Competitive analysis of partitioned scheduling on uniform multiprocessors

Consider the problem of scheduling a set of sporadically arriving tasks on a uniform multiprocessor with the goal of meeting deadlines. A processor p has the speed Sp. Tasks can be preempted but they cannot migrate between processors. We propose an algorithm which can schedule all task sets that any other possible algorithm can schedule assuming that our algorithm is given processors that are three times faster.

Static-priority scheduling over wireless networks with multiple broadcast domains

We propose a wireless medium access control (MAC) protocol that provides static-priority scheduling of messages in a guaranteed collision-free manner. Our protocol supports multiple broadcast domains, resolves the wireless hidden terminal problem and allows for parallel transmissions across a mesh network. Arbitration of messages is achieved without the notion of a master coordinating node, global clock synchronization or out-of-band signaling. The protocol relies on bit-dominance similar to what is used in the CAN bus except that in order to operate on a wireless physical layer, nodes are not required to receive incoming bits while transmitting. The use of bit-dominance efficiently allows for a much larger number of priorities than would be possible using existing wireless solutions. A MAC protocol with these properties enables schedulability analysis of sporadic message streams in wireless multihop networks.

Competitive analysis of static-priority partitioned scheduling on uniform multiprocessors

Consider the problem of scheduling a set of sporadically arriving tasks on a uniform multiprocessor with the goal of meeting deadlines. A processor p has the speed Sp. Tasks can be preempted but they cannot migrate between processors. On each processor, tasks are scheduled according to rate-monotonic. We propose an algorithm that can schedule all task sets that any other possible algorithm can schedule assuming that our algorithm is given processors that are √2 / √2−1 ≈ 3.41 times faster. No such guarantees are previously known for partitioned static-priority scheduling on uniform multiprocessors.

Exploiting a prioritized MAC protocol to efficiently compute interpolations

Consider a network where all nodes share a single broadcast domain such as a wired broadcast network. Nodes take sensor readings but individual sensor readings are not the most important pieces of data in the system. Instead, we are interested in aggregated quantities of the sensor readings such as minimum and maximum values, the number of nodes and the median among a set of sensor readings on different nodes. In this paper we show that a prioritized medium access control (MAC) protocol may advantageously be exploited to efficiently compute aggregated quantities of sensor readings. In this context, we propose a distributed algorithm that has a very low time and message-complexity for computing certain aggregated quantities. Importantly, we show that if every sensor node knows its geographical location, then sensor data can be interpolated with our novel distributed algorithm, and the message-complexity of the algorithm is independent of the number of nodes. Such an interpolation of sensor data can be used to compute any desired function; for example the temperature gradient in a room (e.g., industrial plant) densely populated with sensor nodes, or the gas concentration gradient within a pipeline or traffic tunnel.

A two-competitive approximate schedulability analysis of CAN

Consider the problem of deciding whether a set of n sporadic message streams meet deadlines on a Controller Area Network (CAN) bus for a specified priority assignment. It is assumed that message streams have implicit deadlines and no release jitter. An algorithm to solve this problem is well known but unfortunately it time complexity is non-polynomial. We present an algorithm with polynomial time-complexity for computing an upper bound on the response times. Clearly, if the upper bound on the response time does not exceed the deadline then all deadlines are met. The pessimism of our approach is proven: if the upper bound of the response time exceeds the deadline then the response time exceeds the deadline as well for a CAN network with half the speed.

Exact analysis of TDMA with slot skipping

Consider a communication medium shared among a set of computer nodes; these computer nodes issue messages that are requested to be transmitted and they must finish their transmission before their respective deadlines. TDMA/SS is a protocol that solves this problem; it is a specific type of Time Division Multiple Access (TDMA) where a computer node is allowed to skip its time slot and then this time slot can be used by another computer node. We present an algorithm that computes exact queuing times for TDMA/SS in conjunction with Rate-Monotonic (RM) or Earliest- Deadline-First (EDF).

Delay-bounded medium access for unidirectional wireless links

Consider a wireless network where links may be unidirectional, that is, a computer node A can broadcast a message and computer node B will receive this message but if B broadcasts then A will not receive it. Assume that messages have deadlines. We propose a medium access control (MAC) protocol which replicates a message in time with carefully selected pauses between replicas, and in this way it guarantees that for every message at least one replica of that message is transmitted without collision. The protocol ensures this with no knowledge of the network topology and it requires neither synchronized clocks nor carrier sensing capabilities. We believe this result is significant because it is the only MAC protocol that offers an upper bound on the message queuing delay for unidirectional links without relying on synchronized clocks.

Linearizability and schedulability

Consider the problem of scheduling a set of tasks on a single processor such that deadlines are met. Assume that tasks may share data and that linearizability, the most common correctness condition for data sharing, must be satisfied. We find that linearizability can severely penalize schedulability. We identify, however, two special cases where linearizability causes no or not too large penalty on schedulability.

Preliminary discussion on globally prioritized medium access for multi-channel wireless systems

We discuss the development of a simple globally prioritized multi-channel medium access control (MAC) protocol for wireless networks. This protocol provides “hard” pre-run-time real-time guarantees to sporadic message streams, exploits a very large fraction of the capacity of all channels for “hard” real-time traffic and also makes it possible to fully utilize the channels with non real-time traffic when hard real-time messages do not request to be transmitted. The potential of such protocols for real-time applications is discussed and a schedulability analysis is also presented.

Uniprocessor EDF scheduling with mode change

Consider the problem of scheduling sporadically-arriving tasks with implicit deadlines using Earliest-Deadline-First (EDF) on a single processor. The system may undergo changes in its operational modes and therefore the characteristics of the task set may change at run-time. We consider a well-established previously published mode-change protocol and we show that if every mode utilizes at most 50% of the processing capacity then all deadlines are met. We also show that there exists a task set that misses a deadline although the utilization exceeds 50% by just an arbitrarily small amount. Finally, we present, for a relevant special case, an exact schedulability test for EDF with mode change.

The utilization bound of uniprocessor preemptive slack-monotonic scheduling is 50%

Consider the problem of scheduling a set of sporadically arriving implicit-deadline tasks to meet deadlines on a uniprocessor. Static-priority scheduling is considered using the slack-monotonic priority-assignment scheme. We prove that its utilization bound is 50%.

Schedulability analysis of generalized multiframe traffic on multihop-networks comprising software-implemented ethernet switches

Consider a multihop network comprising Ethernet switches. The traffic is described with flows and each flow is characterized by its source node, its destination node, its route and parameters in the generalized multiframe model. Output queues on Ethernet switches are scheduled by static-priority scheduling and tasks executing on the processor in an Ethernet switch are scheduled by stride scheduling. We present schedulability analysis for this setting.

Global static-priority preemptive multiprocessor scheduling with utilization bound 38%

Consider the problem of scheduling real-time tasks on a multiprocessor with the goal of meeting deadlines. Tasks arrive sporadically and have implicit deadlines, that is, the deadline of a task is equal to its minimum inter-arrival time. Consider this problem to be solved with global static-priority scheduling. We present a priority-assignment scheme with the property that if at most 38% of the processing capacity is requested then all deadlines are met.

Highly scalable aggregate computations in cyber-physical systems: physical environment meets communication protocols

In this paper, we focus on large-scale and dense Cyber- Physical Systems, and discuss methods that tightly integrate communication and computing with the underlying physical environment. We present Physical Dynamic Priority Dominance ((PD)2) protocol that exemplifies a key mechanism to devise low time-complexity communication protocols for large-scale networked sensor systems. We show that using this mechanism, one can compute aggregate quantities such as the maximum or minimum of sensor readings in a time-complexity that is equivalent to essentially one message exchange. We also illustrate the use of this mechanism in a more complex task of computing the interpolation of smooth as well as non-smooth sensor data in very low timecomplexity.

Sporadic multiprocessor scheduling with few preemptions

Consider the problem of scheduling n sporadic tasks so as to meet deadlines on m identical processors. A task is characterised by its minimum interarrival time and its worst-case execution time. Tasks are preemptible and may migrate between processors. We propose an algorithm with limited migration, configurable for a utilisation bound of 88% with few preemptions (and arbitrarily close to 100% with more preemptions).