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In this paper, we shed new light on a classical scheduling problem: given a slot-timed, constant-capacity server, what short-run scheduling decisions must be made to provide long-run service guarantees to competing flows of unit-sized tasks? We model the flows long-run guarantees as worst-case services that map each arrival vector recording a flows cumulative task arrivals to a worst-case acceptable departure vector lower-bounding its cumulative task departures. We show that these services are states that can be updated as tasks arrive and depart, introduce state-based scheduling, and find the schedulability condition that must be preserved to maintain all flows long-run guarantees. We then use this condition to identify, in each slot, all short-run scheduling decisions that preserve schedulability. To illustrate how scheduling complexity can be reduced, we additionally show that special schedules can be efficiently identified by maximizing the servers capacity slack, and that special services can be efficiently specified and updated using properties of the min-plus algebra.
The method of significant moment analysis has been employed to derive instantaneous schedulability tests for real-time systems. However, the instantaneous schedulability can only be checked within a finite time window. On the other hand, worst-case s
This work attempts to approximate a linear Gaussian system with a finite-state hidden Markov model (HMM), which is found useful in solving sophisticated event-based state estimation problems. An indirect modeling approach is developed, wherein a stat
Frequency response and voltage support are vital ancillary services for power grids. In this paper, we design and experimentally validate a real-time control framework for battery energy storage systems (BESSs) to provide ancillary services to power
In Part I of this paper series, several macroscopic traffic model elements for mathematically describing freeway networks equipped with managed lane facilities were proposed. These modeling techniques seek to capture at the macroscopic the complex ph
State and parameter estimation is essential for process monitoring and control. Observability plays an important role in both state and parameter estimation. In simultaneous state and parameter estimation, the parameters are often augmented as extra