Flavio Fabbri

A sociability-based routing scheme for delay-tolerant networks

The problem of choosing the best forwarders in Delay-Tolerant Networks (DTNs) is crucial for minimizing the delay in packet delivery and for keeping the amount of generated traffic under control. In this paper, we introduce sociable routing, a novel routing strategy that selects a subset of optimal forwarders among all the nodes and relies on them for an efficient delivery. The key idea is that of assigning to each network node a time-varying scalar parameter which captures its social behavior in terms of frequency and types of encounters. This sociability concept is widely discussed and mathematically formalized. Simulation results of a DTN of vehicles in urban environment, driven by real mobility traces, and employing sociable routing, is presented. Encouraging results show that sociable routing, compared to other known protocols, achieves a good compromise in terms of delay performance and amount of generated traffic.

A statistical model for the connectivity of nodes in a multi-sink wireless sensor network over a bounded region

In this paper we present a novel mathematical approach to evaluate the degree of connectivity of a multi-sink wireless sensor network. We consider both unbounded and bounded domains, specifically squares and rectangles, and the impact of border effects is also shown. Our channel model takes random fluctuations into account, as well as a distance-dependent deterministic path-loss. In particular, we deal with randomly shaped wireless footprints, rather than with the less realistic (yet widely adopted) disk model, which is a special case of our channel model. Our performance metric is based on the probability that a randomly chosen sensor is not isolated, from which the probability that a certain amount of nodes are connected can be easily derived.

On the Estimation of Randomly Sampled 2D Spatial Fields under Bandwidth Constraints

In this paper, we address the problem of the estimation of a spatial field defined over a two-dimensional space with wireless sensor networks. We assume that the field is (spatially) bandlimited and that it is sampled by a set of sensors which are randomly deployed in a given geographical area. Further, we impose a total bandwidth constraint which forces the quantization error in the sensor-to-FC (Fusion Center) channels to depend on the actual number of sensors in the network. With these assumptions, we derive an analytical expression of the mean-square error (MSE) in the reconstructed random field and, on that basis, an approximate closed-form expression of the optimal sensor density which attains the best trade-off in terms of observation, sampling and quantization noises. The analysis is carried out both in Gaussian and Rayleigh-fading scenarios without transmit Channel State Information (CSI). For the latter scenario, we also derive an expression of the common and constant rate at which the observations must be quantized. Computer simulation results illustrate the dependency of the optimal operating point on the variance of the observation noise or the signal-to-noise ratio in the sensor-to-FC channels, as well as the scaling law of the reconstruction MSE (which is also derived analytically) for both scenarios.

A Multi-Sink Multi-Hop Wireless Sensor Network Over a Square Region: Connectivity and Energy Consumption Issues

In this paper we present a novel mathematical approach to evaluate the degree of connectivity of a multi- sink wireless sensor network, where sink and sensor nodes are uniformly distributed over a given region. We consider both unbounded and bounded domains, specifically squares, and the impact of border effects is also shown. Random fluctuations as well as a distance-dependent deterministic path-loss are accounted for in our radio channel model. In particular, we deal with randomly shaped wireless footprints, rather than with the less realistic (yet widely adopted) disk model, which is a special case of our channel model. Nodes are organized in a tree-based topology with trees rooted at the sinks (multi-hop communications). The approach allows the computation of the probability that a randomly chosen sensor is not isolated, from which the probability that a certain amount of nodes are connected can be easily derived. The mean energy spent by the network is also accounted for. The model provides guidelines to optimally design the tree-based topology, taking into account connectivity and energy consumption issues.

Maximizing area throughput in clustered wireless sensor networks

In this paper we present a mathematical model to study a multi-sink Wireless Sensor Network (WSN). Both sensors and sinks are assumed to be Poisson distributed in a given finite domain. Sinks send periodic queries, and each sensor transmits its sample to a sink, selected among those that are audible, thus creating a clustered network. Our aim is to describe how the Area Throughput, defined as the amount of samples per unit of time successfully transmitted to the sinks from the given area, depends on the density of sensors and the query interval. We jointly account for radio channel, Physical (PHY), Medium Access Control (MAC) and Network (NET) aspects (i.e., different network topologies, packet collisions, power losses and radio channel behaviour), and we compare the performance of two different simple data aggregation strategies. Performance is evaluated by varying the traffic offered to the network (i.e., the density of sensors deployed), the packet size, and, by considering IEEE 802.15.4 as a reference case, the number of Guaranteed Time Slots allocated, and the Superframe Order. The mathematical model shows how the Area Throughput can be optimized.

Analytical study of the outage probability of ALOHA and CSMA in bounded ad hoc networks

The performance of the ALOHA and CSMA protocols is evaluated within a bounded ad hoc network. Our network model comprises packets being distributed in finite space and time according to a 3-D PPP. Upon the formation of each packet, it is transmitted to its intended destination located a fixed distance away, using a fully-distributed MAC protocol. If the SINR of the received packet falls below a certain threshold any time during its transmission, the packet is received in outage. The evaluation metric of our network is outage probability, which is directly related to throughput. Approximate analytical expressions are derived for the outage probability of the different MAC protocols as a function of the spatial density of transmissions and the physical size of the network, and validated by simulations. Our bounded network is shown to yield a lower outage probability than infinite domains, due to the lower level of interference resulted from edge effects. Furthermore, the performance of the different MAC protocols are compared, and CSMA with receiver sensing [1] is shown to yield the lowest outage probability of all the unslotted protocols.

Comments on "Probability Distributions for the Number of Radio Transceivers which can Communicate with One Another"

We discuss the correctness of one of the main results of about the probability density function of the distance between two audible nodes in an infinite 2-dimensional scenario. We prove that result is wrong and derive a more general expression, which is valid for an infinite d-dimensional area. It is worth noting that, although the results on the distribution of the distance between two nodes are wrong, the other results and in particular the fact that the number of audible nodes in an arbitrary area is a Poisson r.v. is correct.

Area Throughput for CSMA based Wireless Sensor Networks

In this paper we present a mathematical approach to evaluate the area throughput of a multi-sink wireless sensor network (WSN), where nodes transmit their packets to a sink, selected among many. Sensors and sinks are both Poisson distributed in a bounded domain. A carrier sensing multiple access (CSMA) based protocol is used by nodes to access the channel. We denote as area throughput the amount of samples per second successfully transmitted to the sinks. This performance metric is strictly related to both connectivity and MAC issues: it depends, in fact, on the probability that a given sensor node is not isolated and that it succeeds in transmitting its packet (i.e., the packet does not collide). The aim of this work is to devise a mathematical model that takes CSMA and connectivity issues into account under a joint approach. Through this model some network optimisation strategies could be derived. As an example, sensors could perform an aggregation procedure, responding sporadically to queries with a single packet composed of all samples taken since the previous transmission. Our model allows the evaluation of the optimum size of the packet that should be transmitted, so that the area throughput is maximised. Finally, the effects of the connectivity on the area throughput are evaluated.

The Impact of Correlated Channel Fluctuations on the Connectivity of Wireless Ad-Hoc Networks

Channel fluctuations affecting links of ad-hoc and sensor networks show an evident spatial correlation, besides the random behavior. Nonetheless, the vast majority of models used in the literature assign edges between pairs of vertices of a graph according to either the deterministic disk model or some random connection model assuming i.i.d. fluctuations. We believe none of the approaches reflects the reality. In this paper we introduce a Correlated Random Connection Model (CRCM) which accounts for angular correlation, by means of a tunable parameter, in the fluctuations that affect two links sharing one of the endpoints. Assuming a constant average number of neighbors, we study the percolating properties of correlated footprints on random graphs by computing the relative size of the two largest components of the graph and the probability of the event of (almost) connectivity. We also compare it to the case of some non- probabilistic shapes of both theoretical and practical flavor. Our results show that the presence of correlation may be beneficial or detrimental, depending of whether one considers undirected or directed graphs, i.e., ultimately, on the application. Index Terms—Channel fluctuations, wireless networks, connectivity.

On the optimal blacklisting threshold for link selection in wireless sensor networks

Empirical studies on link blacklisting show that the delivery rate is sensitive to the calibration of the blacklisting threshold. If the calibration is too restrictive (the threshold is too high), all neighbors get blacklisted. On the other hand, if the calibration is too loose (the threshold is too low), unreliable links get selected. This paper investigates blacklisting analytically. We derive a model that accounts for the joint effect of the wireless channel (signal strength variance and coherence time) and the network (node density). The model, validated empirically with mote-class hardware, shows that blacklisting does not help if the wireless channel is stable or if the network is relatively sparse. In fact, blacklisting is most beneficial when the network is relatively dense and the channel is unstable with long coherence times.