From Preemptive to Non-preemptive Scheduling Using Rejections

International audienceWe study the classical problem of scheduling a set of independent jobs with release dates on a single machine. There exists a huge literature on the preemptive version of the problem, where the jobs can be interrupted at any moment. However, we focus here on the non-preemptive case, which is harder, but more relevant in practice. For instance, the jobs submitted to actual high performance platforms cannot be interrupted or migrated once they start their execution (due to prohibitive management overhead). We target on the minimization of the total stretch objective, defined as the ratio of the total time a job stays in the system (waiting time plus execution time), normalized by its processing time. Stretch captures the quality of service of a job and the minimum total stretch reflects the fairness between the jobs. So far, there have been only few studies about this problem, especially for the non-preemptive case. Our approach is based to the usage of the classical and efficient for the preemptive case shortest remaining processing time (SRPT) policy as a lower bound. We investigate the (offline) transformation of the SRPT schedule to a non-preemptive schedule subject to a recently introduced resource augmentation model, namely the rejection model according to which we are allowed to reject a small fraction of jobs. Specifically, we propose a 2 ǫ-approximation algorithm for the total stretch minimization problem if we allow to reject an ǫ-fraction of the jobs, for any ǫ > 0. This result shows that the rejection model is more powerful than the other resource augmentations models studied in the literature, like speed augmentation or machine augmentation, for which non-polynomial or non-scalable results are known. As a byproduct, we present a O(1)-approximation algorithm for the total flow-time minimization problem which also rejects at most an \epsilon-fraction of jobs

Non-Preemptive Flow-Time Minimization via Rejections

We consider the online problem of minimizing weighted flow-time on unrelated machines. Although much is known about this problem in the resource-augmentation setting, these results assume that jobs can be preempted. We give the first constant-competitive algorithm for the non-preemptive setting in the rejection model. In this rejection model, we are allowed to reject an epsilon-fraction of the total weight of jobs, and compare the resulting flow-time to that of the offline optimum which is required to schedule all jobs. This is arguably the weakest assumption in which such a result is known for weighted flow-time on unrelated machines. While our algorithms are simple, we need a delicate argument to bound the flow-time. Indeed, we use the dual-fitting framework, with considerable more machinery to certify that the cost of our algorithm is within a constant of the optimum while only a small fraction of the jobs are rejected

PREEMPTIVE PRIORITY SCHEDULING WITH AGING TECHNIQUE FOR EFFECTIVE DISASTER MANAGEMENT IN CLOUD

Cloud computing has intern the attention of today’s leading IT industries offering huge potential for more flexible, readily scalable and cost effective IT operation. There is a significant anticipation for emergent innovation and expanded capabilities of a cloud-based environment as the cloud services are still in the infant stage. With all technology innovation, the biggest gain will be realized when the Cloud services are efficiently utilized. One of the prime contributions of Cloud is its capacity to handle a huge amount of data for either processing or storing. The inadequacy of this model is that it is prone to disaster. Some of the popular scheduling techniques applied by the researchers and leading IT industries are Round Robin, Preemptive scheduling etc. This research focuses on a novel approach for disaster management through efficient scheduling mechanism.This paper presents a Priority Preemptive scheduling (PPS) with aging of the low priority jobs in Cloud for disaster management. The implementation results show that the jobs at any instance of time are provided with the resources and henceforth preventing them to enter the starvation, which is one of the prime causes for disaster

Online Non-Preemptive Scheduling to Minimize Weighted Flow-time on Unrelated Machines

In this paper, we consider the online problem of scheduling independent jobs non-preemptively so as to minimize the weighted flow-time on a set of unrelated machines. There has been a considerable amount of work on this problem in the preemptive setting where several competitive algorithms are known in the classical competitive model. However, the problem in the non-preemptive setting admits a strong lower bound. Recently, Lucarelli et al. presented an algorithm that achieves a O(1/epsilon^2)-competitive ratio when the algorithm is allowed to reject epsilon-fraction of total weight of jobs and has an epsilon-speed augmentation. They further showed that speed augmentation alone is insufficient to derive any competitive algorithm. An intriguing open question is whether there exists a scalable competitive algorithm that rejects a small fraction of total weights. In this paper, we affirmatively answer this question. Specifically, we show that there exists a O(1/epsilon^3)-competitive algorithm for minimizing weighted flow-time on a set of unrelated machine that rejects at most O(epsilon)-fraction of total weight of jobs. The design and analysis of the algorithm is based on the primal-dual technique. Our result asserts that alternative models beyond speed augmentation should be explored when designing online schedulers in the non-preemptive setting in an effort to find provably good algorithms

Admission Control to Minimize Rejections and Online Set Cover with Repetitions

We study the admission control problem in general networks. Communication requests arrive over time, and the online algorithm accepts or rejects each request while maintaining the capacity limitations of the network. The admission control problem has been usually analyzed as a benefit problem, where the goal is to devise an online algorithm that accepts the maximum number of requests possible. The problem with this objective function is that even algorithms with optimal competitive ratios may reject almost all of the requests, when it would have been possible to reject only a few. This could be inappropriate for settings in which rejections are intended to be rare events. In this paper, we consider preemptive online algorithms whose goal is to minimize the number of rejected requests. Each request arrives together with the path it should be routed on. We show an $O(\log^2 (mc))$-competitive randomized algorithm for the weighted case, where $m$ is the number of edges in the graph and $c$ is the maximum edge capacity. For the unweighted case, we give an $O(\log m \log c)$-competitive randomized algorithm. This settles an open question of Blum, Kalai and Kleinberg raised in \cite{BlKaKl01}. We note that allowing preemption and handling requests with given paths are essential for avoiding trivial lower bounds

Online Non-preemptive Scheduling on Unrelated Machines with Rejections

When a computer system schedules jobs there is typically a significant cost associated with preempting a job during execution. This cost can be from the expensive task of saving the memory's state and loading data into and out of memory. It is desirable to schedule jobs non-preemptively to avoid the costs of preemption. There is a need for non-preemptive system schedulers on desktops, servers and data centers. Despite this need, there is a gap between theory and practice. Indeed, few non-preemptive \emph{online} schedulers are known to have strong foundational guarantees. This gap is likely due to strong lower bounds on any online algorithm for popular objectives. Indeed, typical worst case analysis approaches, and even resource augmented approaches such as speed augmentation, result in all algorithms having poor performance guarantees. This paper considers on-line non-preemptive scheduling problems in the worst-case rejection model where the algorithm is allowed to reject a small fraction of jobs. By rejecting only a few jobs, this paper shows that the strong lower bounds can be circumvented. This approach can be used to discover algorithmic scheduling policies with desirable worst-case guarantees. Specifically, the paper presents algorithms for the following two objectives: minimizing the total flow-time and minimizing the total weighted flow-time plus energy under the speed-scaling mechanism. The algorithms have a small constant competitive ratio while rejecting only a constant fraction of jobs. Beyond specific results, the paper asserts that alternative models beyond speed augmentation should be explored to aid in the discovery of good schedulers in the face of the requirement of being online and non-preemptive

Fault-tolerant parallel scheduling of arbitrary length jobs on a shared channel

We study the problem of scheduling jobs on fault-prone machines communicating via a shared channel, also known as multiple-access channel. We have $n$ arbitrary length jobs to be scheduled on $m$ identical machines, $f$ of which are prone to crashes by an adversary. A machine can inform other machines when a job is completed via the channel without collision detection. Performance is measured by the total number of available machine steps during the whole execution. Our goal is to study the impact of preemption (i.e., interrupting the execution of a job and resuming later in the same or different machine) and failures on the work performance of job processing. The novelty is the ability to identify the features that determine the complexity (difficulty) of the problem. We show that the problem becomes difficult when preemption is not allowed, by showing corresponding lower and upper bounds, the latter with algorithms reaching them. We also prove that randomization helps even more, but only against a non-adaptive adversary; in the presence of more severe adaptive adversary, randomization does not help in any setting. Our work has extended from previous work that focused on settings including: scheduling on multiple-access channel without machine failures, complete information about failures, or incomplete information about failures (like in this work) but with unit length jobs and, hence, without considering preemption

Towards achieving execution time predictability in web services middleware

Web services middleware are typically designed optimised for throughput. Requests are accepted unconditionally and no differentiation is made in processing. Many use the thread-pool pattern to execute requests in parallel using processor sharing. Clusters hosting web services dispatch requests only to balance out the load among the executors. Such optimisations for throughput work out negatively on the predictability of execution. Processor sharing results in the increase of execution time with the number of concurrent requests, making it impossible to predict or control the execution of a request. Existing works fail to address the need for predictability in web service execution. Some achieve a level of differentiated processing, but fail to consider predictability as their main quality attribute. Some give a probabilistic guarantee on service levels. However, from a predictability perspective they are inconsistent. A few achieve predictable execution times, though only in closed systems where request properties are known at system design time. Web services operate on the Internet, where request properties are relatively unknown. This thesis investigates the problem of achieving predictable times in web service executions. We introduce the notion of a processing deadline for service execution, which the web services engine must adhere to in completing the request in a repeatable and a consistent manner. Reaching such execution deadlines by the services engine is made possible by three main features. Firstly a deadline based scheduling algorithm introduced, ensures the processing deadlines are followed. A laxity based analytical model and an admission control algorithm it is based on, selects requests for execution, resulting in a wider range of laxities to enable more requests with overlapping executions to be scheduled together. Finally, a real-time scheduler component introduced in to the server uses a priority model to schedule the execution of requests by controlling the execution of individual worker threads in custom-made thread pools. Predictability of execution in cluster based deployments is further facilitated by four dispatching algorithms that consider the request deadlines and laxity property in the dispatching process. A performance model derived for a similar system approximates the waiting time where requests with smaller deadlines (having higher priority) experience smaller waiting times than requests with longer deadlines. These techniques are implemented in web services middleware in standalone and cluster-based configurations. They are evaluated against their unmodified versions and techniques such as round-robin and class based dispatching, to measure their predictability gain. Empirical evidence indicate the enhancements enable the middleware to achieve more than 90% of the deadlines, while accepting at least 20% of the requests in high traffic conditions. The enhancements additionally prevent the middleware from reaching overloaded conditions in heavy traffic, while maintaining comparable throughput rates to the unmodified versions of the middleware. Analytical and simulation results for the performance model confirms that deadline based preemptive scheduling results in a better balance of waiting times where high priority requests experience lower waiting times while lower priority requests are not over-starved compared to other techniques such as static priority ordering, First-Come-First-Served, Round-Robin and non-preemptive deadline based scheduling

Random trees in queueing systems with deadlines

AbstractWe survey our research on scheduling aperiodic tasks in real-time systems in order to illustrate the benefits of modelling queueing systems by means of random trees. Relying on a discrete-time single-server queueing system, we investigated deadline meeting properties of several scheduling algorithms employed for servicing probabilistically arriving tasks, characterized by arbitrary arrival and execution time distributions and a constant service time deadline T. Taking a non-queueing theory approach (i.e., without stable-stable assumptions) we found that the probability distribution of the random time sT where such a system operates without violating any task's deadline is approximately exponential with parameter λT = 1μT, with the expectation E[sT] = μT growing exponentially in T. The value μT depends on the particular scheduling algorithm, and its derivation is based on the combinatorial and asymptotic analysis of certain random trees. This paper demonstrates that random trees provide an efficient common framework to deal with different scheduling disciplines and gives an overview of the various combinatorial and asymptotic methods used in the appropriate analysis