Load balancing to adjust for proximity in some network topologies

Each job scheduler in large decentralized load balancing systems generally must consider whether it is advantageous to offload jobs to remote computation servers when the local load is too high. Although processing power may appear to be available at a very distant server, two problems arise due to the transmission delay between the scheduler and server. Predictably, the response time of the job is adversely affected as the job spends valuable time in transit, but a more subtle problem involves the value, or reliability, of the state information regarding job queues. The longer the delay between scheduler and server, the less a scheduler should value the state information of the server (given that the state changes over time). We examine the performance of schedulers in topologies with different average proximity and show a probabilistic algorithm that allows schedulers to dynamically form efficient clusters in the network.     

Randomized self-stabilizing and space optimal leader election under arbitrary scheduler on rings

We present a randomized self-stabilizing leader election protocol and a randomized self-stabilizing token circulation protocol under an arbitrary scheduler on anonymous and unidirectional rings of any size. These protocols are space optimal. We also give a formal and complete proof of these protocols. To this end, we develop a complete model for probabilistic self-stabilizing distributed systems which clearly separates the non deterministic behavior of the scheduler from the randomized behavior of the protocol. This framework includes all the necessary tools for proving the self- stabilization of a randomized distributed system: definition of a probabilistic space and definition of the self-stabilization of a randomized protocol. We also propose a new technique of scheduler management through a self-stabilizing protocol composition (cross-over composition). Roughly speaking, we force all computations to have a fairness property under any scheduler, even under an unfair one. This work was done while Maria Gradinariu was working at LRI, Univ. Paris-Sud, CNRS.     

Design and analysis of a class-aware recursive loop scheduler for class-based scheduling

In this paper, we consider the problem of devising a loop scheduler that allocates slots to users according to their relative weights as smoothly as possible. Instead of the existing notion of smoothness based on balancedness, we propose a variance-based metric which is more intuitive and easier to compute.We propose a recursive loop scheduler for a class-based scheduling scenario based on an optimal weighted round-robin scheduler. We show that it achieves very good allocation smoothness with almost no degradation in intra-class fairness. In addition, we also demonstrate the equivalence between our proposed metric and the balancedness-based metric.     

A logical duality for underspecified probabilistic systems

This paper establishes a Stone-type duality between specifications and infLMPs. An infLMP is a probabilistic process whose transitions satisfy super-additivity instead of additivity. Interestingly, its simple structure can encode a mix of probabilistic and non-deterministic behavior, which, as we show, is strongly related to another well-known such model: probabilistic automata. Our duality puts in relation the category of infLMPs and a category of abstract representations of them based on properties only. We exhibit a Galois connection between these categories and show that we have an adjunct pair of functors when restricted to LMPs only. Our duality also shows that an infLMP can be considered as a demonic representative of a system’s information. Moreover, it carries forward a view where states are less important, and events, or properties, become the main characters, as it should be in probability theory. Along the way, we show that bisimulation and simulation are naturally interpreted in this setting, and we exhibit the interesting relationship between infLMPs and the usual probabilistic modal logics. This paper is an extended version of a Concur ’09 paper [13]; in particular, the comparison of infLMPs with probabilistic automata and the Galois connection are new.     

Branching Bisimulation Congruence for Probabilistic Systems

The notion of branching bisimulation for the alternating model of probabilistic systems is not a congruence with respect to parallel composition. In this paper we first define another branching bisimulation in the more general model allowing consecutive probabilistic transitions, and we prove that it is compatible with parallel composition. We then show that our bisimulation is actually the coarsest congruence relation included in the existing branching bisimulation when restricted to the alternating model.     

Event-Triggered Real-Time Scheduling of Stabilizing Control Tasks

In this note, we revisit the problem of scheduling stabilizing control tasks on embedded processors. We start from the paradigm that a real-time scheduler could be regarded as a feedback controller that decides which task is executed at any given instant. This controller has for objective guaranteeing that (control unrelated) software tasks meet their deadlines and that stabilizing control tasks asymptotically stabilize the plant. We investigate a simple event-triggered scheduler based on this feedback paradigm and show how it leads to guaranteed performance thus relaxing the more traditional periodic execution requirements.     

The crowding approach to niching in genetic algorithms

A wide range of niching techniques have been investigated in evolutionary and genetic algorithms. In this article, we focus on niching using crowding techniques in the context of what we call local tournament algorithms. In addition to deterministic and probabilistic crowding, the family of local tournament algorithms includes the Metropolis algorithm, simulated annealing, restricted tournament selection, and parallel recombinative simulated annealing. We describe an algorithmic and analytical framework which is applicable to a wide range of crowding algorithms. As an example of utilizing this framework, we present and analyze the probabilistic crowding niching algorithm. Like the closely related deterministic crowding approach, probabilistic crowding is fast, simple, and requires no parameters beyond those of classical genetic algorithms. In probabilistic crowding, subpopulations are maintained reliably, and we show that it is possible to analyze and predict how this maintenance takes place. We also provide novel results for deterministic crowding, show how different crowding replacement rules can be combined in portfolios, and discuss population sizing. Our analysis is backed up by experiments that further increase the understanding of probabilistic crowding.     

Supervisory control for real-time scheduling of periodic and sporadic tasks with resource constraints

In the framework of supervisory control of timed discrete event systems, this paper addresses the design problem of a real-time scheduler that meets stringent time constraints of periodic tasks and sporadic tasks which exclusively access shared resources. For this purpose, we present the timed discrete event models of execution of periodic tasks and sporadic tasks and resource access for shared resources. Based on these models, we present the notion of deadlock-free and schedulable languages that contain only deadline-meeting sequences which do not reach deadlock states. In addition, we present the method of systematically computing the largest deadlock-free and schedulable language, and it is also shown that schedulability analysis can be done using this language. We further show that the real-time scheduler achieving the largest deadlock-free and schedulable language is optimal in the sense that there are no other schedulers to achieve schedulable cases more than those achieved by the optimal scheduler.     

Parallel evidence propagation on multicore processors

We propose a parallel evidence propagation method on general-purpose multicore processors. Evidence propagation is a major step in exact inference, a key problem in exploring probabilistic graphical models. We explore the parallelism in evidence propagation at various levels. First, given an arbitrary junction tree, we construct a directed acyclic graph (DAG) with weighted nodes, each denoting a computation task for evidence propagation. Since the execution time of the tasks varies significantly, we develop a workload-aware scheduler to allocate the tasks to the cores of the processors. The scheduler monitors the workload of each core and dynamically allocates tasks to support load balance across the cores. In addition, we integrate a module in the scheduler to partition the tasks converted from cliques with large potential tables so as to achieve improved load balance. We implemented the proposed method using Pthreads on both AMD and Intel quadcore processors. For a representative set of junction trees, our method achieved almost linear speedup. The execution time of our method was around twice as fast as an OpenMP-based implementation on both the platforms.     

Extracting safe thread schedules from incomplete model checking results

Model checkers frequently fail to completely verify a concurrent program, even if partial-order reduction is applied. The verification engineer is left in doubt whether the program is safe and the effort toward verifying the program is wasted. We present a technique that uses the results of such incomplete verification attempts to construct a (fair) scheduler that allows the safe execution of the partially verified concurrent program. This scheduler restricts the execution to schedules that have been proven safe (and prevents executions that were found to be erroneous). We evaluate the performance of our technique and show how it can be improved using partial-order reduction. While constraining the scheduler results in a considerable performance penalty in general, we show that in some cases our approach—somewhat surprisingly—even leads to faster executions.

     

Providing QoS with the Deficit Table Scheduler

A key component for networks with Quality of Service (QoS) support is the egress link scheduling algorithm. An ideal scheduling algorithm implemented in a high-performance network with QoS support should satisfy two main properties: good end-to-end delay and implementation simplicity. Table-based schedulers try to offer a simple implementation and good latency bounds. Some of the latest proposals of network technologies, like Advanced Switching and InfiniBand, include in their specifications one of these schedulers. However, these table-based schedulers do not work properly with variable packet sizes, as is usually the case in current network technologies. We have proposed a new table-based scheduler, which we have called Deficit Table (DTable) scheduler, that works properly with variable packet sizes. Moreover, we have proposed a methodology to configure this table-based scheduler in such a way that it permits us to decouple the bounding between the bandwidth and latency assignments. In this paper, we thoroughly review the provision of QoS with the DTable scheduler and our configuration methodology, and evaluate the performance of our proposals in a multimedia scenario. Simulation results show that our proposals are able to provide a similar latency performance than more complex scheduling algorithms. Moreover, we show the advantages of our decoupling configuration methodology over the usual ways of configuring this kind of table-based schedulers.     

A Probabilistic Scheduler for the Analysis of Cryptographic Protocols

When modelling cryto-protocols by means of process calculi which express both nondeterministic and probabilistic behavior, it is customary to view the scheduler as an intruder. It has been established that the traditional scheduler needs to be carefully calibrated in order to more accurately reflect the intruder's capabilities for controlling communication channels. We propose such a class of schedulers through a semantic variant called PPC_νσ, of the Probabilistic Poly-time Calculus (PPC) of Mitchell et al. [J.C. Mitchell, A. Ramanathan, A. Scedrov, and V. Teague. A probabilistic polynomial-time process calculus for the analysis of cryptographic protocols. Theoretical Computer Science, 353:118–164, 2006] and we illustrate the pertinence of our approach by an extensive study of the Dining Cryptographers (DCP) [David Chaum. The dining cryptographers problem: Unconditional sender and recipient untraceability. J. Cryptology, 1(1):65–75, 1988] protocol. Along these lines, we define a new characterization of Mitchell et al.'s observational equivalence [J.C. Mitchell, A. Ramanathan, A. Scedrov, and V. Teague. A probabilistic polynomial-time process calculus for the analysis of cryptographic protocols. Theoretical Computer Science, 353:118–164, 2006] more suited for taking into account any observable trace instead of just a single action as required in the analysis of the DCP.     

Admission Control with Immediate Notification

When admission control is used, an on-line scheduler chooses whether or not to complete each individual job successfully by its deadline. An important consideration is at what point in time the scheduler determines if a job request will be satisfied, and thus at what point the scheduler is able to provide notification to the job owner as to the fate of the request. In the loosest model, often seen in real-time systems, such a decision can be deferred up until the job's deadline passes. In the strictest model, more suitable for customer-based applications, a scheduler would be required to give notification at the instant that a job request arrives.Unfortunately there seems to be little existing research which explicitly studies the effect of the notification model on the performance guarantees of a scheduler. We undertake such a study by reexamining a problem from the literature. Specifically, we study the effect of the notification model on the non-preemptive scheduling of a single resource in order to maximize utilization. At first glance, it appears severely more restrictive to compare a scheduler required to give immediate notification to one which need not give any notification. Yet we are able to present alternate algorithms which provide immediate notification, while matching most of the performance guarantees which are possible by schedulers which provide no such notification. In only one case are we able to give evidence that providing immediate notification may be more difficult.     

On the Foundations of Probabilistic Relaxation with Product Support

Traditional probabilistic relaxation, as proposed by Rosenfeld, Hummel and Zucker, uses a support function which is a double sum over neighboring nodes and labels. Recently, Pelillo has shown the relevance of the Baum-Eagon theorem to the traditional formulation. Traditional probabilistic relaxation is now well understood in an optimization framework.Kittler and Hancock have suggested a form of probabilistic relaxation with product support, based on an evidence combining formula. In this paper we present a formal basis for Kittler and Hancocks probabilistic relaxation. We show that it too has close links with the Baum-Eagon theorem, and may be understood in an optimization framework. We provide some proofs to show that a stable stationary point must be a local maximum of an objective function.We present a new form of probabilistic relaxation that can be used as an approximate maximizer of the global labeling with maximum posterior probability.     

Determinization of timed Petri nets behaviors

In this paper we are interested in sequentialization of formal power series with coefficients in the semiring \((\mathbb {R}\cup \{- \infty \},\max ,+)\) which represent the behavior of timed Petri nets. Several approaches make it possible to derive nondeterministic (max, + ) automata modeling safe timed Petri nets. Their nondeterminism is a serious drawback since determinism is a crucial property for numerous results on (max, + ) automata (in particular, for applications to performance evaluation and control) and existing procedures for determinization succeed only for restrictive classes of (max, + ) automata. We present a natural semi-algorithm for determinization of behaviors based on the semantics of bounded timed Petri nets. The resulting deterministic (max, + ) automata can be infinite, but a sufficient condition called strong liveness is proposed to ensure the termination of the semi-algorithm. It is shown that strong liveness is closely related to bounded fairness, which has been widely studied for Petri nets and other models for concurrency. Moreover, if the net cannot be sequentialized we propose a restriction of its logical behavior so that the sufficient condition becomes satisfied for the restricted net. The restriction is based on the synchronous product with non injectively labeled scheduler nets that are built in an incremental hierarchical way from simple scheduler nets.     

Algebraic analysis of the generating functional for discrete random sets and statistical inference for intensity in the discrete Boolean random-set model

We consider binary digital images as realizations of a uniformly bounded discrete random set, a mathematical object that can be defined directly on a finite lattice. In this setting we show that it is possible to move between two equivalent probabilistic model specifications. We formulate a restricted version of the discrete-case analog of a Boolean random-set model, obtain its probability mass function, and use some methods of morphological image analysis to derive tools for its statistical inference.This research was partially supported by National Science Foundation grant NSFD CDR 8803012 through the Engineering Research Centers program.     

Scheduling in the situation calculus: A case study

We illustrate the utility of the situation calculus for representing complex scheduling tasks by axiomatizing a deadline driven scheduler in the language. The actions arising in such a scheduler are examples of natural actions, as investigated in the concurrent situation calculus by Pinto (PhD thesis, 1994), and later by Reiter (Proc. Common Sense 96, 1996). Because the deadline driven scheduler is sequential, we must first suitably modify Reiter's approach to natural actions so it applies to the sequential case. Having done this, we then show how the situation calculus axiomatization of this scheduler yields a very simple simulator in GOLOG, a situation calculus-based logic programming language for dynamic domains. This revised version was published online in June 2006 with corrections to the Cover Date.     

Knowledge Compilation Meets Database Theory: Compiling Queries to Decision Diagrams

The goal of Knowledge Compilation is to represent a Boolean expression in a format in which it can answer a range of “online-queries” in PTIME. The online-query of main interest to us is model counting, because of its application to query evaluation on probabilistic databases, but other online-queries can be supported as well such as testing for equivalence, testing for implication, etc. In this paper we study the following problem: given a database query q, decide whether its lineage can be compiled efficiently into a given target language. We consider four target languages, of strictly increasing expressive power (when the size of compilation is restricted to be polynomial in the data size): read-once Boolean formulae, OBDD, FBDD and d-DNNF. For each target, we study the class of database queries that admit polynomial size representation: these queries can also be evaluated in PTIME over probabilistic databases. When queries are restricted to conjunctive queries without self-joins, it was known that these four classes collapse to the class of hierarchical queries, which is also the class of PTIME queries over probabilistic databases. Our main result in this paper is that, in the case of Unions of Conjunctive Queries (UCQ), these classes form a strict hierarchy. Thus, unlike conjunctive queries without self-joins, the expressive power of UCQ differs considerably with respect to these target compilation languages. Moreover, we give a complete characterization of the first two target languages, based on the query’s syntax.     

A unification of probabilistic choice within a design-based model of reversible computation

We see reversible computing as a generalisation of sequential computation obtained by revoking the law of the excluded miracle. Our execution language includes naked guarded commands and non-deterministic choice. Choices which lead to miraculous continuations invoke reverse computation, and non-deterministic choice plays the rôle of provisional choice within a backtracking context. We require probabilistic choice for symmetry breaking and sampling large search spaces, but must formulate it differently from previous approaches to obtain the required interactions between probabilistic choice and non-deterministic choice and between probabilistic choice and feasibility. Our formulation allows us to derive the post-distributions which characterise a program, and we use these to construct a relational model. We consider refinement as containment of convex closures within distribution space, qualified with additional conditions to avoid over-refinement. We link the non-probabilistic and probabilistic versions of the model with a Galois connection and show that classical designs are a retract of our probabilistic designs. We consider the interaction between probabilistic and non-deterministic choice and find the same initially counter-intuitive results that have been noted by other investigators. We provide an alternative formulation, within the same model, of oblivious non-determinism, which allows all non-deterministic choices to be moved to the start of a computation. We consider the interaction between probabilistic choice and feasibility that is required to match an operational interpretation in which infeasible commands provoke reverse execution, and we present a small case study to show how the interaction between probabilistic choice and feasibility can be exploited in a practical program. All programming structures described here are supported by our implementation platform, the Reversible Virtual Machine, whose development has accompanied our theoretical investigations.     

DESCRIPTION OF PROBABILISTICAL SYSTEMS WITH STRONGLY STATISTICALLY DEPENDENT ELEMENTS

We propose the f-divergences of two probability distributions as the measures of the organization of a probabilistic system with respect to its probabilistic uncertainty. A probabilistic system consist of stochastical objects on which random variables are defined which are statistically dependent. Using Shannon's f-divergence for the organization of a probabilistic system we express it in terms of the probability distributions of the element random variables and their statistical linkages. Then we find the maximum entropy of a probabilistic system if the statistical linkages between its elements are given as input data. We show that an important class of physical statistical systems can be described by the probabilistic systems of Gibbsian type.