This paper studies a wireless network consisting of multiple transmitter-receiver pairs where interference is treated as noise. Previously, the throughput region of such networks was characterized for either one time slot or an infinite time horizon. We aim to fill the gap by investigating the throughput region for transmissions over a finite time horizon. Unlike the infinite-horizon throughput region, which is simply the convex hull of the throughput region of one time slot, the finite-horizon throughput region is generally non-convex. Instead of directly characterizing all achievable rate-tuples in the finite-horizon throughput region, we propose a metric termed the rate margin, which not only determines whether any given rate-tuple is within the throughput region (i.e., achievable or unachievable), but also tells the amount of scaling that can be done to the given achievable (unachievable) rate-tuple such that the resulting rate-tuple is still within (brought back into) the throughput region. Furthermore, we derive an efficient algorithm to find the rate-achieving policy for any given rate-tuple in the finite-horizon throughput region.
@cite_24: It is well known that max-weight policies based on a queue backlog index can be used to stabilize stochastic networks, and that similar stability results hold if a delay index is used. Using Lyapunov optimization, we extend this analysis to design a utility maximizing algorithm that uses explicit delay information from the head-of-line packet at each user. The resulting policy is shown to ensure deterministic worst-case delay guarantees and to yield a throughput utility that differs from the optimally fair value by an amount that is inversely proportional to the delay guarantee. Our results hold for a general class of 1-hop networks, including packet switches and multiuser wireless systems with time-varying reliability .
@cite_4: We first consider a multi-user, single-hop wireless network with arbitrarily varying (and possibly non-ergodic) arrivals and channels. We design an opportunistic scheduling algorithm that guarantees all sessions have a bounded worst case delay. The algorithm has no knowledge of the future, but yields throughput-utility that is close to (or better than) that of a T-slot lookahead policy that makes “ideal” decisions based on perfect knowledge up to T slots into the future. We then extend the algorithm to treat worst case delay guarantees in multi-hop networks. Our analysis uses a sample-path version of Lyapunov optimization together with a novel virtual queue structure.
We stress that in light of the studies on infinite-horizon throughput region, a small number of studies have introduced the concept of finite-horizon throughput region. However, they did not analyze any property of the finite-horizon throughput region: The work in @cite_4 proposed a @math -slot lookahead utility which helped to analyze the short-term performance for the proposed opportunistic scheduling algorithm, but no analysis on finite-horizon throughput region was presented; @cite_24 , the rate-tuple over a finite time horizon was defined, but it was only employed to derive the infinite-horizon throughput region when the number of time slots goes to infinity. A possible reason for the lack of study on the finite-horizon throughput region might be that the finite-horizon throughput region was thought to have similar properties as its infinite-horizon counterpart. As we will discuss in this work, however, the finite-horizon throughput region behaves very differently as compared with the infinite-horizon throughput region.