The uplink data arriving at the Machine-to-Machine (M2M) Application Server (AS) via M2M Aggregators (MAs) is fairly heterogeneous along several dimensions such as maximum tolerable packet delay, payload size and arrival rate, thus necessitating the design of Quality-of-Service (QoS) aware packet scheduler. In this paper, we classify the M2M uplink data into multiple QoS classes and use sigmoidal function to map the delay requirements of each class onto utility functions. We propose a proportionally fair delay-optimal multiclass packet scheduler at AS that maximizes a system utility metric. We note that the average class delay under any work-conserving scheduling policy can be realized by appropriately time-sharing between all possible preemptive priority policies. Therefore the optimal scheduler is determined using an iterative process to determine the optimal time-sharing between all priority scheduling policies, such that it results in maximum system utility. The proposed scheduler can be implemented online with reduced complexity due to the iterative optimization process. We then extend this work to determine jointly optimal MA-AS channel allocation and packet scheduling scheme at the MAs and AS. We first formulate a joint optimization problem that is solved centrally at the AS and then propose a low complexity distributed optimization problem solved independently at MAs and AS. We show that the distributed optimization solution converges quickly to the centralized optimization result with minimal information exchange overhead between MAs and AS. Using Monte-Carlo simulations, we verify the optimality of the proposed scheduler and show that it outperforms other state-of-the-art packet schedulers such as weighted round robin, max-weight scheduler etc. Another desirable feature of proposed scheduler is low delay jitter for delay-sensitive traffic.
Another line of work considers the design of packet schedulers for real-time control applications (see @cite_23 and references therein) and assume hybrid task sets comprising of periodic tasks with hard deadlines and aperiodic tasks with hard, soft or non-real-time requirements. The goal of these schedulers is to guarantee schedulability for critical tasks (with hard deadlines) while providing a best-effort service for other tasks. The periodic tasks from different flows are processed by assuming a fixed-priority assignment and with service deadline equal to the arrival period of that flow, while the aperiodic tasks from various flows are aggregated and served using First-Come-First-Serve policy. Some of the popular algorithms include Rate Monotonic scheduling @cite_27 , Polling Server, Deferrable Server @cite_22 , Priority Exchange @cite_24 , Sporadic Server @cite_5 and Slack-Stealing @cite_1 . However for most of the practical M2M systems, the arrival rate and delay requirements are potentially different for each aperiodic flow and thus aggregating the aperiodic flows will degrade the overall delay performance. Furthermore, these schemes define a , a virtual periodic task with certain computation time and priority level to process outstanding aperiodic tasks. But the determination of delay-optimal period and capacity for given traffic characteristics is not clear.
@cite_22 @cite_1 @cite_24 @cite_27 @cite_23 @cite_5
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The proliferation of high-volume time-critical Web services such as online trading calls for a scalable server design that allows meeting individual response-time guarantees of real time transactions. A main challenge is to honor these guarantees despite unpredictability in incoming server load. The extremely high volume of real-time service requests mandates constant-time scheduling and schedulability analysis algorithms (as opposed to polynomial or logarithmic ones in the number of current requests). The paper makes two major contributions towards developing an architecture and theoretical foundations for scalable real-time servers operating in dynamic environments. First, we derive a tight utilization bound for schedulability of aperiodic tasks (requests) that allows implementing a constant time schedulability test on the server. We demonstrate that Liu and Layland's schedulable utilization bound of ln 2 does not apply to aperiodic tasks, and prove that an optimal arrival-time independent scheduling policy will meet all aperiodic task deadlines if utilization is maintained below 1 1+ spl radic (1 2). Second, we show that aperiodic deadline-monotonic scheduling is the optimal arrival-time-independent scheduling policy for aperiodic tasks. This result is used to optimally prioritize server requests. Evaluation of a utilization control loop that maintains server utilization below the bound shows that the approach is effective in meeting all individual deadlines in a high performance real-time server. Most existing scheduling algorithms for hard real-time systems apply either to periodic tasks or aperiodic tasks but not to both. In practice, real-time systems require an integrated, consistent approach to scheduling that is able to simultaneously meet the timing requirements of hard deadline periodic tasks, hard deadline aperiodic (alert-class) tasks, and soft deadline aperiodic tasks. This paper introduces the Deferrable Server (DS) algorithm which will be shown to provide improved aperiodic response time performance over traditional background and polling approaches. Taking advantage of the fact that, typically, there is no benefit in early completion of the periodic tasks, the Deferrable Server (DS) algorithm assigns higher priority to the aperiodic tasks up until the point where the periodic tasks would start to miss their deadlines. Guaranteed alert-class aperiodic service and greatly reduced response times for soft deadline aperiodic tasks are important features of the DS algorithm, and both are obtained with the hard deadlines of the periodic tasks still being guaranteed. The results of a simulation study performed to evaluate the response time performance of the new algorithm against traditional background and polling approaches are presented. In all cases, the response times of aperiodic tasks are significantly reduced (often by an order of magnitude) while still maintaining guaranteed periodic task deadlines. > This thesis develops the Sporadic Server (SS) algorithm for scheduling aperiodic tasks in real-time systems. The SS algorithm is an extension of the rate monotonic algorithm which was designed to schedule periodic tasks. This thesis demonstrates that the SS algorithm is able to guarantee deadlines for hard-deadline aperiodic tasks and provide good responsiveness for soft-deadline aperiodic tasks while avoiding the schedulability penalty and implementation complexity of previous aperiodic service algorithms. It is also proven that the aperiodic servers created by the SS algorithm can be treated as equivalently-sized periodic tasks when assessing schedulability. This allows all the scheduling theories developed for the rate monotonic algorithm to be used to schedule aperiodic tasks. For scheduling aperiodic and periodic tasks that share data, this thesis defines the interactions and schedulability impact of using the SS algorithm with the priority inheritance protocols. For scheduling hard-deadline tasks with short deadlines, an extension of the rate monotonic algorithm and analysis is developed. To predict performance of the SS algorithm, this thesis develops models and equations that allow the use of standard queueing theory models to predict the average response time of soft-deadline aperiodic tasks serviced with a high-priority sporadic server. Implementation methods are also developed to support the SS algorithm in Ada and on the Futurebus+. Real-time scheduling theory offers constant-time schedulability tests for periodic and sporadic tasks based on utilization bounds. Unfortunately, the periodicity or the minimal interarrival-time assumptions underlying these bounds make them inapplicable to a vast range of aperiodic workloads such as those seen by network routers, Web servers, and event-driven systems. This paper makes several important contributions toward real-time scheduling theory and schedulability analysis. We derive the first known bound for schedulability of aperiodic tasks. The bound is based on a utilization-like metric we call synthetic utilization, which allows implementing constant-time schedulability tests at admission control time. We prove that the synthetic utilization bound for deadline-monotonic scheduling of aperiodic tasks is 1 1+ spl radic 1 2. We also show that no other time-independent scheduling policy can have a higher schedulability bound. Similarly, we show that EDF has a bound of 1 and that no dynamic-priority policy has a higher bound. We assess the performance of the derived bound and conclude that it is very efficient in hit-ratio maximization.