Extra back-off flow control in multi-hop wireless networks

Tandem queueing networks with neighbor blocking and back-offs

“…In fact, even deriving stability conditions and throughput values turns out to be a formidable task. For the case of N = 3 and k = 1, we obtained in [15] exact and approximative results for the stationary distribution and the throughput using the theory of quasi birth-death processes. However, this approach does not extend to larger networks.…”

“…The stationary distribution of X 3 (t) may then be numerically obtained using the matrix-analytic method, along with the exact values of θ 1 (η; {3}) and θ 2 (η; {3}) = θ 3 (η; {3}). Figure 1 shows the throughputs of nodes 1 and 2 calculated from the numerical solution to a quasi-birth-death process in [15]. For small back-off parameters, nodes 2 and 3 benefit, while larger back-offs eventually lead to lower throughputs for all three nodes.…”

“…For small back-off parameters, nodes 2 and 3 benefit, while larger back-offs eventually lead to lower throughputs for all three nodes. Although the throughput values converge to each other rapidly-in fact θ 1 (η) − θ 2 (η) = O(η −3 ), see [15]-they will never be exactly equal, and hence the tandem network will never be stable.…”

“…The next proposition, which is taken from [15], provides exact expressions for the critical value η * and the throughput θ(η), η ≥ η * , for a 3-node network with nearestneighbor blocking (k = 1). …”

“…This issue, known as the node-in-the-middle problem, can cause extreme unfairness and starvation effects, manifesting themselves in poor throughput and severe congestion. In order to remedy this issue and ensure a smoother flow of packets in multi-hop networks, various forms of flow control have been proposed; see [15] for an overview.…”