Competitive On-line Scheduling Research Articles

Deadline Constrained Packet Scheduling in the Presence of an Energy Harvesting Jammer

Maintaining data communication in the presence of jammer nodes is an important feature required in several modern wireless networks. In this article, we analyze a three node system, where a legitimate link between the transmitter and the receiver is adversarially affected by independent Gaussian noise injected by a jammer. The transmitter is battery powered, and has data arriving as packets. All the data need to be delivered to the receiver before a common deadline. The transmitter's goal is to accomplish this task using as minimum an energy as possible, while the jammer's objective is the opposite, viz. increase the transmitter's energy as much as possible by strategically injecting noise. We consider a jammer node which relies on dynamic energy harvesting sources to power its hardware. The adversarial interactions are modeled by posing a min-max game between the transmitter and the jammer. Solving this, we derive the equilibrium scheduling policies of the transmitter and the jammer for the offline model, and present an iterative algorithm to compute these policies. Competitive online scheduling policies are then proposed, whose competitive ratio is bounded using ideas from the offline policies derived earlier. A constant competitive ratio is shown when the last data packet does not arrive too early, and a significant fraction of the jamming energy is harvested before this arrival.

Equilibria of Online Scheduling Algorithms

We describe a model for competitive online scheduling algorithms. Two servers, each with a single observable queue, compete for customers. Upon arrival, each customer strategically chooses the queue with minimal expected wait time. Each scheduler wishes to maximize its number of customers, and can strategically select which scheduling algorithm, such as First-Come-First-Served (FCFS), to use for its queue. This induces a game played by the servers and the customers. We consider a non-Bayesian setting, where servers and customers play to maximize worst-case payoffs. We show that there is a unique subgame perfect safety-level equilibrium and we describe the associated scheduling algorithm (which is not FCFS). The uniqueness result holds for both randomized and deterministic algorithms, with a different equilibrium algorithm in each case. When the goal of the servers is to minimize competitive ratio, we prove that it is an equilibrium for each server to apply FCFS: each server obtains the optimal competitive ratio of 2.

Competitive online scheduling of perfectly malleable jobs with setup times

We study how to efficiently schedule online perfectly malleable parallel jobs with arbitrary arrival times on m ⩾ 2 processors. We take into account both the linear speedup of such jobs and their setup time, i.e., the time to create, dispatch, and destroy multiple processes. Specifically, we define the execution time of a job with length p j running on k j processors to be p j / k j + ( k j − 1) c, where c > 0 is a constant setup time associated with each processor that is used to parallelize the computation. This formulation accurately models data parallelism in scientific computations and realistically asserts a relationship between job length and the maximum useful degree of parallelism. When the goal is to minimize makespan, we show that the online algorithm that simply assigns k j so that the execution time of each job is minimized and starts jobs as early as possible has competitive ratio 4( m − 1)/ m for even m ⩾ 2 and 4 m/( m + 1) for odd m ⩾ 3. This algorithm is much simpler than previous offline algorithms for scheduling malleable jobs that require more than a constant number of passes through the job list.

Competitive online scheduling for server systems

Our goal here is to illustrate the competitive online scheduling research community's approach to online server scheduling problems by enumerating some of the results obtained for problems related to response and slowdown, and by explaining some of the standard analysis techniques.

IMPROVED COMPETITIVE ALGORITHMS FOR TWO-PROCESSOR REAL-TIME SYSTEMS

The problem of competitive on-line scheduling in two-processor real-time environments is studied. The model of Koren and Shasha is followed: Every task has a deadline and a value that it obtains only if it completes by its deadline – the value being its computation time. The goal is to design on-line schedulers with worst-case guarantees compared with a clairvoyant scheduler. Koren and Shasha gave algorithms for the migration and no-migration models, with competitive multipliers of 2 and 3, respectively. In this article, we give an algorithm for the no-migration model with an improved competitive multiplier of [Formula: see text]. We also show that the competitive multiplier for the migration model can be lowered by using a fast processor and a slow processor, compared with using several parallel and identical processors with the same aggregate computing power.

Competitive on-line scheduling with level of service

Motivated by an application in thinwire visualization, we study an abstract on-line scheduling problem where the size of each requested service can be scaled down by the scheduler. Thus, our problem embodies a notion of "Level of Service" that is increasingly important in multimedia applications. We give two schedulers FirstFit and EndFit based on two simple heuristics, and generalize them into a class of greedy schedulers. We show that both FirstFit and EndFit are 2-competitive, and any greedy scheduler is 3-competitive. These bounds are shown to be tight.

Competitive On-line Scheduling of Continuous-Media Streams

Multimedia applications require a guaranteed level of service for accessing continuous-media data. To obtain such guarantees, the database server where the data are residing must employ an admission control scheme to limit the number of clients that can be served concurrently. We investigate the problem of on-line admission control, where the decision of whether to accept or reject a request must be made without any knowledge about future requests. Employing competitive analysis techniques, we address the problem in its most general form with the following key contributions: (1) We prove a tight upper bound on the competitive ratio of the conventional Work-Conserving (WC) policy, showing that it is within a factor 1+Δ1−ρ of the optimal clairvoyant strategy, where Δ is the ratio of the maximum to minimum request length (i.e., time duration), and ρ is the maximum fraction of the server's bandwidth that a request can demand; (2) we prove a lower bound of Ω(logΔ1−ρ) on the competitive ratio of any deterministic or randomized admission control scheme, demonstrating an exponential gap between greedy and optimal on-line solutions; (3) we propose simple deterministic schemes based on the idea of bandwidth prepartitioning that guarantee competitive ratios within a small constant factor of logΔ (i.e., they are provably near-optimal) if ρ<1/⌈logΔ⌉; and (4) we introduce a novel admission control policy that partitions the server bandwidth based on the expected popularities of different request lengths and experimentally demonstrate its benefits compared to WC.

Competitive on-line scheduling of imprecise computations

The on-line scheduling of systems of imprecise computation tasks is investigated. The system objective is to maximize the value obtained. A formal model is defined. Under certain reasonable assumptions-formalized here as the weak feasible mandatory constraint-a competitive on-line scheduling algorithm is presented for the commonly studied uniform-density task systems. It is proven, however, that an on-line algorithm may, in general, perform arbitrarily poorly as compared to a clairvoyant scheduler.

A 2. 79 competitive online algorithm for two processor real-time systems with uniform value density

We consider the problem of competitive on-line scheduling in two processor real-time systems. In our model all tasks have common value density. Each task has a release time, an execution time and a deadline. The scheduler is given no information about a task until it is released. And the value will be achieved if and only if the task is completed by its deadline. Moreover, we suppose that migration is not allowed. The goal of the scheduler is to obtain as much value as possible. In this paper we show that the competitive multiplier of Safe-Risky-fixed Algorithm in [4] is really 3 and presents a modified algorithm (Safe-Risky-unfixed Algorithm) that achieves a competitive multiplier of 2. 79.

MOCA: a multiprocessor on-line competitive algorithm for real-time system scheduling

We study competitive on-line scheduling in multiprocessor real-time environments. In our model, every task has a deadline and a value that it obtains only if it completes by its deadline. A task can be assigned to any processor, all of which are equally powerful. The problem is to design an on-line scheduling algorithm (i.e. one in which the scheduler has no knowledge of a task unit it is released) with worst-case guarantees as to the total value obtained by the system. We study systems with two or more processors. We present an inherent limit on the best competitive guarantee that any on-line parallel real-time scheduler can give. Then we present a competitive algorithm that achieves a worst-case guarantee which is within a small factor from the best possible guarantee in many cases. These are the most general results yet known for competitive scheduling of multiprocessor real-time systems.