Greedy Scheduling Research Articles

Supporting Fault-Tolerance for Time-Critical Events in Distributed Environments

In this paper, we consider the problem of supporting fault tolerance foradaptiveandtime-criticalapplications in heterogeneous and unreliable grid computing environments. Our goal for this class of applications is to optimize a user-specifiedbenefit functionwhile meeting the time deadline. Our first contribution in this paper is a multi-objective optimization algorithm for scheduling the application onto the most efficient and reliable resources. In this way, the processing can achieve the maximum benefit while also maximizing thesuccess-rate, which is the probability of finishing execution without failures. However, for the cases where failures do occur, we have developed ahybrid failure recoveryscheme to ensure that the application can complete within the pre-specified time interval. Our experimental results show that our scheduling algorithm can achieve better benefit when compared to several heuristics-based greedy scheduling algorithms, while still having a negligible overhead. Benefit is further improved when we apply the hybrid failure recovery scheme, and the success-rate becomes 100%.

A scheduling Algorithm based on Potential Game for a Cluster Grid

This paper introduces an algorithm whose aim is to increase scheduling efficiency on a distributed system like a Cluster Grid. In order to measure this efficiency, we have classified jobs in homogeneous classes and observed the throughput on homogeneous class of compute server. The scheduler is based on a defined Potential function applied to the Prisoner’s Dilemma problem of the Game Theory and this approach allows avoiding inefficiency caused by generic greedy scheduler policies. Moreover for this kind of games, we have verified that all Nash equilibrium solutions correspond to the Potential Function minimum.

Design of the Switching Controller for the High-Capacity Non-Blocking Internet Router

The sequential greedy scheduling (SGS) algorithm is a scalable maximal matching algorithm. This algorithm was conceptually proposed and well received since it provides non-blocking in an Internet router with input buffers and a cross-bar, unlike other existing implementations. In this paper, we implement a new design of the SGS algorithm, and determine its exact behaviour, performance and QoS that it provides. We examine different design options and measure the performance of their implementations in terms of their scalability and speed. It will be shown that multiple scheduler modules of a terabit Internet router can be implemented on a low-cost field-programmable gate-array (FPGA) device, and that the processing can be performed within the desired time slot duration. Proper functioning of the implemented scheduler was confirmed through thorough software and hardware testing.

An efficient greedy scheduler for zero-forcing dirty-paper coding

In this paper, an efficient greedy scheduler for zero-forcing dirty-paper coding (ZF-DPC), which can be incorporated in complex Householder QR factorization of the channel matrix, is proposed. The ratio of the complexity of the proposed scheduler to the complexity of the channel matrix factorization required by ZF-DPC is O(M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> ), while such ratio for the original greedy scheduler is O(M), where M is the number of transmitters. Therefore, the new scheduler reduces the overhead of scheduling from being the bottleneck of ZF-DPC to being negligible.

Simplified Fair Scheduling and Antenna Selection Algorithms for Multiuser MIMO Orthogonal Space-Division Multiplexing Downlink

We consider the downlink of a multiuser multiple-input multiple-output (MIMO) system, where the base station and the mobile receivers are equipped with multiple antennas. We propose simplified algorithms for channel-aware multiuser scheduling in conjunction with receive antenna selection for two downlink multiuser orthogonal space-division multiplexing techniques: block diagonalization and successive optimization. The algorithms greedily maximize the weighted sum rate. The algorithms add the best user at a time from the set of users that are not selected yet to the set of selected users until the desired number of users has been selected. To apply the proportional fairness criterion, simplified user scheduling metrics are proposed for block diagonalization and successive optimization. Two receive antenna selection algorithms are also proposed, which further enhance the power gain of the equivalent single-user channel after orthogonal precoding by selecting a subset of the receive antennas that contributes the most toward the total power gain of the channel. A user grouping technique is used to further lower the complexity of the selection algorithms. We compare various multiuser MIMO scheduling strategies that are applied to block diagonalization and successive optimization transmission techniques through simulation. Simulation results demonstrate the effectiveness of the proposed algorithms in ensuring throughput fairness among users. Results also show that when the number of users is large, the proposed scheduling algorithms perform close to the exhaustive search algorithms and previously proposed greedy scheduling algorithms, but with much lower complexity.

Greedy scheduling with custom-made objectives

We present a methodology to automatically generate an online job scheduling method for a custom-made objective and real workloads. The scheduling problem comprises independent parallel jobs and parallel identical machines and occurs in Massively Parallel Processing systems and computational Grids. The system administrator defines the scheduling objective that may consider job properties and priorities of users or user groups. Our scheduling method combines a Greedy scheduling algorithm with the dynamic sorting of the waiting queue. This sorting algorithm uses a criterion that is modifiable by a set of parameters. Finding good parameter settings for the sorting criterion is viewed as a nonlinear optimization problem which is solved with the help of Evolution Strategies. We evaluate our scheduling method with real workload data and compare it to approximated optimal offline solutions and to the online results of the standard EASY backfill algorithm.

Channel Asymmetry in Cellular OFDMA-TDD Networks

This paper studies time division duplex- (TDD-) specific interference issues in orthogonal frequency division multiple access- (OFDMA-) TDD cellular networks arising from various uplink (UL)/downlink (DL) traffic asymmetries, considering both line-of-sight (LOS) and non-LOS (NLOS) conditions among base stations (BSs). The study explores aspects both of channel allocation and user scheduling. In particular, a comparison is drawn between the fixed slot allocation (FSA) technique and a dynamic channel allocation (DCA) technique for different UL/DL loads. For the latter, random time slot opposing (RTSO) is assumed due to its simplicity and its low signaling overhead. Both channel allocation techniques do not obviate the need for user scheduling algorithms, therefore, a greedy and a fair scheduling approach are applied to both the RTSO and the FSA. The systems are evaluated based on spectral efficiency, subcarrier utilization, and user outage. The results show that RTSO networks with DL-favored traffic asymmetries outperform FSA networks for all considered metrics and are robust to LOS between BSs. In addition, it is demonstrated that the greedy scheduling algorithm only offers a marginal increase in spectral efficiency as compared to the fair scheduling algorithm, while the latter exhibits up to 20% lower outage.

Stability bounds in networks with dynamic link capacities

We address the problem of stability in networks where the link capacities can change dynamically. We show that every network running a greedy scheduling policy is universally stable at any injection rate r < 1 / ( C d ) , where d is the largest number of links crossed by any packet and C is the maximum link capacity. We also show that system-wide time priority scheduling policies are universally stable at any injection rate r < 1 / ( C ( d − 1 ) ) .

A two-stage hardware scheduler combining greedy and optimal scheduling

Greedy scheduling heuristics provide a low complexity and scalable albeit particularly sub-optimal strategy for hardware-based crossbar schedulers. In contrast, the maximum matching algorithm for Bipartite graphs can be used to provide optimal scheduling for crossbar-based interconnection networks with a significant complexity and scalability cost. In this paper, we show how maximum matching can be reformulated in terms of Boolean operations rather than the more traditional formulations. By leveraging the inherent parallelism available in custom hardware design, we reformulate maximum matching in terms of Boolean operations rather than matrix computations and introduce three maximum matching implementations in hardware. Specifically, we examine a Pure Logic Scheduler with three dimensions of parallelism, a Matrix Scheduler with two dimensions of parallelism and a Vector Scheduler with one dimension of parallelism. These designs reduce the algorithmic complexity for an N × N network from O ( N 3 ) to O ( 1 ) , O ( K ) , and O ( K N ) , respectively, where K is the number of optimization steps. While an optimal scheduling algorithm requires K = 2 N − 1 steps, by starting with our hardware-based greedy strategy to generate an initial schedule, our simulation results show that the maximum matching scheduler can achieve 99% of the optimal schedule when K = 9 . We examine hardware and time complexity of these architectures for crossbar sizes of up to N = 1024 . Using FPGA synthesis results, we show that a greedy schedule for crossbars, ranging from 8×8 to 256×256, can be optimized in less than 20 ns per optimization step. For crossbars reaching 1024×1024 the scheduling can be completed in approximately 10 μs with current technology and could reach under 90 ns with future technologies.

Scheduling Efficiency of Distributed Greedy Scheduling Algorithms in Wireless Networks

We consider the problem of distributed scheduling in wireless networks subject to simple collision constraints. We define the efficiency of a distributed scheduling algorithm to be the largest number (fraction) such that the throughput under the distributed scheduling policy is at least equal to the efficiency multiplied by the maximum throughput achievable under a centralized policy. For a general interference model, we prove a lower bound on the efficiency of a distributed scheduling algorithm by first assuming that all of the traffic only uses one hop of the network. We also prove that the lower bound is tight in the sense that, for any fraction larger than the lower bound, we can find a topology and an arrival rate vector within the fraction of the capacity region such that the network is unstable under a greedy scheduling policy. We then extend our results to a more general multihop traffic scenario and show that similar scheduling efficiency results can be established by introducing prioritization or regulators to the basic greedy scheduling algorithm

Optimization of the Scheduler for the Non-Blocking High-Capacity Router

The sequential greedy scheduling (SGS) is a scalable maximal matching algorithm that provides non-blocking in an Internet router with input buffers and a cross-bar. In this paper, we will present the FPGA design of the SGS scheduler. We have optimized scheduler components, and we will prove their correct functioning. The scheduler optimization significantly reduces the worst-case packet delay through the router.

Scheduling and performance analysis of multicast interconnects

Multicast is an important operation in various emerging computing/networking applications. In particular, many multicast applications require not only multicast capability but also predictable communication performance, such as guaranteed multicast latency and bandwidth, called quality-of-service (QoS). In this paper, we consider scheduling in multicast interconnects, which aims to minimize the multicast latency for a set of multicast requests. Unfortunately, such a problem has been proved to be NP-Complete, which means that it is unlikely to find a fast exact algorithm for the multicast scheduling problem. We then turn to propose a simple, fast greedy multicast scheduling algorithm and derive a lower bound and an upper bound on the performance of the algorithm. As can be seen, while a lower bound is fairly straightforward, the upper bound is much more difficult to obtain. By translating the multicast scheduling problem into a graph theory problem and employing a random graph approach, we are able to obtain a probabilistic upper bound on the performance of the multicast scheduling algorithm. Our analytical and simulation results show that the performance of the proposed multicast scheduling algorithm is quite close to the lower bound and is statistically guaranteed by the probabilistic upper bound.

The Virtue of Patience in Low-Complexity Scheduling of Packetized Media With Feedback

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> We consider streaming pre-encoded and packetized media over best-effort networks in the presence of acknowledgment feedbacks. We first review a rate-distortion (RD) optimization framework that can be employed in such scenarios. As part of the framework, a scheduling algorithm selects the data to send over the network at any given time, so as to minimize the end-to-end distortion, given an estimate of channel resources and a history of previous transmissions and received acknowledgements. In practice, a greedy scheduling strategy is often considered to limit the solution search space, and reduce the computational complexity associated to the RD optimization framework. Our work observes that popular greedy schedulers are strongly penalized by early retransmissions. Therefore, we propose a scheduling algorithm that avoids premature retransmissions, while preserving the low computational complexity aspect of the greedy paradigm. Such a scheduling strategy maintains close to optimal RD performance when adapting to network bandwidth fluctuations. Our experimental results demonstrate that the proposed patient greedy scheduler provides a reduction of up to 50% in transmission rate relative to conventional greedy approaches, and that it brings up to 2 dB of quality improvement in scheduling classical MPEG-based packet video streams. </para>

Effects of Gradual Enhancement for Receivers at Mobile Terminals in Different Locations with Greedy Scheduling

Receiver enhancement at mobile terminals such as using receiver diversity is a way of achieving greater downlink capacity. The enhancement, however, is achieved not instantaneously by a network operator but gradually by the individual users that choose and purchase their own mobile terminals. We investigate in this letter the effect of gradually introducing enhanced receivers at mobiles in different locations. With greedy scheduling, capacity, fairness and coverage are quantified and numerically compared according to locations of enhanced mobiles. The results show that the enhancement made at mobiles nearer to the base provides the greater capacity but this capacity-driving introduction of the enhancement makes the fairness and the coverage poorer.

Impacts of Radio Channel Characteristics, Heterogeneous Traffic Intensity, and Near–Far Effect on Rate Adaptive Scheduling Algorithms

Applying adaptive modulation combined with scheduling in a shared data channel can substantially improve the spectral efficiency for wireless systems. This performance gain results from the multiuser diversity, which exploited independent channel variations across multiple users. In this paper, we present a cross-layer analysis to integrate physical-layer channel characteristics, media access control (MAC) layer scheduling strategies, and the network layer issue of heterogeneous traffic intensity across near-far users. Specifically, for radio channel characteristics, we take account of path loss, slowly varying log-normal shadowing and fast-varying Nakagami fading. We also evaluate the impact of selective transmit diversity on the throughput and fairness of wireless data networks. Furthermore, we consider three MAC schedulers: random scheduler, greedy scheduler (GS), and a newly proposed queue-length-based scheduler (QS). By applying the proposed cross-layer analytical framework, the following insights can be gained. First, for the three considered schedulers, channel fluctuations induced by Nakagami fading or log-normal shadowing can improve both total throughput and fairness. Second, using selective transmit diversity can improve throughput, but is unfavorable for the fairness performance. Third, the GS and the QS methods can improve throughput at the expense of unfairness to the far users. However, the throughput improvement from using the GS and the QS decreases as the traffic intensity of the far user increases. In summary, this cross-layer analysis can be used to develop new scheduling mechanisms for achieving better tradeoff between the fairness and throughput for wireless data networks

On Capacity of Quality-Based Channel-State Reporting in Mobile Systems With Greedy Transmission Scheduling

Greedy transmission scheduling achieves great capacity by maximally exploiting independent time-varying channels across different mobile users. The improvement in capacity, however, depends on the degree of completeness of the channel quality information (CQI) fed back from the receiver to the transmitter. To be motivated by an insight that too many CQI feedbacks may rather impair the capacity gain, due to causing congestion in feedback link, this letter proposes a quality-based CQI reporting (QBR) scheme where the CQIs are fed back to the transmitter only for receivers whose signal quality is above a predefined threshold. The capacity is provided in terms of the threshold and feedback-error rate. The results show that QBR achieves outstanding performance when the feedback error is present. In addition, it quickly approaches an unimpaired ideal capacity, as the number of users increases if the error is not assumed

Greedy scheduling performance for a zero-forcing dirty-paper coded system

This letter presents two results for multiuser wireless systems employing dirty-paper coding strategies along with greedy scheduling over the broadcast multiple-input multiple-output channel. Specifically, an efficient and suboptimal downlink scheduler is proposed to approximate the maximum sum rate using equal power allocation, and it is shown to approach the maximum sum rate of optimal power allocation for a large number of users under optimal scheduling. The second result demonstrates that the average maximum sum rate can be tightly upper bounded when spatial multiplexing is maximized.

Source routing and scheduling in packet networks

We study routing and scheduling in packet-switched networks. We assume an adversary that controls the injection time, source, and destination for each packet injected. A set of paths for these packets is admissible if no link in the network is overloaded. We present the first on-line routing algorithm that finds a set of admissible paths whenever this is feasible. Our algorithm calculates a path for each packet as soon as it is injected at its source using a simple shortest path computation. The length of a link reflects its current congestion. We also show how our algorithm can be implemented under today's Internet routing paradigms.When the paths are known (either given by the adversary or computed as above), our goal is to schedule the packets along the given paths so that the packets experience small end-to-end delays. The best previous delay bounds for deterministic and distributed scheduling protocols were exponential in the path length. In this article, we present the first deterministic and distributed scheduling protocol that guarantees a polynomial end-to-end delay for every packet.Finally, we discuss the effects of combining routing with scheduling. We first show that some unstable scheduling protocols remain unstable no matter how the paths are chosen. However, the freedom to choose paths can make a difference. For example, we show that a ring with parallel links is stable for all greedy scheduling protocols if paths are chosen intelligently, whereas this is not the case if the adversary specifies the paths.

Greedy Tree Growing Heuristics on Block-Test Scheduling Under Power Constraints

Greedy scheduling algorithms are proposed here to improve the test concurrency under power limits. An extended tree growing technique is used to model the power-constrained test scheduling problem in these algorithms. A constant additive model is employed for power dissipation analysis and estimation. The efficiency of this approach is assessed with test scheduling examples and the experimental results are presented. Known list scheduling approaches are proven to give acceptable power-constrained test scheduling results quickly, but not guaranteed to be optimal.

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.