It is well known that the generalized max-weight matching (GMWM) scheduling policy, and in general throughput-optimal scheduling policies, often require the solution of a complex optimization problem, making their implementation prohibitively difficult in practice. This has motivated many researchers to develop distributed sub-optimal algorithms that approximate the GMWM policy. One major assumption commonly shared in this context is that the time required to find an appropriate schedule vector is negligible compared to the length of a timeslot. This assumption may not be accurate as the time to find schedule vectors usually increases polynomially with the network size. On the other hand, we intuitively expect that for many sub-optimal algorithms, the schedule vector found becomes a better estimate of the one returned by the GMWM policy as more time is given to the algorithm. We thus, in this paper, consider the problem of scheduling from a new perspective through which we carefully incorporate channel variations and time-efficiency of sub-optimal algorithms into the scheduler design. Specifically, we propose a dynamic control policy (DCP) that works on top of a given sub-optimal algorithm, and dynamically but in a large time-scale adjusts the time given to the algorithm according to queue backlog and channel correlations. This policy does not require the knowledge of the structure of the given sub-optimal algorithm, and with low-overhead can be implemented in a distributed manner. Using a novel Lyapunov analysis, we characterize the stability region induced by DCP, and show that our characterization can be tight. We also show that the stability region of DCP is at least as large as the one for any other static policy. Finally, we provide two case studies to gain further intuition into the performance of DCP.
Throughput optimal scheduling policies in general require the solution of a complex and often NP-hard optimization problem. Related literature has shown that in the context of time-varying channels, randomized scheduling policies can be employed to reduce the complexity of the optimization problem but at the expense of a memory requirement that is exponential in the number of data flows. In this paper, we consider a linear-memory randomized scheduling policy (LM-RSP) that is based on a pick-and-compare principle in a time-varying network with N one-hop data flows. For general ergodic channel processes, we study the performance of LM-RSP in terms of its stability region and average delay. Specifically, we show that LM-RSP can stabilize a fraction of the capacity region. Our analysis characterizes this fraction as well as the average delay as a function of channel variations and the efficiency of LM-RSP in choosing an appropriate schedule vector. Applying these results to a class of Markovian channels, we provide explicit results on the stability region and delay performance of LM-RSP. A resource allocation model that has within its scope a number of computer and communication network architectures was introduced by Tassiulas and Ephremides (1992) and scheduling methods that achieve maximum throughput were proposed. Those methods require the solution of a complex optimization problem at each packet transmission time and as a result they are not amenable to direct implementations. We propose a class of maximum throughput scheduling policies for the model introduced by Tassiulas and Ephremides that have linear complexity and can lead to practical implementations. They rely on a randomized, iterative algorithm for the solution of the optimization problem arising in the scheduling, in combination with an incremental updating rule. The proposed policy is of maximum throughput under some fairly general conditions on the randomized algorithm.