On the Catalyzing Effect of Randomness on the Per-Flow Throughput in Wireless Networks

This paper investigates the throughput capacity of a flow crossing a multi-hop wireless network, whose geometry is characterized by general randomness laws including Uniform, Poisson, Heavy-Tailed distributions for both the nodes' densities and the number of hops. The key contribution is to demonstrate \textit{how} the \textit{per-flow throughput} depends on the distribution of 1) the number of nodes $N_j$ inside hops' interference sets, 2) the number of hops $K$, and 3) the degree of spatial correlations. The randomness in both $N_j$'s and $K$ is advantageous, i.e., it can yield larger scalings (as large as $\Theta(n)$) than in non-random settings. An interesting consequence is that the per-flow capacity can exhibit the opposite behavior to the network capacity, which was shown to suffer from a logarithmic decrease in the presence of randomness. In turn, spatial correlations along the end-to-end path are detrimental by a logarithmic term

Towards a System Theoretic Approach to Wireless Network Capacity in Finite Time and Space

In asymptotic regimes, both in time and space (network size), the derivation of network capacity results is grossly simplified by brushing aside queueing behavior in non-Jackson networks. This simplifying double-limit model, however, lends itself to conservative numerical results in finite regimes. To properly account for queueing behavior beyond a simple calculus based on average rates, we advocate a system theoretic methodology for the capacity problem in finite time and space regimes. This methodology also accounts for spatial correlations arising in networks with CSMA/CA scheduling and it delivers rigorous closed-form capacity results in terms of probability distributions. Unlike numerous existing asymptotic results, subject to anecdotal practical concerns, our transient one can be used in practical settings: for example, to compute the time scales at which multi-hop routing is more advantageous than single-hop routing

An Analytical Model for Wireless Mesh Networks with Collision-Free TDMA and Finite Queues

Wireless mesh networks are a promising technology for connecting sensors and actuators with high flexibility and low investment costs. In industrial applications, however, reliability is essential. Therefore, two time-slotted medium access methods, DSME and TSCH, were added to the IEEE 802.15.4 standard. They allow collision-free communication in multi-hop networks and provide channel hopping for mitigating external interferences. The slot schedule used in these networks is of high importance for the network performance. This paper supports the development of efficient schedules by providing an analytical model for the assessment of such schedules, focused on TSCH. A Markov chain model for the finite queue on every node is introduced that takes the slot distribution into account. The models of all nodes are interconnected to calculate network metrics such as packet delivery ratio, end-to-end delay and throughput. An evaluation compares the model with a simulation of the Orchestra schedule. The model is applied to Orchestra as well as to two simple distributed scheduling algorithms to demonstrate the importance of traffic-awareness for achieving high throughput.Comment: 17 pages, 14 figure

Capacity and interference modeling of CSMA/CA networks using SSI point processes

International audienceThe relative location of simultaneous transmitters, i.e. the set of nodes transmitting a frame at a given time, has a crucial impact on the performance of multi hop wireless networks. Two fundamental aspects of wireless network performances are related to these locations: capacity and interference. Indeed, as interference results from the summation of signals stemmed by concurrent transmitters, it directly depends on the transmitters' location. On the other hand, the network capacity is proportional to the number of simultaneous transmitters. In this paper, we investigate original point processes that can be used to model the location of transmitters that comply with the CSMA/CA policies, i.e. the Medium Access Control protocol used in 802.15.4 and 802.11 families of wireless technologies. We first propose the use of the Simple Sequential Inhibition point process to model CSMA/CA networks where clear channel assessment depends on the strongest emitter only. We then extend this point process to model a busy medium detection based on the strength of all concurrent signals. We finally compare the network capacity obtained through realistic simulations to a theoretical capacity estimated using the intensity of the SSI point process. It turns out that the proposed model is validated by the simulations