text: In this work, we investigate the stability region, the throughput performance, and the queueing delay of an asymmetric relay-assisted cooperative random access wireless network with multipacket reception (MPR) capabilities. We consider a network of @math saturated source users that transmit packets to a common destination node with the cooperation of two relay nodes. The relays are equipped with infinite capacity buffers, and assist the users by forwarding the packets that failed to reach the destination. Moreover, the relays have also packets of their own to transmit to the destination. We assume random access of the medium and slotted time. With the relay-assisted cooperation, the packets originated by each user can be transmitted to the destination through multiple relaying paths formed by the relays. We assume that the relays employ an adaptive retransmission control mechanism. In particular, a relay node is aware of the status of the other relay, and accordingly adapts its transmission probability. Such a protocol is towards self-aware networks and leads to substantial performance gains in terms of delay. We investigate the stability region and the throughput performance for the full MPR model. Moreover, for the two-user, two-relay case we derive the generating function of the stationary joint queue-length distribution at the relays by solving a Riemann-Hilbert boundary value problem. Finally, for the symmetric case we obtain explicit expressions for the average queueing delay in a relay node without the need of solving a boundary value problem. Numerical examples are presented providing insights on the system performance.
  @cite_24: We revisit the stability problem of systems consisting of N buffered terminals accessing a common receiver over the collision channel by means of the standard ALOHA protocol. We find that in the slotted ALOHA system queues have "instability rank" based on their individual average arrival rates and transmission probabilities. If a queue is stable, then the queue with lower instability rank is stable as well. The instability rank is used to intelligently set up the dominant systems. And the stability inner and outer bounds can be found by bounding the idle probability of some queues in the dominant system. Through analyzing those dominant systems one by one, we are able to obtain inner and outer bounds for stability. These bounds are tighter than the known ones although they still fail to identify the exact stability region for cases of N>2. The methodology used is new and holds promise for successfully addressing other similar stability problems.
  @cite_26: The standard discrete-time slotted ALOHA system with a finite number of buffered terminals is considered. The stability (ergodicity) region for this system is known only for the case of two terminals and for the case of any number of symmetric terminals. The stability of the system is studied by means of a simple concept of dominance. It is shown that the stability region for the case of two terminals can be obtained in a simple way. Lower (inner) bounds are obtained for the stability region of the system with an arbitrary finite number of terminals that are tighter than the ones already known. A similarity between these stability results and the achievable region of the no-feedback collision channel is pointed out that suggests a connection between the two problems. >
  @cite_2: A fundamental question arising in the analysis of queueing systems is whether a system is stable or unstable. For systems modeled by infinite Markov chains, we may study the ergodicity and nonergodicity of the chains. Foster showed that sufficient conditions for ergodicity are linked with the average drift. However, complications arise when multidimensional Markov chains are analyzed. We present three methods that provide sufficient conditions for ergodicity and nonergodicity of a multidimensional Markov chain. These methods are next applied to two multidimensional queueing systems: buffered contention packet broadcast systems and coupled processor systems.
summary: The characterization of the stable throughput region, i.e. the stability region, which gives the set of arrival rates such that there exist transmission probabilities under which the system is stable, is a meaningful metric to measure the impact of bursty traffic and the concept of interacting nodes in a network; e.g., @cite_24 @cite_26 @cite_2 .