Computable Bounds in Fork-Join Queueing Systems

The Stroop interference effect—slower responses to the color of an incongruent color-word stimulus (e.g., GREEN in red ink) compared to a neutral stimulus (e.g., XXXX in red ink)—is one of the most robust findings in cognitive psychology. This thesis investigated why the effect is so robust, focusing on the unique perceptual architecture of the Stroop stimulus. Specifically, in a Stroop stimulus, the visual word form and color are integrated into a visual object, and hence attending to the color inevitably results in the word receiving attention as well. Across four empirical chapters, I demonstrated that presenting the distractor word in advance of a Stroop stimulus (a manipulation termed <i>distractor priming</i>—e.g., presenting the word GREEN in white ink followed by the same word GREEN in red ink) significantly reduced—and in some cases eliminated—the Stroop interference effect. I argued that this occurred because the distractor prime broke the integration of the visual word form and color in the Stroop stimulus, allowing rapid disengagement of attention from the word. Crucially, I examined response time (RT) distributions. In standard Stroop stimuli, the interference effect increased with slower responses, yielding a positively sloped delta plot. When the integration was disrupted by distractor priming, the delta slope flattened—that is, the interference effect remained constant across the RT distribution. Chapter 2 introduced the distractor priming paradigm. Consistent with prior studies of distractor priming that used oral color-naming responses, distractor priming in a manual Stroop task sped up responses to the color. Importantly, it eliminated the Stroop interference effect across the entire RT distribution (i.e., it removed the positively sloped delta). Chapter 3 demonstrated that this reduction in Stroop interference and removal of the positively sloped delta occurred only with a prime visually identical to the distractor. Stroop interference remained large, and the positively sloped delta persisted when the prime was conceptually related but not visually identical to the distractor word (e.g., LEAF - GREENred) or an auditory word (e.g., hearing “green”). Chapter 4 explored the relative “automaticity” of the distractor priming benefit and demonstrated that even when the word precue was only 50% predictive of the upcoming distractor word (unlike 100% as in the previous studies), Stroop interference was reduced and the positively sloped delta removed. Additionally, this experiment showed that the delta slope pattern of the Stroop interference effect found in the distractor-primed (identity precue) condition differed from that in the response-precue condition (e.g., the word RED followed by the word GREEN in red ink). Chapter 5 tested the assumption underlying the distractor priming benefit—that the positively sloped delta was removed when the integration between the word and color was disrupted—using the primed Stroop task. This paradigm differed from the standard Stroop task in that the word and color were not integrated into a single visual object; instead, the distractor word was presented ahead of a row of colored Xs. Across two experiments, RT distributions in the primed Stroop task mirrored those in distractor priming, in that Stroop interference was small and the positively sloped delta was eliminated. Together, these findings indicate that the robustness of the Stroop interference effect stems from the perceptual integration of the distractor word and color into a single visual object. Chapter 6 provides a discussion of the implication of our interpretation of Stroop interference on how the Stroop task is used as a tool to study selective attention.

Although response times (RTs) are the dependent measure of choice in the majority of studies of visual attention, changes in RTs can be hard to interpret. First, they are inherently ambiguous, since they may reflect a change in the central tendency or skew (or both) of a distribution. Second, RT measures may lack sensitivity, since meaningful changes in RT patterns may not be picked up if they reflect two or more processes having opposing influences on mean RTs. Here we describe RT distributions for repetition priming in visual search, fitting ex-Gaussian functions to RT distributions. We focus here on feature and conjunction search tasks, since priming effects in these tasks are often thought to reflect similar mechanisms. As expected, both tasks resulted in strong priming effects when target and distractor identities repeated, but a large difference between feature and conjunction search was also seen, in that the σ parameter (reflecting the standard deviation of the Gaussian component) was far more affected by search repetition in conjunction than in feature search. Although caution should clearly be used when particular parameter estimates are matched to specific functions or processes, our results suggest that analyses of RT distributions can inform theoretical accounts of priming in visual search tasks, in this case showing quite different repetition effects for the two differing search types, suggesting that priming in the two paradigms partly reflects different mechanisms.

In this paper, we describe an elementary combinatorial approach for deriving the waiting and response time distributions in a few classical priority queueing models. By making use of lattice paths that are linked in a natural way to the stochastic processes analyzed, the proposed method offers new insights and complements the results previously obtained by inverting the associated Laplace transforms.

In response time (RT) research, RT outliers are typically excluded from statistical analysis to improve the signal-to-noise ratio. Nevertheless, there exist several methods for outlier exclusion. This poses the question, how these methods differ with respect to recovering the uncontaminated RT distribution. In the present simulation study, two RT distributions with a given population difference were simulated in each iteration. RTs were replaced by outliers following two different approaches. The first approach generated outliers at the tails of the distribution, the second one inserted outliers overlapping with the genuine RT distribution. We applied ten different outlier exclusion methods and tested, how many pairs of distributions significantly differed. Outlier exclusion methods were compared in terms of bias. Bias was defined as the deviation of the proportion of significant differences after outlier exclusion from the proportion of significant differences in the uncontaminated samples (before introducing outliers). Our results showed large differences in bias between the exclusion methods. Some methods showed a high rate of Type-I errors and should therefore clearly not be used. Overall, our results showed that applying an exclusion method based on z-scores / standard deviations introduced only small biases, while the absence of outlier exclusion showed the largest absolute bias.

Previous analyses of response time distributions have shown that the Stroop effect is observed in the mode (μ) and standard deviation (σ) of the normal part of the distribution, as well as its tail (τ). Specifically, interference related to semantic and response processes has been suggested to specifically affect the mode and tail, respectively. However, only one study in the literature has directly manipulated semantic interference, and none manipulating response interference. The present research aims to address this gap by manipulating both semantic and response interference in a manual response Stroop task, and examining how these components of Stroop interference affect the response time distribution. Ex-Gaussian analysis showed both semantic and response conflict to only affect τ. Analyzing the distribution by rank-ordered response times (Vincentizing) showed converging results as the magnitude of both semantic and response conflict increased with slower response times. Additionally, response conflict appeared earlier on the distribution compared to semantic conflict. These findings further highlight the difficulty in attributing specific psychological processes to different parameters (i.e., μ, σ, and τ). The effect of different response modalities on the makeup of Stroop interference is also discussed.

In this work, a preliminary conceptual model of the hydrogeological functioning of a binary karst aquifer located in southern Spain is presented, based on the natural responses of the springs and the dye tracer tests. Results derived from the long-term analysis of cross-correlation function (CCF) (global average time of recharge input) have been validated with those obtained from a dye tracer test, performed during a specific recharge event. The overall response times (CCF results) obtained for the three springs studied were 58 (SP-1), 72 (SP-3), and 81 h (SP-2). This pattern in response times was contrasted with the first detection times of the BTC-Tracer Breakthrough Curve—at the same three springs (30.9, 35.3, and 47 h) and their respective recovery rates (2.03, 21.9, and 78.4% for S1, S2, and S3, respectively). The distribution of response times, both those determined by long-term statistical analysis and the ones derived from the use of dye tracer test, is directly related to the karst network development in each of the drainage routes. Additionally, the rate of tracer recovery at each of the springs is linked to the hierarchy of flow paths from the selected injection point toward each spring, within the overall drainage network scheme. An accurate knowledge of all factors affecting the hydrogeological behavior as well as groundwater flow paths (from swallow holes to the springs) is crucial for suitable management of the resource and to mitigate the pollution risks derived from fast infiltration of surface water.KeywordsCross-correlationDye tracer testKarst aquiferTime lagAquifer functioning

The current study examined the effects of responses on error-adjacent trials (i.e., those immediately preceding or following errors) on age differences in measures of intraindividual variability and the shape of response time (RT) distributions on a two-back task. Removing error-adjacent responses reduced variability as measured by the coefficient of variation, but did so similarly for younger and older adults. However, older adults’ standard deviations (SDs) were less than those of younger adults with comparable RTs, raising questions regarding the validity of the coefficient of variation. An ex-Gaussian analysis revealed that removing the RTs on error-adjacent trials reduced the length of the tails of distributions and the skewness of the distributions. These properties were reduced more for older adults than for younger adults. These results indicate that the influence of error-adjacent trials should be considered when analyzing intraindividual variability and the shape of RT distributions to test theories of cognitive aging.

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, e.g., 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.

The mental experience of attention capture has attracted a great deal of intrigue among researchers seeking to explain the interactions between stimulus-driven and goal-driven attentional control. In recent years, researchers have increasingly begun to analyze cumulative response time (RT) distributions to test modern accounts of the capture phenomenon, particularly accounts claiming that there are changes in susceptibility to distraction as a function of time. In this paper, we raise a criticism of this approach, which centers on a problematic assumption. The assumption is that variability in these distributions is primarily determined by fluctuations in the observer's internal control state (e.g., readiness for the trial). However, it is also the case that faster segments of the distributions are overrepresented by trials that are objectively easy, while slower segments are overrepresented by trials that are objectively difficult. That is, incidental aspects of the trial stimuli influence task performance independently of the observer's internal control state. Here, we demonstrate empirically that contributions of incidental stimulus factors distort cumulative RT distributions in such a way that confounds proper interpretation of experimental data. The results have implications for theoretical accounts of attentional control, and they also raise caution about the assumptions that are sometimes made when analyzing cumulative RT distributions.

A transaction scheduling mechanism is designed for a shared memory, multiprocessor database system. The scheduler used is a variant of static locking, adapted for real time and more than one processor. It is assumed that transactions arrive according to a Poisson process, execution times of transactions are independent and exponentially distributed and all transactions use the same number of data items. The system is then represented as a Markov model. A steady state is derived from this model. By examining the path through the system of a single transaction, a recursive relation that describes all moments of a transaction's response time is derived. The response time distribution is approximated by fitting a distribution to the first two moments. Simulation shows that this approximation gives excellent results.

The response time distributions of the frames sent on a Controller Area Network (CAN) bus are of prime interest to dimension and validate automotive electronic architectures. However, the existing work on the timing behaviour of the CAN network does not take into account that all the data exchanges between the Electronic Control Units (ECUs) are driven by different and independent clocks which are subject to clock drifts. This paper proposes a model for clock drifts and describes their impact on the CAN frame response time distributions. By implementing the clock drifts in a CAN simulation tool, we show experimentally that the response time distributions converge, for drift values chosen randomly within the same range on all ECUs, whatever the initial phasings between the sending nodes. Furthermore, we show that, as a result of the clock drifts, the situations leading to the worst case response times are transient.

Queueing systems with redundancy have received considerable attention recently. The idea of redundancy is to reduce latency by replicating each incoming job a number of times and to assign these replicas to a set of randomly selected servers. As soon as one replica completes service the remaining replicas are cancelled. Most prior work on queueing systems with redundancy assumes that the job durations of the different replicas are i.i.d., which yields insights that can be misleading for computer system design. In this paper we develop a differential equation, using the cavity method, to assess the workload and response time distribution in a large homogeneous system with redundancy without the need to rely on this independence assumption. More specifically, we assume that the duration of each replica of a single job is identical across the servers and follows a general service time distribution. Simulation results suggest that the differential equation yields exact results as the system size tends to infinity and can be used to study the stability of the system.

I describe a technique for comparing two simple accounts of a distribution of response times: A mixture model and a generalized-shift model. In the mixture model, a target distribution is assumed to be a mixture of response times from two other (reference) distributions. In the generalized-shift model, the target distribution is assumed to be a quantile average of the reference distributions. In order to distinguish these two possibilities, quantiles for the target distribution are estimated from the quantiles of the reference distributions assuming either a shift or a mixture, and the predicted quantiles are used to calculate the multinomial likelihood of the obtained data. Monte Carlo simulations reported here demonstrate that the index is relatively unbiased, is effective with moderate sample sizes and modest spreads between the reference distributions, is relatively unaffected by changes in the number of bins or by data trimming, can be used with data aggregated across subjects, and is relatively insensitive to a range of subject variations in distribution shape and in mixture or shift proportion. As an illustration, the index is applied to the interpretation of three effects from distinct paradigms: residual switch costs in the task-switching paradigm, the psychological refractory period effect, and sequential effects in the Simon task. I conclude that the multinomial likelihood index provides a useful and easily applied tool for the interpretation of effects on response time distributions.

Cloud computing is considered a pattern for distributed and heterogeneous computing derived from many resources, and requests aim to share resources. Recently, cloud computing is graded among the top best technologies globally, which must be scheduled favorably to maximize providers’ profit and improve service quality for their customers. Scheduling specifies how users’ requests are assigned to virtual machines, and it plays a vital role in the efficiency and capability of the system. Its objective is to have a throughput or complete jobs in minimum time and the highest standard. Scheduling jobs in heterogeneous distributed systems is an NP-hard polynomial indecisive problem that is not solvable in polynomial time for real-time scheduling. The time complexity of jobs is growing exponentially, and this problem has a considerable effect on the quality of cloud services and providers’ efficiencies. The optimization of scheduling-related parameters using heuristic and meta-heuristic algorithms can reduce the search space complexity and execution time. This study intends to represent a fitness function to minimize time and cost parameters. The proposed method uses a multi-purposed weighted genetic algorithm that provides six basic parameters: utility, task execution cost, response time, wait time, Makespan, and throughput to provide comprehensive optimization. The proposed approach improved response and wait times, throughput, Makespan, and utility 16, 9, 7, 8 percentages, respectively, by only a one cost unit reduction, which is dispensable. As a result, both providers and users will experience better services. The statistical tests show that the achieved improvement is valid for 94% of experiments.

In this paper, the waiting time and response time processes in continuous-time two parallel queueing systems are analyzed as well as the system size process in discrete-time two parallel queueing systems. Upon arrival, each job splits into two tasks, denoted by task 1 and task 2. Task k, $k = 1,2$, is assigned to the kth queueing system to be served on a FCFS (first-come-first-served) basis. Each queueing system consists of a single server and an infinite-capacity queue. For the continuous-time queueing system, we assume that jobs arrive in a state-independent Poisson fashion with rate $\lambda $; the servers have exponential service times with rates $\mu _1 $ and $\mu _2 $, respectively. A closed-form expression for the Laplace transform of the ergodic bivariate waiting time distribution is derived. The distribution of the sum of the two waiting times is then obtained. The distribution of the response time when $\mu _1 = \mu _2 $ is derived analytically. For the discrete-time queueing systems, it is assu...