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This letter presents sufficient conditions for the existence and uniqueness of the limiting stationary distribution in random access Poisson networks with packet queueing and under Rayleigh fading and a general path loss model. This system model is traditionally used in the literature assuming uniqueness of the stationary distribution. We demonstrate here through a counterexample that this assumption might not always hold. From the sufficient conditions, an interesting and perhaps counterintuitive result emerged, that is, the arrival rate of packets per node greater than 1/e guarantees uniqueness of the limiting distribution. When that is the case, then setting the medium access probability to 1 minimizes the proportion of unstable nodes.

This paper investigates the performance of a wireless network that consists of two pairs of transmitter-receiver sharing the same channel, modeled using two coupled queues. In this analysis, we use the power metric $\mathscr {P}$ , defined as the ratio of throughput and mean delay, to understand the compromise between these two metrics. We show that, when the users’ transmit power levels are adjusted to maximize $\mathscr {P}$ , two transmission regimes emerge. When the coupling degree between the queues is strong, but the traffic is not heavy, there will be plenty of opportunities for non-concurrent transmissions. Our analysis shows that, in this case, the best strategy is to prioritize one user over the other through appropriate transmit powers adjustment and to use the highest modulation order available. On the other hand, for heavy traffic, none of the users should be prioritized, and there is an optimum combination of robust modulation orders and transmit power ratio to achieve the best performance.

A simple analytical solution is proposed for the stationary loss system of two parallel queues with finite capacity K, in which new customers join the shortest queue, or one of the two with equal probability if their lengths are equal. The arrival process is Poisson, service times at each queue have exponential distributions with the same parameter, and both queues have equal capacity. Using standard generating function arguments, a simple expression for the blocking probability is derived, which as far as we know is original. Using coupling arguments and explicit formulas, comparisons with related loss systems are then provided. Bounds are similarly obtained for the average total number of customers, with the stationary distribution explicitly determined on $$\{K, \ldots , 2K \}$$ , and elsewhere upper bounded. Furthermore, from the balance equations, all stationary probabilities are obtained as explicit combinations of their values at states (0, k) for $$0 \le k \le K$$ . These expressions extend to the infinite capacity and asymmetric cases, i.e., when the queues have different service rates. For the initial symmetric finite capacity model, the stationary probabilities of states (0, k) can be obtained recursively from the blocking probability. In the other cases, they are implicitly determined through a functional equation that characterizes their generating function. The whole approach shows that the stationary distribution of the infinite capacity symmetric process is the limit of the corresponding finite capacity distributions. Finally, application of the results for limited capacity to mean-field models for large bike-sharing networks with a local JSQ policy is briefly discussed.