Discussions on Event-Driven Traffic Patterns for Wireless

The motivation behind this section comes from the fact that many sen-sor networks are event-driven and have spatially-correlated transmissions.

Indeed, most sensor networks can be grouped in subsets since they are de-ployed in the same geographical area. This is done to increase reliability and fault-tolerance.

Consider a wireless sensor network formed bynnodes and one collector over an area of Θ(n). This could be easily extended to the case of say h(n) collectors. Indeed, for simplicity we make some assumptions for the particular scenario of interest, but this analysis could be extended to other scenarios. Among these assumptions is the fact that we consider that nodes have an infinite buffer and events happen continuously. No burstiness or periodicity of events is considered for the moment, this leads to a continuous sensing and transmission of nodes. The creation of packets occurs at a regular and deterministic rate. The analysis of the impact of buffer size, queueing delays and times of arrival of events are beyond the scope of this section, but note that this is a direction one should consider for completeness.

We assume that not all the nodes that sense an event need to report it. By using the cell partitioning of Section 2.4, only one node in the vicinity of an event in a cellc^∗ (e.g. an event that happens in a cellc^∗) is elected to report this event. One can imagine a transmission policy in which nodes cooperate by exchanging informations about a given event and decide which node is to report it. This is motivated by the fact that all the observations made by the nodes inc^∗ are highly correlated, and in order to decrease traffic and concurrent transmissions only one session from a source node (in the vicinity of a given event) to the collector is allowed. It is then convenient to assume that all the events are distributed uniformly on the area of the network or by a homogeneous Poisson point process, such that for any regionR of area A(R), the number of events in the region has a Poisson distribution with parameterσA(R), i.e.,

Pr[k inR] = e^−σA(R)(σA(R))^k

k! (2.17)

The main parameter is the the event density given by, σ(n) = #of events

area

2.5. Throughput Capacity Expressions 41 The number of events is closely linked to the geographical area Θ(n). Thus, the large network model (fixed density of nodes) is suitable for the state of this application. If we increase the network area, the events to be reported will increase. An example application could be intelligent transportation sys-tems [43], where vehicles detects dangerous situations in traffic. The number of events in this example clearly increases with the area covered by the roads.

Moreover, for some applications, we may resort to a non-homogeneous Pois-son point process where the density depends on the geographical location, mainly when the event intensity is higher in some regions. This will make the analysis more complex since the traffic and relay load will depend on the geographical region. To simplify the analysis, one can study the worst-case scenario, in which the throughput is determined by considering that all traffic loads are equal to the load generated by the region with the highest density. In the following, the only key parameter that matters is the event density. It will allow the computations of the number of source collector S-C pairs, and the relay traffic and load produced by reporting these events.

Finally, we assume that all the events are detected correctly by the nodes.

For future directions, one could think of extending this model in order to take into account the probability of correct detection of an event.

Again in order to derive the throughput capacity of an event-driven model for wireless sensor networks, we use the deterministic scheme de-scribed above and the technical Lemmas derived in Section 2.4. We keep the same cell partition as described in Section 2.4. The connectivity condi-tion on the cell size is kept the same as above. Remember, the cell size was determined by the condition that no cell is empty asngets large. We do not change the transmission policy (each node in a cell can transmit to a node in the same cell or in the neighboring cells), and we assume that the traffic overhead between nodes in a given cell induced by the election of a source of event reports is negligible compared to the traffic source collector. One can suppose that a sub-channel is dedicated for intra-cell communications in order to avoid interference. With this model, one can show that the number of source-collector pairs is of the order of the number of events occurring in a network of area Θ(n), i.e. O(nσ(n)). The throughput is determined by the relay load, and we need to compute the number of routes going through each cell. Since the collector is placed in the center of the network area, the source collector mean path distance is of the order Θ(√

n). Using the results

of Lemma 2.3, the number of routes passing through a cell is:

Θ

(#cells traversed by a route) (#S-C pairs)

#total of cells

= Θ σ(n)p

nlogn Thus, the event reporting throughputλ(n) achieved by the model and under the deterministic scheme and routing strategy described above is:

λ(n) = Ω This result is quite encouraging as an initial derivation. It means that for an event density of the order ofO

√1 is achievable. This is quite realistic, it means that the number of events needed to be reported is of the order of O(√

n), where n is the number of nodes in a network of area Θ(n). Similarly, for an event density of the order ofO

√ 1 nlogn

, a per-event throughput of Ω(1) is achievable. The result in Eq.(2.18) could also be written in a large network of area Θ(n) as:

λ(n) = Ω The increase of throughput is due to the reduction of traffic load in the network since we haveO(√

n) communications instead ofO(n). This result could even be improved, if we introduce some randomness in the arrival of events, in order to model the rarity of events and the fact that the nodes do not have to transmit all the time.