Delay-Optimal Buffer-Aware Probabilistic Scheduling with Adaptive Transmission

Cross-layer scheduling is a promising way to improve Quality of Service (QoS) given a power constraint. In this paper, we investigate the system with random data arrival and adaptive transmission. Probabilistic scheduling strategies aware of the buffer state are applied to generalize conventional deterministic scheduling. Based on this, the average delay and power consumption are analysed by Markov reward process. The optimal delay-power tradeoff curve is the Pareto frontier of the feasible delay-power region. It is proved that the optimal delay-power tradeoff is piecewise-linear, whose vertices are obtained by deterministic strategies. Moreover, the corresponding strategies of the optimal tradeoff curve are threshold-based, hence can be obtained by a proposed effective algorithm. On the other hand, we formulate a linear programming to minimize the average delay given a fixed power constraint. By varying the power constraint, the optimal delay-power tradeoff curve can also be obtained. It is demonstrated that the algorithm result and the optimization result match each other, and are further validated by Monte-Carlo simulation.Comment: 6 pages, 4 figures, accepted by IEEE ICCC 201

How to compute the Hilbert depth of a graded ideal

We give two algorithms for computing the Hilbert depth of a \emph{graded ideal} in the polynomial ring. These algorithms work efficiently for (squarefree) lex ideals. As a consequence, we construct counterexamples to some conjectures made by Shen in \cite{B:Sh2}.Comment: In this new version, we have added some materials about comparing Algorithm 2.16 to Popescu's algorithm and Bruns et al's algorith