  In this paper, we revisit the stability region of a cellular time division
duplex (TDD) network. We characterize the queuing stability region of a network
model that consists of two types of communications: (i) users communicating
with the base station and (ii) users communicating with each other by passing
through the base station. When a communication passes through the base station
(BS) then a packet cannot be delivered to the destination UE until it is first
received by the BS queue from the source UE. Due to the relaying functionality
at the BS level, a coupling is created between the queues of the source users
and the BS queues. In addition, contrarily to the majority of the existing
works where an ON/OFF model of transmission is considered, we assume a link
adaptation model (i.e. multiple rate model) where the bit rate of a link
depends on its radio conditions. The coupling between the queues as well as the
multiple rate model are the main challenges that highly increase the complexity
of the stability region characterization. In this paper, we propose a simple
approach that permits to overcome these challenges and to provide a full
characterization of the exact stability region as a convex polytope with a
finite number of vertices. An approximated model is proposed for reducing the
computational complexity of the exact stability region. For the multi-user
scenario, a trade-off is established between the complexity and the preciseness
of the approximated stability region compared to the exact one. Furthermore,
numerical results are presented to corroborate our claims.
