  In this paper, we consider the random access of nodes having energy
harvesting capability and a battery to store the harvested energy. Each node
attempts to transmit the head-of-line packet in the queue if its battery is
nonempty. The packet and energy arrivals into the queue and the battery are all
modeled as a discrete-time stochastic process. The main contribution of this
paper is the exact characterization of the stability region of the packet
queues given the energy harvesting rates when a pair of nodes are randomly
accessing a common channel having multipacket reception (MPR) capability. The
channel with MPR capability is a generalized form of the wireless channel
modeling which allows probabilistic receptions of the simultaneously
transmitted packets. The results obtained in this paper are fairly general as
the cases with unlimited energy for transmissions both with the collision
channel and the channel with MPR capability can be derived from ours as special
cases. Furthermore, we study the impact of the finiteness of the batteries on
the achievable stability region.
