Pfair scheduling of generalized pinwheel task systems

[[abstract]]The scheduling of generalized pinwheel task systems is considered. It is shown that pinwheel scheduling is closely related to the fair scheduling of periodic task systems. This relationship is exploited to obtain new scheduling algorithms for generalized pinwheel task systems. When compared to traditional pinwheel scheduling algorithms, these new algorithms are both more efficient from a run-time complexity point of view, and have a higher density threshold, on a very large subclass of generalized pinwheel task systems.

Bamboo Garden Trimming Problem (Perpetual Maintenance of Machines with Different Attendance Urgency Factors)

International audienc

Quasi-regular sequences and optimal schedules for security games

We study security games in which a defender commits to a mixed strategy for protecting a finite set of targets of different values. An attacker, knowing the defender's strategy, chooses which target to attack and for how long. If the attacker spends time $t$ at a target $i$ of value $\alpha_i$, and if he leaves before the defender visits the target, his utility is $t \cdot \alpha_i$; if the defender visits before he leaves, his utility is 0. The defender's goal is to minimize the attacker's utility. The defender's strategy consists of a schedule for visiting the targets; it takes her unit time to switch between targets. Such games are a simplified model of a number of real-world scenarios such as protecting computer networks from intruders, crops from thieves, etc. We show that optimal defender play for this continuous time security games reduces to the solution of a combinatorial question regarding the existence of infinite sequences over a finite alphabet, with the following properties for each symbol $i$: (1) $i$ constitutes a prescribed fraction $p_i$ of the sequence. (2) The occurrences of $i$ are spread apart close to evenly, in that the ratio of the longest to shortest interval between consecutive occurrences is bounded by a parameter $K$. We call such sequences $K$-quasi-regular. We show that, surprisingly, $2$-quasi-regular sequences suffice for optimal defender play. What is more, even randomized $2$-quasi-regular sequences suffice for optimality. We show that such sequences always exist, and can be calculated efficiently. The question of the least $K$ for which deterministic $K$-quasi-regular sequences exist is fascinating. Using an ergodic theoretical approach, we show that deterministic $3$-quasi-regular sequences always exist. For $2 \leq K < 3$ we do not know whether deterministic $K$-quasi-regular sequences always exist.Comment: to appear in Proc. of SODA 201

Perpetual maintenance of machines with different urgency requirements

A garden $G$ is populated by $n\ge 1$ bamboos $b_1, b_2, ..., b_n$ with the respective daily growth rates $h_1 \ge h_2 \ge \dots \ge h_n$. It is assumed that the initial heights of bamboos are zero. The robotic gardener maintaining the garden regularly attends bamboos and trims them to height zero according to some schedule. The Bamboo Garden Trimming Problem (BGT) is to design a perpetual schedule of cuts to maintain the elevation of the bamboo garden as low as possible. The bamboo garden is a metaphor for a collection of machines which have to be serviced, with different frequencies, by a robot which can service only one machine at a time. The objective is to design a perpetual schedule of servicing which minimizes the maximum (weighted) waiting time for servicing. We consider two variants of BGT. In discrete BGT the robot trims only one bamboo at the end of each day. In continuous BGT the bamboos can be cut at any time, however, the robot needs time to move from one bamboo to the next. For discrete BGT, we show a simple $4$-approximation algorithm and, by exploiting relationship between BGT and the classical Pinwheel scheduling problem, we derive a $2$-approximation algorithm for the general case and a tighter approximation when the growth rates are balanced. A by-product of this last approximation algorithm is that it settles one of the conjectures about the Pinwheel problem. For continuous BGT, we propose approximation algorithms which achieve approximation ratios $O(\log (h_1/h_n))$ and $O(\log n)$

Patrolling a path connecting a set of points with unbalanced frequencies of visits

Patrolling consists of scheduling perpetual movements of a collection of mobile robots, so that each point of the environment is regularly revisited by any robot in the collection. In previous research, it was assumed that all points of the environment needed to be revisited with the same minimal frequency. In this paper we study efficient patrolling protocols for points located on a path, where each point may have a different constraint on frequency of visits. The problem of visiting such divergent points was recently posed by Gąsieniec et al. in [14], where the authors study protocols using a single robot patrolling a set of n points located in nodes of a complete graph and in Euclidean spaces. The focus in this paper is on patrolling with two robots. We adopt a scenario in which all points to be patrolled are located on a line. We provide several approximation algorithms concluding with the best currently known 3 -approximation

Timing analysis in existing and emerging cyber physical systems

A main mission of safety-critical cyber-physical systems is to guarantee timing correctness. The examples of safety- critical systems are avionic, automotive or medical systems in which timing violations could have disastrous effects, from loss of human life to damage to machines and/or the environment. Over the past decade, multicore processors have become increasingly common for their potential of efficiency, which has made new single-core processors become relatively scarce. As a result, it has created a pressing need to transition to multicore processors. However, existing safety-critical software that has been certified on single-core processors is not allowed to be fielded on a multicore system as is. The issue stems from, namely, serious inter- core interference problems on shared resources in current multicore processors, which create non-deterministic timing behavior. Since meeting the timing constraints is the crucial requirement of safety-critical real-time systems, the use of more than one core in a multicore chip is currently not certified yet by the authorities. Academia has paid relatively little attention to non-determinism due to uncoordinated I/O communications, as compared with other resources such as cache or memory, although industry considers it as one of the most troublesome challenges. Hence we focused on I/O synchronization, requiring no information of Worst Case Execution Time (WCET) that can get impacted by other interference sources. Traditionally, a two-level scheduling, such as Integrated Modular Avionics system (IMA), has been used for providing temporal isolation capability. However, such hierarchical approaches introduce significant priority inversions across applications, especially in multicore systems, ultimately leading to lower system utilization. To address these issues, we have proposed a novel scheduling mechanism called budgeted generalized rate monotonic analysis (Budgeted GRMS) in which different applications’ tasks are globally scheduled for avoiding unnecessary priority inversions, yet the CPU resource is still partitioned for temporal isolation among applications. Incorporating the issues of no information of WCETs and I/O synchronization, this new scheduling paradigm enables the “safe” use of multicore processors in safety-critical real-time systems. Recently, newly emerging Internet of Things (IoT) and Smart City applications are becoming a part of cyber- physical systems, as the needs are required and the feasibility are getting visible. What we need to pay attention to is that the promises and challenges arising from IoT and Smart City applications are providing new research landscapes and opportunities and fundamentally transforming real-time scheduling. As mentioned earlier, in traditional real-time systems, an instance of a program execution (a process) is described as a scheduling entity, while, in the emerging applications, the fundamental schedulable units are chunks of data transported over communication media. Another transformation is that, in IoT and Smart City applications, there are multiple options and combinations to choose to utilize and schedule since there are massively deployed heterogeneous kinds of sensing devices. This is contrary to the existing real-time work which is given a fixed task set to be analyzed. For that reason, they also suggest variants of performance or quality optimization problems. Suppose a disaster response infrastructure in a troubled area to ensure safety of humanitarian missions. Cameras and other sensors are deployed along key routes to monitor local conditions, but turned off by default and turned on on-demand to save limited battery life. To determine a safe route to deliver humanitarian shipments, a decision-maker must collect reconnaissance information and schedule the data items to support timely decision-making. Such data items acquired from the time-evolving physical world are in general time-sensitive - a retrieved item may become stale and no longer be accurate/relevant as conditions in the physical environment change. Therefore, “when to acquire” affects the performance and correctness of such applications and thus the overall system safety and data timeliness should be carefully considered. For the addressed problem, we explored various algorithmic options for maximizing quality of information, and developed the optimal algorithm for the order of retrievals of data items to make multiple decisions. I believe this is a significant initial step toward expanding timing-safety research landscapes and opportunities in the emerging CPS area

Improving Candidate-Quality Preference-Specification Mechanisms: Incorporating (Gender-Empowering) Voter-Chosen Quotas

I conceptualize the informal outlines of a new voting system/mechanism that is more holistic and democratically just; the proposed alternative would incorporate (gender) quotas amongst other fundamental, important aspects. This conceptual outline seeks to resolve the primary (intellectual) obstacles for the adoption of quotas in their current form which, I contend, is their discordance with mainstream conceptions of democratic justice. More precisely, the conceptualized voting system/mechanism seeks to increase the sophistication of preference-specification in voting procedures (thereby presenting an alternative to the prevailing, privileged paradigm of geospatial-constituency representation). I do not present results in the conventional sense; no data was analysed, no experiments run, and no software implemented. A rationale is provided for why this proposed voting system/mechanism, in addition to potentially solving/tackling some problems identified by feminist scholarship, could also solve an even larger class of fundamental political and democratic problems related to intersectionality (e.g., race, ethnicity, income, class, caste, disability, sexuality, education, age, occupation etc.) through enhancing the translation, representation, and implementation of voters’ interests. In terms of conclusions within the paper, they are largely intermediate conclusions as they relate to the investigation of problems as well as the informal conceptual outline of the proposed voting system/mechanism