Solving a Slick Problem; Morally Preferable; Objectors by Conscience

News release announces a UD biologist\u27s solutions for cleaning up the massive oil spill in the Persian golf, a senior research scientist\u27s comments on the use of smart weapons in the Persian Gulf, and counseling concerning the selective service law and legal option for members of the UD community will be offered

Co-Inventor of Jet Engine to Donate Draper Prize Medal to UD

News release announces that Hans von Ohain will present the Charles Stark Draper medal to the University of Dayton

Provisioning and Performance Evaluation of Parallel Systems with Output Synchronization

Parallel server frameworks are widely deployed in modern large-data processing applications. Intuitively, splitting and parallel processing of the workload provides accelerated application response times and scaling flexibility. Examples of such frameworks include MapReduce, Hadoop, and Spark. For many applications, the dynamics of such systems are naturally captured by a Fork-Join (FJ) queuing model, where incoming jobs are split into tasks each of which is mapped to exactly one server. When all the tasks that belong to one job are executed, the job is reassembled and leaves the system. We consider this behavior at the output as a synchronization constraint. In this article, we study the performance of such parallel systems for different server properties, i.e., work-conservingness, phase-type behavior, and as suggested by recent evidence, for bursty input job arrivals. We establish a Large Deviations Principle for the steady-state job waiting times in an FJ system based on Markov-additive processes. Building on that,we present a performance analysis framework for FJ systems and provide computable bounds on the tail probabilities of the steady-state waiting times. We validate our bounds using estimates obtained through simulations. In addition, we define and analyze provisioning, a flexible division of jobs into tasks, in FJ systems. Finally, we use this framework together with real-world traces to show the benefits of an adaptive provisioning system that adjusts the service within an FJ system based on the arrival intensity

Optimizing Stochastic Scheduling in Fork-Join Queueing Models: Bounds and Applications

Fork-Join (FJ) queueing models capture the dynamics of system parallelization under synchronization constraints, for example, for applications such as MapReduce, multipath transmission and RAID systems. Arriving jobs are first split into tasks and mapped to servers for execution, such that a job can only leave the system when all of its tasks are executed. In this paper, we provide computable stochastic bounds for the waiting and response time distributions for heterogeneous FJ systems under general parallelization benefit. Our main contribution is a generalized mathematical framework for probabilistic server scheduling strategies that are essentially characterized by a probability distribution over the number of utilized servers, and the optimization thereof. We highlight the trade-off between the scaling benefit due to parallelization and the FJ inherent synchronization penalty. Further, we provide optimal scheduling strategies for arbitrary scaling regimes that map to different levels of parallelization benefit. One notable insight obtained from our results is that different applications with varying parallelization benefits result in different optimal strategies. Finally, we complement our analytical results by applying them to various applications showing the optimality of the proposed scheduling strategies.Comment: 16 pages, 8 figure

Optimizing Stochastic Scheduling in Fork-Join Queueing Models: Bounds and Applications

Fork-Join (FJ) queuing models capture the dynamics of system parallelization under synchronization constraints, for example, for applications such as MapReduce, multipath transmission and RAID systems. Arriving jobs are first split into tasks and mapped to servers for execution, such that a job can only leave the system when all of its tasks are executed. In this paper, we provide computable stochastic bounds for the waiting and response time distributions for heterogeneous FJ systems under general parallelization benefit. Our main contribution is a generalized mathematical framework for probabilistic server scheduling strategies that are essentially characterized by a probability distribution over the number of utilized servers, and the optimization thereof. We highlight the trade-off between the scaling benefit due to parallelization and the FJ inherent synchronization penalty. Further, we provide optimal scheduling strategies for arbitrary scaling regimes that map to different levels of parallelization benefit. One notable insight obtained from our results is that different applications with varying parallelization benefits result in different optimal strategies. Finally, we complement our analytical results by applying them to various applications showing the optimality of the proposed scheduling strategies

Quasi-steady-state approximations derived from the stochastic model of enzyme kinetics

The paper outlines a general approach to deriving quasi-steady-state approximations (QSSAs) of the stochastic reaction networks describing the Michaelis–Menten enzyme kinetics. In particular, it explains how different sets of assumptions about chemical species abundance and reaction rates lead to the standard QSSA, the total QSSA, and the reverse QSSA. These three QSSAs have been widely studied in the literature in deterministic ordinary differential equation settings, and several sets of conditions for their validity have been proposed. With the help of the multiscaling techniques introduced in Ball et al. (Ann Appl Probab 16(4):1925–1961, 2006), Kang and Kurtz (Ann Appl Probab 23(2):529–583, 2013), it is seen that the conditions for deterministic QSSAs largely agree (with some exceptions) with the ones for stochastic QSSAs in the large-volume limits. The paper also illustrates how the stochastic QSSA approach may be extended to more complex stochastic kinetic networks like, for instance, the enzyme–substrate–inhibitor system

Approximate Lumpability for Markovian Agent-based Models Using Local Symmetries

We study a Markovian agent-based model (MABM) in this paper. Each agent is endowed with a local state that changes over time as the agent interacts with its neighbours. The neighbourhood structure is given by a graph. In a recent paper [Simon et al. 2011], the authors used the automorphisms of the underlying graph to generate a lumpable partition of the joint state space ensuring Markovianness of the lumped process for binary dynamics. However, many large random graphs tend to become asymmetric rendering the automorphism-based lumping approach ineffective as a tool of model reduction. In order to mitigate this problem, we propose a lumping method based on a notion of local symmetry, which compares only local neighbourhoods of vertices. Since local symmetry only ensures approximate lumpability, we quantify the approximation error by means of Kullback-Leibler divergence rate between the original Markov chain and a lifted Markov chain. We prove the approximation error decreases monotonically. The connections to fibrations of graphs are also discussed.Comment: 28 pages, 4 figure