Semi-online Scheduling with Lookahead

The knowledge of future partial information in the form of a lookahead to design efficient online algorithms is a theoretically-efficient and realistic approach to solving computational problems. Design and analysis of semi-online algorithms with extra-piece-of-information (EPI) as a new input parameter has gained the attention of the theoretical computer science community in the last couple of decades. Though competitive analysis is a pessimistic worst-case performance measure to analyze online algorithms, it has immense theoretical value in developing the foundation and advancing the state-of-the-art contributions in online and semi-online scheduling. In this paper, we study and explore the impact of lookahead as an EPI in the context of online scheduling in identical machine frameworks. We introduce a $k$-lookahead model and design improved competitive semi-online algorithms. For a $2$-identical machine setting, we prove a lower bound of $\frac{4}{3}$ and design an optimal algorithm with a matching upper bound of $\frac{4}{3}$ on the competitive ratio. For a $3$-identical machine setting, we show a lower bound of $\frac{15}{11}$ and design a $\frac{16}{11}$-competitive improved semi-online algorithm.Comment: 14 pages, 1 figur

Queuing with future information

We study an admissions control problem, where a queue with service rate $1-p$ receives incoming jobs at rate $\lambda\in(1-p,1)$, and the decision maker is allowed to redirect away jobs up to a rate of $p$, with the objective of minimizing the time-average queue length. We show that the amount of information about the future has a significant impact on system performance, in the heavy-traffic regime. When the future is unknown, the optimal average queue length diverges at rate $\sim\log_{1/(1-p)}\frac{1}{1-\lambda}$, as $\lambda\to 1$. In sharp contrast, when all future arrival and service times are revealed beforehand, the optimal average queue length converges to a finite constant, $(1-p)/p$, as $\lambda\to1$. We further show that the finite limit of $(1-p)/p$ can be achieved using only a finite lookahead window starting from the current time frame, whose length scales as $\mathcal{O}(\log\frac{1}{1-\lambda})$, as $\lambda\to1$. This leads to the conjecture of an interesting duality between queuing delay and the amount of information about the future.Comment: Published in at http://dx.doi.org/10.1214/13-AAP973 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Lookahead scheduling in a real-time context: Models, algorithms, and analysis

Our research considers job scheduling, a special type of resource assignment problem. For example, at a cross-docking facility trucks must be assigned to doors where they will be unloaded. The cargo on each truck has various destinations within the facility, and the unloading time for a truck is dependent on the distance from the assigned door to these destinations. The goal is to assign the trucks to doors while minimizing the amount of time to unload all trucks.;We study scheduling algorithms for problems like the cross-docking example that are different from traditional algorithms in two ways. First, we utilize real-time, where the algorithm executes at the same time as when the jobs are handled. Because the time used by the algorithm to make decisions cannot be used to complete a job, these decisions must be made quickly Second, our algorithms utilize lookahead, or partial knowledge of jobs that will arrive in the future.;The three goals of this research were to demonstrate that lookahead algorithms can be implemented effectively in a real-time context, to measure the amount of improvement gained by utilizing lookahead, and to explore the conditions in which lookahead is beneficial.;We present a model suitable for representing problems that include lookahead in a real-time context. Using this model, we develop lookahead algorithms for two important job scheduling systems and argue that these algorithms make decisions efficiently. We then study the performance of lookahead algorithms using mathematical analysis and simulation.;Our results provide a detailed picture of the behavior of lookahead algorithms in a real-time context. Our analytical study shows that lookahead algorithms produce schedules that are significantly better than those without lookahead. We also found that utilizing Lookahead-1, or knowledge of the next arriving job, produces substantial improvement while requiring the least effort to design. When more lookahead information is used, the solutions are better, but the amount of improvement is not significantly larger than a Lookahead-1 algorithm. Further, algorithms utilizing more lookahead are more complex to design, implement, and analyze. We conclude that Lookahead-1 algorithms are the best balance between improvement and design effort

Backfilling with fairness and slack for parallel job scheduling

Parallel jobs have different runtimes and numbers of threads/processes. Thus, scheduling parallel jobs involves a packing problem. If jobs are packed as tightly as possible, utilization will be improved. Otherwise, some resources have to stay idle. The common solution to deal with idle resources is backfilling, which schedule smaller jobs submitted later to execute earlier as long as they do not postpone the first job or all the previous jobs in the waiting queue. Traditionally, backfilling uses first fit for idle resources, according to the submission order. However, in this case, better packing of jobs could be missed. Hence, we propose an algorithm which looks further ahead if significantly improving utilization. However at the same time, this could be unfair to some jobs ahead in the queue. So we use a delay factor as a constraint to limit unfairness. We propose a branch and bound algorithm which selects jobs for backfilling which keep utilization high, while trying to stay close to First-Come-First-Served (FCFS). We evaluate relative response time and utilization and compare to other backfilling approaches. The selection of jobs for backfilling to optimize for high utilization and low delay is implemented as an extension of the existing Scojo-PECT preemptive scheduler

Novel control approaches for the next generation computer numerical control (CNC) system for hybrid micro-machines

It is well-recognised that micro-machining is a key enabling technology for manufacturing high value-added 3D micro-products, such as optics, moulds/dies and biomedical implants etc. These products are usually made of a wide range of engineering materials and possess complex freeform surfaces with tight tolerance on form accuracy and surface finish.In recent years, hybrid micro-machining technology has been developed to integrate several machining processes on one platform to tackle the manufacturing challenges for the aforementioned micro-products. However, the complexity of system integration and ever increasing demand for further enhanced productivity impose great challenges on current CNC systems. This thesis develops, implements and evaluates three novel control approaches to overcome the identified three major challenges, i.e. system integration, parametric interpolation and toolpath smoothing. These new control approaches provide solid foundation for the development of next generation CNC system for hybrid micro-machines.There is a growing trend for hybrid micro-machines to integrate more functional modules. Machine developers tend to choose modules from different vendors to satisfy the performance and cost requirements. However, those modules often possess proprietary hardware and software interfaces and the lack of plug-and-play solutions lead to tremendous difficulty in system integration. This thesis proposes a novel three-layer control architecture with component-based approach for system integration. The interaction of hardware is encapsulated into software components, while the data flow among different components is standardised. This approach therefore can significantly enhance the system flexibility. It has been successfully verified through the integration of a six-axis hybrid micro-machine. Parametric curves have been proven to be the optimal toolpath representation method for machining 3D micro-products with freeform surfaces, as they can eliminate the high-frequency fluctuation of feedrate and acceleration caused by the discontinuity in the first derivatives along linear or circular segmented toolpath. The interpolation for parametric curves is essentially an optimization problem, which is extremely difficult to get the time-optimal solution. This thesis develops a novel real-time interpolator for parametric curves (RTIPC), which provides a near time-optimal solution. It limits the machine dynamics (axial velocities, axial accelerations and jerk) and contour error through feedrate lookahead and acceleration lookahead operations. Experiments show that the RTIPC can simplify the coding significantly, and achieve up to ten times productivity than the industry standard linear interpolator. Furthermore, it is as efficient as the state-of-the-art Position-Velocity-Time (PVT) interpolator, while achieving much smoother motion profiles.Despite the fact that parametric curves have huge advantage in toolpath continuity, linear segmented toolpath is still dominantly used on the factory floor due to its straightforward coding and excellent compatibility with various CNC systems. This thesis presents a new real-time global toolpath smoothing algorithm, which bridges the gap in toolpath representation for CNC systems. This approach uses a cubic B-spline to approximate a sequence of linear segments. The approximation deviation is controlled by inserting and moving new control points on the control polygon. Experiments show that the proposed approach can increase the productivity by more than three times than the standard toolpath traversing algorithm, and 40% than the state-of-the-art corner blending algorithm, while achieving excellent surface finish.Finally, some further improvements for CNC systems, such as adaptive cutting force control and on-line machining parameters adjustment with metrology, are discussed in the future work section.It is well-recognised that micro-machining is a key enabling technology for manufacturing high value-added 3D micro-products, such as optics, moulds/dies and biomedical implants etc. These products are usually made of a wide range of engineering materials and possess complex freeform surfaces with tight tolerance on form accuracy and surface finish.In recent years, hybrid micro-machining technology has been developed to integrate several machining processes on one platform to tackle the manufacturing challenges for the aforementioned micro-products. However, the complexity of system integration and ever increasing demand for further enhanced productivity impose great challenges on current CNC systems. This thesis develops, implements and evaluates three novel control approaches to overcome the identified three major challenges, i.e. system integration, parametric interpolation and toolpath smoothing. These new control approaches provide solid foundation for the development of next generation CNC system for hybrid micro-machines.There is a growing trend for hybrid micro-machines to integrate more functional modules. Machine developers tend to choose modules from different vendors to satisfy the performance and cost requirements. However, those modules often possess proprietary hardware and software interfaces and the lack of plug-and-play solutions lead to tremendous difficulty in system integration. This thesis proposes a novel three-layer control architecture with component-based approach for system integration. The interaction of hardware is encapsulated into software components, while the data flow among different components is standardised. This approach therefore can significantly enhance the system flexibility. It has been successfully verified through the integration of a six-axis hybrid micro-machine. Parametric curves have been proven to be the optimal toolpath representation method for machining 3D micro-products with freeform surfaces, as they can eliminate the high-frequency fluctuation of feedrate and acceleration caused by the discontinuity in the first derivatives along linear or circular segmented toolpath. The interpolation for parametric curves is essentially an optimization problem, which is extremely difficult to get the time-optimal solution. This thesis develops a novel real-time interpolator for parametric curves (RTIPC), which provides a near time-optimal solution. It limits the machine dynamics (axial velocities, axial accelerations and jerk) and contour error through feedrate lookahead and acceleration lookahead operations. Experiments show that the RTIPC can simplify the coding significantly, and achieve up to ten times productivity than the industry standard linear interpolator. Furthermore, it is as efficient as the state-of-the-art Position-Velocity-Time (PVT) interpolator, while achieving much smoother motion profiles.Despite the fact that parametric curves have huge advantage in toolpath continuity, linear segmented toolpath is still dominantly used on the factory floor due to its straightforward coding and excellent compatibility with various CNC systems. This thesis presents a new real-time global toolpath smoothing algorithm, which bridges the gap in toolpath representation for CNC systems. This approach uses a cubic B-spline to approximate a sequence of linear segments. The approximation deviation is controlled by inserting and moving new control points on the control polygon. Experiments show that the proposed approach can increase the productivity by more than three times than the standard toolpath traversing algorithm, and 40% than the state-of-the-art corner blending algorithm, while achieving excellent surface finish.Finally, some further improvements for CNC systems, such as adaptive cutting force control and on-line machining parameters adjustment with metrology, are discussed in the future work section

Phase-based tuning for better utilized performance-asymmetric multicores

The latest trend towards performance asymmetry among cores on a single chip of a multicore processor is posing new software engineering challenges for developers. A key challenge is that for effective utilization of these performance-asymmetric multicore processors, application threads must be assigned to cores such that the resource needs of a thread closely matches resource availability at the assigned core. Determining this assignment manually is tedious, error prone, and it significantly complicates software development. We contribute a transparent and fully-automatic program analysis, which we call phase-guided tuning, to solve this problem. Phase-guided tuning adapts an application to effectively utilize performance-asymmetric cores of a processor. Our technique does not require any changes in the compiler or operating system, thus it is easy to deploy in existing tool chains. It does not require any input from the programmer except the application. Furthermore, it is independent of the characteristics (performance-asymmetry) of the target multicore processor, which has two benefits. First, it avoids the need to create multiple customizations of the binary for each target architecture, and second it relieves the programmer of the burden of anticipating the target architecture. Last but not least, our technique significantly improves performance. Compared to the stock Linux scheduler, our best technique shows 215% improvement in throughput and 36% average process speedup, while maintaining fairness and with negligible overheads