L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignemen[r]

The principle limitation of the current technique is that the number of semidefinite constraints it generates is pro- portional to the number of paths. This path dependent formulation may be too huge for large **networks**. Though the state of art semidefinite programming software is rel- atively advanced we need techniques to effectively handle this path dependency **in** the formulation. One such idea may be to evaluate heuristics to determine paths that are most likely of becoming the critical path. This could be then used to reduce the number of semidefinite constraints [1], [22]. Another promising technique could be one that uses cutting plane techniques to solve the semidefinite pro- gram with huge number of semidefinite constraints effec- tively [14]. It is necessary to evaluate and develop these techniques and then test them effectively on large projects with large number of paths.

En savoir plus
5 Evaluation of the flexibility of W ave
5.1 Simulation parameters
**In** this section, we conduct a comparative performance evaluation of W ave with a well-known centralized **scheduling** algorithm T MCP [7] and DeT AS [12] a distributed **scheduling** algorithm. This evaluation is qualitative for DeTAS and is quantitative for TMCP. For the quantitative evaluation, we use our simulation tool based on GNU Octave [19] to evaluate the number of slots required by these conflict-free **scheduling** algorithms. The number of nodes varies from 10 to 100. To generate routing graphs, we use the Galton-Watson process as a branching **stochastic** process: the maximum number of children per node is 3. We suppose that all the nodes except the sink have a single radio interface and we vary the number of sink radio interfaces from 1 to 3. The number of available channels varies from 2 to 3. We consider both cases: 1) homogeneous traffic demands, where each node different from the sink generates one packet and 2) heterogeneous traffic demands where the number of packets locally generated on a node is randomly chosen between 1 and 5. **In** the following, each result depicted **in** a curve is the average of 20 simulation runs for topologies with a number of nodes ≤ 30 and 100 runs for larger topologies.

En savoir plus
Wireless **networks** performances study motivates various research works. WMNs deployment **in** operational situations such as urban areas needs QoS guarantees because of capacity constraints. Indeed it has been prooved under some hypotesis that random network performances degrade with a factor at least O(1/ √ n) when its size, n, grows [5, 6, 7]. Some capacity evaluation frameworks have been developped to get a network behaviour estimation and a **stochastic** analysis confirmation [8, 9]. **In** WMNs, it is known that routers far from the gateways may be starved by routers close to the gateways. Therefore, we consider a max-min model to achieve high throughput but with a good fairness. **In** this work, we focus on the problem of providing fair throughput guarantees for multi-hop transmissions considering interferences among multiple simultaneous transmissions.

En savoir plus
This work is a first attempt towards utilizing a combination of controlled mobility and wireless transmission for data collection **in** **stochastic** and dynamic wireless **networks**. Therefore, there are many related open problems. **In** this paper we have utilized a simple wireless communication model based on a communication range. **In** the future we intend to study more advanced wireless communi- cation models such as modeling the transmission rate as a function of the transmission distance. For the case of multiple-collectors whose transmissions are subject to interference constraints, we intend to study interference models that do not restrict the collectors’ motion to a grid. Note that such a joint server routing and **scheduling** problem is significantly more involved. For instance, the stability region of such a system depends on the interference constraints, and it is unknown since there are uncountably many possible activation vectors.

En savoir plus
D-30167 Hannover, Germany
Abstract
**In** this paper, we propose a new **stochastic** approach for the automatic detection of network structures **in** raster data. We represent a network as a set of trees with acyclic planar graphs. We embed this model **in** the probabilistic frame- work of spatial point processes and determine the most probable configuration of trees by **stochastic** sampling. That is, different configurations are constructed randomly by modifying the graph parameters and by adding or removing nodes and edges to/ from the current trees. Each configuration is evaluated based on the probabilities for these changes and an energy function describing the con- formity with a predefined model. By using the Reversible jump Markov chain Monte Carlo sampler, an approximation of the global optimum of the energy function is iteratively reached. Although our main target application is the ex- traction of rivers and tidal channels **in** digital terrain models, experiments with other types of **networks** **in** images show the transferability to further applica- tions. Qualitative and quantitative evaluations demonstrate the competitiveness of our approach with respect to existing algorithms.

En savoir plus
Index Terms—Maximum weight **scheduling**, backlog/delay bounds, capacity region, order optimal delay
I. I NTRODUCTION
Wireless **scheduling** has been known to be a key problem for throughput/capacity optimization **in** wireless **networks**. The well-known maximum weight **scheduling** algorithm has been proposed by Tassiulas **in** his seminal paper [1] where he proved its throughput optimality. Latter developments **in** this area include extension of this maximum weight **scheduling** algorithm to wireless **networks** with rate/power control [2], [3], network control when offered trafﬁc is outside the ca- pacity region [4], and other **scheduling** policies with lower- complexity [5]-[8]. While most existing works **in** the area of **stochastic** network control focused on throughput perfor- mance of optimal and suboptimal **scheduling** policies, delay properties of most **scheduling** policies proposed for wireless ad hoc **networks** remain unknown. **In** this paper, we study backlog/delay properties of the maximum weight **scheduling** algorithm **in** wireless ad hoc **networks**.

En savoir plus
I. I NTRODUCTION
Weather-related outages **in** electricity distribution **networks** (DNs) continue to show an upward trend as utilities face the dual problems of deteriorating power grid infrastructure and higher frequency of natural disasters such as hurricanes [1], [2]. Prolonged delays **in** restoring the power supply for Puerto Rico **in** the aftermath of Hurricane Maria highlight the importance of strategic planning and efficient response to extreme events. This paper is motivated by the need for developing a modeling framework that (i) accounts for the likely locations of component failures for damage as- sessment; and (ii) enables the design of pre-storm resource allocation strategies as well as post-storm repair operations. To address these issues, we formulate a two-stage **stochastic** optimization problem based on an uncertainty model of storm-induced failures.

En savoir plus
Rule-based: These types of methods use more or less complex rule-based systems to solve the power system **scheduling** problem. These rules may be static (i.e.: predefined and fixed through time) or they may evolve **in** time whenever machine learning techniques are employed. **In** addition, these rules may be simple rule-of-thumb ones (e.g.: successively commit generators having the lowest average incremental cost until the requirements of the problem are met) or they may be composed of more or less complex inference systems. These systems try to mimic the actions of an expert [49] based on actual human expert inputs (**in** which case they are commonly called expert systems) or they may be created from historical data. **In** this last case, inference systems based on artificial neural **networks** are widely used **in** the literature [50]. These inference systems may be static or they may evolve **in** time “learning” from experience [51]. Finally, the rules incorporated by these rule-based systems may take the form of single values (i.e.: crisp values) or by fuzzy numbers. **In** the first case, the single values may define, for instance, thresholds to respect. It the second case it is more or less the same with the difference that these thresholds are no longer represented by crisp values, but by fuzzy numbers. These fuzzy numbers may model the uncertainty around a given numeric value (e.g.: the system load will be between 200 MW and 250 MW), or they may translate some qualitative measure (e.g.: the system load will be average). Consequently, when fuzzy numbers are used, the **scheduling** process has to incorporate fuzzy logic (provided by fuzzy set theory) for **scheduling** the power system [52].

En savoir plus
263 En savoir plus

d = 1 **in** Figure 3(b)).
The traffic is single-hop and the arrival process to each link of the network is assumed to be **stochastic**, with characteristics not necessarily known by the network designers. The goal is to schedule active links at each step **in** order to insure the stability of the system and, **in** particular, to activate links which are the most loaded. **In** the primary node interference model this corresponds to finding a maximum matching or a large matching. Centralized algorithms have been proposed to solve this problem both for random arrivals **in** [23, 24] and deterministic arrivals **in** [13]. As example, if the network is a square grid of 4 nodes (Figure 1) with the primary node interference model (d = 0), we can activate at one step either vertical links (Figure 1(a)) or horizontal links (Figure 1(b)). It is also possible to have a single active link **in** the network but we consider only the two previous sets of active links (maximal sets). A good **scheduling** algorithm has to insure the stability of the system (stability of the four queues associating to the four links **in** Figure 1). For example if the capacity of each link is 1 (if a link is active during a step, it sends 1 message), and if

En savoir plus
A nonconforming discretization of DFN allows to reduce the number of un- knowns and facilitate mesh refinement. Sharp angles are managed by a staircase- like discretizations of the fractures’ contours [34]. The non-matching feature at the fractures’ intersections is handled via a Mortar method [4, 5, 1] developed for DFN **in** [33, 34] for a mixed hybrid finite element formulation. It consists **in** defining, for each intersection between fractures, master and slave sides. Due to the staircase- like discretizations, a shared edge may be labeled several times with master and/or slave properties, it is called **in** the paper a multi-labeled edge. Continuity conditions are enforced between the unknowns on both sides. The derived linear system has only inner and master traces of hydraulic head as unknowns. The matrix A of this system is a symmetric definite positive (SPD) arrow matrix **in** presence of Dirichlet boundary conditions [34].

En savoir plus
Figure 2 Measurements of the dimensions at a station i of the net- work. The elliptic approximation appears **in** red.
Figure 3 Schematisation of the width-height ratio.
The data used for this paper consists **in** 49 different net- works, shared with us by various speleologists during two pre- vious studies ( Collon et al. , 2017 ; Jouves et al. , 2017 ) and presented **in** Appendix A. The extent of these **networks** can be quite different, the widest one, Sieben Hengste (Switzerland), extending itself over 80 kilometers with 15340 data points, while the smallest one, Baume Galinière (France), has less than 200 meters of conduits with 50 data points. Most of them are rather small, their median length being 2135 meters long, and are sampled with a median number of 269 points. The av- erage sampling distance is every 7.5 meters. It has to be noted that the sampling is not homogeneous and some network parts lack geometrical information. There is also a great uncertainty about the sampling itself.

En savoir plus
6 CONCLUSION
We formulated the pump **scheduling** problem **in** water dis- tribution network as a new generic non-compact linear program, based on the approximation of the head at the water tanks and on the relaxation of the pump aging con- straints. This approximation turned out to be both tight and easy to solve when experimented on two **networks** with different characteristics. We were then able to quickly find low cost feasible solutions by searching **in** a neighborhood of the approximated solutions. These results lead us to believe that this method could deal with **networks** larger than with the currently known approaches. Failing to dispose of such study cases, we envisage to build new realistic instances to confirm our claim. Perspectives to extend our method are, first, to exploit the new LP approximation **in** a global optimization approach, and, second, to exploit historical data of network operations to build the configuration set. REFERENCES

En savoir plus
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignemen[r]

We notice that the colors (time slots) used **in** the weighted min-max cliques around the gateways is enough to color all routes. The weighted min-max cliques around the gateway can be determined by a distribution of the total flow comming from the nodes over its links. The cliques are generated **in** a way to minimize the maximal one, consequently it will minimize the total number of colors needed (total routing time W ). The figure 6.a shows an example of a bad traffic distribution giving a worse result and the best configuration for grid **networks** with the gateway **in** the center. The best configuration shows that there is 4 nodes close to the gateway that have to go far from it and come back after through the central cliques. This routing minimizes the maximal cliques. The Grid result **in** figure 6.a has been proved **in** [6]. Another result can be seen **in** figure 6.b, we show a larger network and the maximum clique with weight equals the optimal value.

En savoir plus
These multi-hop **networks** are expected to carry high throughput. The ca- pacity of WMNs, that is, the throughput offered to each flow, is however affected by many factors such as network topology, traffic pattern, resource sharing and radio interferences [2, 3]. Several analytical studies on the capacity of wireless ad-hoc **networks** have all shown that the capacity decreases as the network size increases [4, 5]. Unlike ad-hoc **networks**, WMNs are stationary **networks** **in** which traffic is mainly router-to-gateway (respectively gateway-to-router) ori- ented. This special feature makes a bottleneck appear around the gateways, lead- ing to a more constrained available capacity per node [6]. Optimization-based approaches have been investigated trying to maximize the network capacity [7]. A key issue **in** wireless networking is to cope with the interferences produced by concurrent transmissions. If many concurrent transmissions are successful, they have to be pairwise non interfering. Consequently, MAC protocols achieving conflict-free link **scheduling** have been developed to avoid interferences [2, 8]. The evolution of a network can thus be seen as the sequential activation of conflict- free sets of links, called rounds **in** the following.

En savoir plus
I. I NTRODUCTION
**In** wireless **networks**, the communication channels are shared among the terminals. Thus, one of the major problems faced is the reduction of capacity due to interferences caused by simultaneous transmissions [1]. **In** this work, we call a round a collection of links that can be simultaneously activated **in** the network. We address the problem called Round Weight- ing Problem (RWP) [2] that consider joint routing and schedul- ing. We present a cross-layer formulation of the problem. We have to find a minimum-length schedule of selected links **in** a TDMA (Time Division Multiple Access) based wireless network. As we deal with multi-hop **networks**, these selected links represent a routing solution (paths) providing enough capacity to achieve the routers requirements of bandwidth. **Scheduling** methods such TDMA can guarantee achieving higher capacities by allowing time slots to be shared by simultaneous transmissions.

En savoir plus
The Shu ffledJoinRDD implementation is very similar to ShuffledRDD. Instead of fetch- ing map output partitions from just one dependency, it fetches the corresponding map out- put partitions from both dependencies. The user specificies the number of Shu ffledJoin- RDD partitions and each paritition requests a corresponding fraction of the map output partitions. For instance, Shu ffledJoinRDD partition 1 will fetch Dataset1 Partition 1 and Dataset2 Partition 1 from all of the workers. Once these partitions are fetched, it creates a map with the key-value pairs of the smaller partition. Subsequently, it iterates through the keys of the bigger partition, seeing if they are present **in** this map, and if so, adding the intersection to the output.

En savoir plus
Abstract: We consider a multi-hop wireless mesh network composed by routers which route traffic to the Internet through several gateway. **In** such network, a bottleneck phenomenon limits the performances around the gateways, the net- work capacity does not scale with its size. **In** this work, we propose a traffic **scheduling** strategy around the gateways **in** a 802.11-based wireless mesh net- work. We distinguish two kinds of nodes according to their location **in** the network and the medium sharing strategy used: those located within k-hop of the gateway run a TDMA medium access protocol while the nodes further run a CSMA/CA MAC layer. We investigate on the impact of the size of the TDMA area on the network capacity when an optimal **scheduling** is im- plemented. Through extensive simulations, it is shown that network capacity, fairness and packet loss rate are improved by our approach.

En savoir plus