The Power of Migration for Online Slack Scheduling

We investigate the power of migration in online scheduling for parallel identical machines. Our objective is to maximize the total processing time of accepted jobs. Once we decide to accept a job, we have to complete it before its deadline d that satisfies d >= (1+epsilon)p + r, where p is the processing time, r the submission time and the slack epsilon > 0 a system parameter. Typically, the hard case arises for small slack epsilon << 1, i.e. for near-tight deadlines. Without migration, a greedy acceptance policy is known to be an optimal deterministic online algorithm with a competitive factor of (1+epsilon)/epsilon (DasGupta and Palis, APPROX 2000). Our first contribution is to show that migrations do not improve the competitive ratio of the greedy acceptance policy, i.e. the competitive ratio remains (1+epsilon)/epsilon for any number of machines. Our main contribution is a deterministic online algorithm with almost tight competitive ratio on any number of machines. For a single machine, the competitive factor matches the optimal bound of (1+epsilon)/epsilon of the greedy acceptance policy. The competitive ratio improves with an increasing number of machines. It approaches (1+epsilon) ln((1+epsilon)/epsilon) as the number of machines converges to infinity. This is an exponential improvement over the greedy acceptance policy for small epsilon. Moreover, we show a matching lower bound on the competitive ratio for deterministic algorithms on any number of machines

Interval Scheduling: A Survey

In interval scheduling, not only the processing times of the jobs but also their starting times are given. This article surveys the area of interval scheduling and presents proofs of results that have been known within the community for some time. We first review the complexity and approximability of different variants of interval scheduling problems. Next, we motivate the relevance of interval scheduling problems by providing an overview of applications that have appeared in literature. Finally, we focus on algorithmic results for two important variants of interval scheduling problems. In one variant we deal with nonidentical machines: instead of each machine being continuously available, there is a given interval for each machine in which it is available. In another variant, the machines are continuously available but they are ordered, and each job has a given "maximal" machine on which it can be processed. We investigate the complexity of these problems and describe algorithms for their solution

A New Competitive Ratio for Network Applications with Hard Performance Guarantee

Online algorithms are used to solve the problems which need to make decisions without future knowledge. Competitive ratio is used to evaluate the performance of an online algorithm. This ratio is the worst-case ratio between the performance of the online algorithm and the offline optimal algorithm. However, the competitive ratios in many current studies are relatively low and thus cannot satisfy the need of the customers in practical applications. To provide a better service, a practice for service provider is to add more redundancy to the system. Thus we have a new problem which is to quantify the relation between the amount of increased redundancy and the system performance. In this dissertation, to address the problem that the competitive ratio is not satisfactory, we ask the question: How much redundancy should be increased to fulfill certain performance guarantee? Based on this question, we will define a new competitive ratio showing the relation between the system redundancy and performance of online algorithm compared to offline algorithm. We will study three applications in network applications. We propose online algorithms to solve the problems and study the competitive ratio. To evaluate the performances, we further study the optimal online algorithms and some other commonly used algorithms as comparison. We first study the application of online scheduling for delay-constrained mobile offloading. WiFi offloading, where mobile users opportunistically obtain data through WiFi rather than through cellular networks, is a promising technique to greatly improve spectrum efficiency and reduce cellular network congestion. We consider a system where the service provider deploys multiple WiFi hotspots to offload mobile traffic with unpredictable mobile users’ movements. Then we study online job allocation with hard allocation ratio requirement. We consider that jobs of various types arrive in some unpredictable pattern and the system is required to allocate a certain ratio of jobs. We then aim to find the minimum capacity needed to meet a given allocation ratio requirement. Third, we study online routing in multi-hop network with end-to-end deadline. We propose reliable online algorithms to schedule packets with unpredictable arriving information and stringent end-to-end deadline in the network

New data structures, models, and algorithms for real-time resource management

Real-time resource management is the core and critical task in real-time systems. This dissertation explores new data structures, models, and algorithms for real-time resource management. At first, novel data structures, i.e., a class of Testing Interval Trees (TITs), are proposed to help build efficient scheduling modules in real-time systems. With a general data structure, i.e., the TIT* tree, the average costs of the schedulability tests in a wide variety of real-time systems can be reduced. With the Testing Interval Tree for Vacancy analysis (TIT-V), the complexities of the schedulability tests in a class of parallel/distributed real-time systems can be effectively reduced from 0(m²nlogn) to 0(mlogn+mlogm), where m is the number of processors and n is the number of tasks. Similarly, with the Testing Interval Tree for Release time and Laxity analysis (TIT-RL), the complexity of the online admission control in a uni-processor based real-time system can be reduced from 0(n²) to 0(nlogn), where n is the number of tasks. The TIT-RL tree can also be applied to a class of parallel/distributed real-time systems. Therefore, the TIT trees are effective approaches to efficient real-time scheduling modules. Secondly, a new utility accrual model, i.e., UAM+, is established for the resource management in real-time distributed systems. UAM+ is constructed based on the timeliness of computation and communication. Most importantly, the interplay between computation and communication is captured and characterized in the model. Under UAM+, resource managers are guided towards maximizing system-wide utility by exploring the interplay between computation and communication. This is in sharp contrast to traditional approaches that attempt to meet the timing constraints on computation and communication separately. To validate the effectiveness of UAM+, a resource allocation algorithm called IAUASA is developed. Simulation results reveal that IAUASA is far superior to two other resource allocation algorithms that are developed according to traditional utility accrual model and traditional idea. Furthermore, an online algorithm called IDRSA is also developed under UAM+, and a Dynamic Deadline Adjustment (DDA) technique is incorporated into IDRSA algorithm to explore the interplay between computation and communication. The simulation results show that the performance of IDRSA is very promising, especially when the interplay between computation and communication is tight. Therefore, the new utility accrual model provides a more effective approach to the resource allocation in distributed real-time systems. Thirdly, a general task model, which adapts the concept of calculus curve from the network calculus domain, is established for those embedded real-time systems with random event/task arrivals. Under this model, a prediction technique based on history window and calculus curves is established, and it provides the foundation for dynamic voltage-frequency scaling in those embedded real-time systems. Based on this prediction technique, novel energy-efficient algorithms that can dynamically adjust the operating voltage-frequency according to the predicted workload are developed. These algorithms aim to reduce energy consumption while meeting hard deadlines. They can accommodate and well adapt to the variation between the predicted and the actual arrivals of tasks as well as the variation between the predicted and the actual execution times of tasks. Simulation results validate the effectiveness of these algorithms in energy saving