Vincenzo Bonifaci

The Preemptive Uniprocessor Scheduling of Mixed-Criticality Implicit-Deadline Sporadic Task Systems

Systems in many safety-critical application domains are subject to certification requirements. For any given system, however, it may be the case that only a subset of its functionality is safety-critical and hence subject to certification, the rest of the functionality is non safety critical and does not need to be certified, or is certified to a lower level of assurance. An algorithm called EDF-VD (for Earliest Deadline First with Virtual Deadlines) is described for the scheduling of such mixed-criticality task systems. Analyses of EDF-VD significantly superior to previously-known ones are presented, based on metrics such as processor speedup factor (EDF-VD is proved to be optimal with respect to this metric) and utilization bounds.

Mixed-criticality scheduling of sporadic task systems

We consider the scheduling of mixed-criticality task systems, that is, systems where each task to be scheduled has multiple levels of worst-case execution time estimates. We design a scheduling algorithm, EDF-VD, whose effectiveness we analyze using the processor speedup metric: we show that any 2-level task system that is schedulable on a unit-speed processor is correctly scheduled by EDF-VD using speed φ here φ 2 criticality levels. We finally consider 2-level instances on m identical machines. We prove speedup bounds for scheduling an independent collection of jobs and for the partitioned scheduling of a 2-level task system.

Stackelberg Routing in Arbitrary Networks

We investigate the impact of Stackelberg routing to reduce the price of anarchy in network routing games. In this setting, an α fraction of the entire demand is first routed centrally according to a predefined Stackelberg strategy and the remaining demand is then routed selfishly by (nonatomic) players. Although several advances have been made recently in proving that Stackelberg routing can, in fact, significantly reduce the price of anarchy for certain network topologies, the central question of whether this holds true in general is still open. We answer this question negatively by constructing a family of single-commodity instances such that every Stackelberg strategy induces a price of anarchy that grows linearly with the size of the network. Moreover, we prove upper bounds on the price of anarchy of the largest-latency-first (LLF) strategy that only depend on the size of the network. Besides other implications, this rules out the possibility to construct constant-size networks to prove an unbounded price of anarchy. In light of this negative result, we consider bicriteria bounds. We develop an efficiently computable Stackelberg strategy that induces a flow whose cost is at most the cost of an optimal flow with respect to demands scaled by a factor of 1 + √1-α. Finally, we analyze the effectiveness of an easy-to-implement Stackelberg strategy, called SCALE. We prove bounds for a general class of latency functions that includes polynomial latency functions as a special case. Our analysis is based on an approach that is simple yet powerful enough to obtain (almost) tight bounds for SCALE in general networks.

Feasibility Analysis of Sporadic Real-Time Multiprocessor Task Systems

We give the first algorithm for testing the feasibility of a system of sporadic real-time tasks on a set of identical processors, solving an open problem in the area of multiprocessor real-time scheduling (Baruah and Pruhs in Journal of Scheduling 13(6):577–582, 2009). We also investigate the related notion of schedulability and a notion that we call online feasibility. Finally, we show that discrete-time schedules are as powerful as continuous-time schedules, which answers another open question in the above mentioned survey.

Physarum can compute shortest paths: convergence proofs and complexity bounds

Physarum polycephalum is a slime mold that is apparently able to solve shortest path problems. A mathematical model for the slimes behavior in the form of a coupled system of differential equations was proposed by Tero, Kobayashi and Nakagaki [TKN07]. We prove that a discretization of the model (Euler integration) computes a (1+e)-approximation of the shortest path in O( mL (logn+logL)/e3) iterations, with arithmetic on numbers of O(log(nL/e)) bits; here, n and m are the number of nodes and edges of the graph, respectively, and L is the largest length of an edge. We also obtain two results for a directed Physarum model proposed by Ito et al. [IJNT11]: convergence in the general, nonuniform case and convergence and complexity bounds for the discretization of the uniform case.

Data Gathering in Wireless Networks

In this chapter, we address the problem of gathering information in a specific node of a radio network when interference constraints are present. Nodes can communicate data using a radio device; we consider a synchronous time model, where time is divided into rounds. The interference constraints limit the possibility of simultaneous data communication of nodes to the same region of the network. The survey focuses on two interference models, the general interference model and the distance-2 interference model. We survey recent complexity results and approximation algorithms for several variants of the problem. We consider several interference scenarios, the uniform and non-uniform data models, different optimization parameters, and the off-line and online settings of the problem. The objective functions we consider are the minimization of maximum completion time, maximum flow time, and average flow time.

A Constant-Approximate Feasibility Test for Multiprocessor Real-Time Scheduling

We devise the first constant-approximate feasibility test for sporadic multiprocessor real-time scheduling. We give an algorithm that, given a task system and i¾?> 0, correctly decides either that the task system can be scheduled using the earliest deadline first algorithm on mspeed-(2 i¾? 1/m+ i¾?) machines, or that the system is infeasible for mspeed-1 machines. The running time of the algorithm is polynomial in the size of the task system and 1/i¾?. We also provide an improved bound trading off speed for additional machines. Our analysis relies on a new concept for counting the workload of an interval, that might also turn useful for analyzing other types of task systems.

Minimizing flow time in the wireless gathering problem

We address the problem of efficient data gathering in a wireless network through multihop communication. We focus on two objectives related to flow times, that is, the times spent by data packets in the system: minimization of the maximum flow time and minimization of the average flow time of the packets. For both problems we prove that, unless P=NP, no polynomial-time algorithm can approximate the optimal solution within a factor less than Ω(m1−&epsis;) for any 0<&epsis;<1, where m is the number of packets. We then assess the performance of two natural algorithms by proving that their cost remains within the optimal cost of the respective problem if we allow the algorithms to transmit data at a speed 5 times higher than that of the optimal solutions to which we compare them.

Feasibility analysis of sporadic real-time multiprocessor task systems

We give the first algorithm for testing the feasibility of a system of sporadic real-time tasks on a set of identical processors, solving an open problem in the area of multiprocessor real-time scheduling [S. Baruah and K. Pruhs, Journal of Scheduling, 2009]. We also investigate the related notion of schedulability and a notion that we call online feasibility. Finally, we show that discrete-time schedules are as powerful as continuous-time schedules, which answers another open question in the above mentioned survey.

The Distributed Wireless Gathering Problem

We address the problem of data gathering in a wireless network using multihop communication; our main goal is the analysis of simple algorithms suitable for implementation in realistic scenarios. We study the performance of distributed algorithms, which do not use any form of local coordination, and we focus on the objective of minimizing average flow times of data packets. We prove a lower bound of ?(logm) on the competitive ratio of any distributed algorithm minimizing the maximum flow time, where mis the number of packets. Next, we consider a distributed algorithm which sends packets over shortest paths, and we use resource augmentation to analyze its performance when the objective is to minimize the average flow time. If interferences are modeled as in Bar-Yehuda et al. (J. of Computer and Systems Science, 1992) we prove that the algorithm is (1 + ?)-competitive, when the algorithm sends packets a factor O(log(?/?) logΔ) faster than the optimal offline solution; here ?is the diameter of the network and Δthe maximum degree. We finally extend this result to a more complex interference model.