  In this paper, we present two randomized distributed algorithms in wireless
ad hoc networks. We consider that the network is structured into pairs of nodes
(sender, receiver) in a decay space. We take into account the following: Each
node has its own power assignment and the distance between them does not follow
the symmetry property. Then, we consider a non-uniform network or a realistic
wireless network, which is beyond the geometry. Our model is based on the
Signal to Interference plus Noise Ratio (SINR) model. In this work, the main
problem is to solve the scheduling task aiming the successful transmission of
messages in a realistic environment. Therefore, we propose the first randomized
scheduling and power selection algorithm in a decay space and is called as
SPAIDS. In order to solve the problem in this non-uniform network, we introduce
a new way to study the affectance (the interference) among the links, which is
defined as Weighted Average Affectance (WAFF). Moreover, we study the online
broadcast problem in a metric space, in which the nodes are activated in case
that they receive packets. We propose an online algorithm in a metric space
which is denoted as OAMS. Our aim is to obtain the maximum subset of nodes that
receive the message from a sender node with enough energy supplies. Finally, we
compare the performance of OAMS to the optimal.
