to the sources and sink consume relatively high energy. The latter is natural and unavoidable especially as there may not be many good forwarding options near the sources and sink. Besides, by comparing Fig. 15 to Fig. 14, energy consumption in TH-SPEED is more evenly distributed among those between source and sink. It can be expected that TH-SPEED will have a longer system lifetime due to the balancing. However, the cost is the tradeoff in packet delay performance. As shown in Table 3, in this WSN, TH-SPEED will have a larger packet average delay by the residual energy consideration. However, even now, the DMR in TH-SPEED is still smaller than that in SPEED. That is, the DMR which is highly concerned in real-time service has not been sacrificed in the node energy consumption balancing.

Discussions

It is worth noting that, in the current design, the 2-hop link delay updating will generally lead to more overheads than that required for conventional 1-hop information updating. More feedback packets will be sent to the corresponding parent nodes. However, one can consider to reduce the overheads by piggybacking the updated information in ACK. These data will be sent together only when an ACK is to be sent. This can help to keep in a small number of feedback packets although the packet size will be larger. A drawback is that the 2-hop delay information may not be updated frequently enough. However, since the link delay estimation is based on the combination of history average value and the recent one, there could be minor difference to the estimation performance even if the update is not immediate and especially in WSN with low mobility. An investigation is expected in a future work.

In our simulation, the deadline requirement is assumed constant in all nodes. For different deadlines in different packet types, MM-SPEED [START_REF] Felemban | MMSPEED: Multipath multi-SPEED protocol for QoS guarantee of Reliability and timeliness in wireless sensor network[END_REF] has designed a prioritized MAC and multi-SPEED routing to provide service differentiation. In [START_REF] Akkaya | An energy-aware QoS routing protocol for wireless sensor networks[END_REF], RT and non-RT packets are separated with classifier and assigned different bandwidth according to different priorities. It is also possible to integrate cross-layer method with priority scheduling to our current design which does not include service differentiation with prioritized MAC mechanisms.

Conclusion

The idea of using multi-hop neighborhood information to make routing decision is investigated in this paper.

Through the asymptotic performance study of a routing decision obtained from different hops of neighborhood information a priori, we see a significant improvement potential from 1-hop to 2-hop based routing decision, which inspires us to design a 2-hop neighborhood information based real-time routing protocol for WSN. We adopt the approach of mapping packet deadline to a velocity as SPEED; however, the routing decision is made based on the 2-hop velocity. An energy efficient probabilistic drop is designed to improve energy utilization efficiency. When packet deadline requirement is not stringent, a design is integrated to release nodes from heavy consumption. Energy balance over nodes is thus improved. Simulation results show that, compared with existing protocol SPEED that only utilizes 1-hop information, TH-SPEED achieves lower end-to-end deadline miss ratio and higher energy efficiency. In future work, we are interested to see how to support differentiated QoS and keep the required information exchange in a minimum necessary amount. The results reported here may also lead to other interesting protocols and designs.

Figure 1 .

 1 Figure 1. A comparison of reachability with different depths of neighborhood information.

Figure 2 .

 2 Figure 2. A comparison of average number of hops required from source to sink in different depths of neighborhood information.

Figure 3 .

 3 Figure 3. A case study to show their difference: SPEED and TH-SPEED.

  -80m)/0.1s = 200 m/s, S B S = (100m -76m)/0.14s = 171.4 m/s, S C S = (100m -85m)/0.09s = 166.7 m/s.

  -60)/(0.14 + 0.06) m/s = 200 m/s which is greater than S set and is the largest one among all the pairs, as S A→E S = 137.5 m/s, S A→F S = 194.4 m/s, S B→H S = 184.2 m/s, and S C→I S

FFigure 4 .

 4 Figure 4. Two-hop delay update.

Figure 5 .

 5 Figure 5. Packet reception rates at difference distances.

Figure 7 .

 7 Figure 6. A comparison of packet deadline miss ratio among the three strategies.

Figure 8 .Figure 9 .

 89 Figure 8. DMR under different deadlines requirements. Number of nodes = 200. Number of source nodes = 10.

Figure 10 .

 10 Figure 10. End-to-end delay comparison.

Figure 11 .

 11 Figure 11. DMR under different number of source nodes. Number of nodes = 200.

Figure 12 .

 12 Figure 12. ECP in comparison.

Figure 13 .

 13 Figure 13. The topology of 200 nodes in the study of energy consumption distribution. Solid and dashed rectangles indicate SPEED and TH-SPEED respectively.

Figure 14 .Figure 15 .

 1415 Figure 14. Node energy consumption in SPEED. Number of nodes = 200.

Table 1 . Link quality model following Fig. 5

 1 Distance d (m) Mean µ Variance σ 2

	0-7	0.97	0.02
	7-14	0.70	0.14
	14-26	0.93	0.06
	26-30	0.53	0.08
	30-40	0.01	0.005

Table 2 . Mica2 Motes based energy model

 2

	Operation	Time (ms) I (mA)
	CPU active	N/A	8.0
	CPU idle	N/A	3.2
	Transmit (0 dBm) 0.5	8.5
	Receive	0.5	7.0

Table 3 . Performance of TH-SPEED after in- cluding residual energy consideration. The result is compared to SPEED.

 3

	Routing Protocol	SPEED TH-SPEED
	Deadline Miss Ratio	17%	0%
	Average Delay (ms)	603.92 963.15
	Energy Utility (mA×ms/packet) 2472.3 2486.8

Here, we simply assume the 2-hop information is available.

TH-SPEED finds a routing path that can meet the required velocity in terms of 2-hop knowledge.

This work was partially carried out during the tenure of an ERCIM "Alain Bensoussan" Fellowship Programme.