Load is a key magnitude for studying network performance for large-scale wireless sensor networks that are expected to support pervasive applications like personalized health-care, smart city and smart home, etc., in assistive environments (e.g., those supported by the Internet of Things). In these environments, nodes are usually spread at random, since deliberate positioning is not a practical approach. Due to this randomness it is necessary to use average values for almost all networks’ magnitudes, load being no exception. However, a consistent definition for the average load is not obvious, since both nodal load and position are random variables. Current literature circumvents randomness by computing the average value over nodes that happen to fall within small areas. This approach is insufficient, because the area’s average is still a random variable and also it does not permit us to deal with single points. This paper proposes a definition for the area’s average load, based on the statistical expected value
, whereas a point’s average load is seen as the load of an area that has been reduced (or contracted) to that point. These new definitions are applied in the case of traffic load in multi-hop networks. An interesting result shows that traffic load increases in steps
. The simplest form of this result is the constant step
, which results in an analytical expression for the traffic load case. A comparison with some real-world networks shows that most of them are accurately described by the constant step model.
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