Delay-oriented analysis and design of optimal scheduling algorithms

The main focus of this research is in the area of optimal cross-layer scheduling in wireless networks. In the literature, back-pressure-based scheduling algorithms (e.g., maximal weight matching algorithm [100]) have been developed typically focusing on the throughput/utility optimality, while little emphasis is given to delay constraints or queuing delay analysis. However, in practical implementations, delay is an important metric for wireless multimedia applications such as Video-on-Demand (VoD), Voice-over-IP (VoIP), IPTV, etc. In this research, delay-oriented scheduling with optimal throughput/utility is studied. An important delay-related factor is finite buffer property. By Little’s Law, finite buffer sizes lead to upper-bounded end-to-end delay on a per-flow basis. In addition, the finite buffer property is also an important factor for Quality of Service (QoS) sensitive wireless network applications. Algorithms with finite buffer property can find their application in resource-limited wireless networks such as wireless sensor networks. In this research, to improve delay performance and ensure finite buffer sizes, a novel virtual queue is first proposed that acts as a weight on the actual queue when scheduling link rates. Specifically, the product of the virtual and actual queue backlogs has been employed as a weight in the maximal weight matching schedules in [110][109][112] and as a weight on the random access probability in the CSMA algorithm in [117]. The network stability is achieved by shifting the burden from actual queues to the proposed virtual queues, while the actual queues are upper-bounded ii by a finite buffer size. As a direct result, the delay performance is significantly improved. In the proof of the stability and throughput/utility optimality, a novel type of Lyapunov function is employed which multiplies the virtual queue backlog to the quadratic term of actual queue backlogs. This particular structure of Lyapunov function leads to the product form of virtual and actual queue backlogs in the proposed algorithms. The scheduling algorithms with finite buffers are proposed and analyzed in both centralized and distributed settings. Specifically, in multi-hop wireless networks, a centralized cross-layer scheduling algorithm [110] is designed with a novel concept of virtual queues to achieve a throughput “ǫ-close” to the optimality with a tradeoff of O( ǫ ) in average end-to-end delay guarantees. The structure of this algorithm is employed to design centralized optimal power control algorithms with finite buffers in [109][112]. In [117], distributed cross-layer CSMA algorithms are proposed in a singlehop setting to guarantee finite buffer sizes. The algorithm is shown to achieve a utility arbitrarily close to the optimal value with a tradeoff in the finite buffer sizes. Both implementation and numerical results [117] show a far better delay performance for comparable utility levels in comparison with recent optimal CSMA algorithms (e.g., Q-CSMA in [83]). An underlying reason for large delays under the throughput-optimal random access algorithms [83, 85, 28] is temporal starvation [61], the phenomenon of links “being starved for prolonged periods indefinitely often despite having good stationary throughput”. Temporal starvation also leads to bursty service and undesirable jitter performance. To address the delay and temporal starvation issues, A v(t)-regulated CSMA algorithm is proposed in [111] that achieves fully local implementation without global message passing. Under the proposed algorithm, only links with weights above