Energy efficient low complexity joint scheduling and routing for wireless networks

Distributed Control and Quality-of-Service in Multihop Wireless Networks

“…By the Arzela-Ascoli theorem [25], we can see that for any sequence S f ij (n, t) with n → ∞, there exists a subsequence n k → ∞ along which S f ij (n k , t) → s f ij (t), as n k → ∞ wp 1, u.o.c. This implies the second part of (11). The resultant s f ij is Lipschitz, being the result of uniform convergence of a sequence of Lipschitz functions.…”

“…Techniques based on Markov Decision processes (MDPs) are also popular [10]. In [11], [12], the problem of minimizing power while providing mean and hard delay guarantees is studied. However the algorithm requires knowledge of system statistics and is not throughput optimal.…”

A distributed algorithm for Quality-of-Service provisioning in multihop networks

“…However, this additional assumption may not always hold. In [13], the authors Another traditional approach is to use Markov Decision Processes [10]. In multihop scenarios, however, such an approach is generally not tractable owing to the huge dimension of the state space.…”