A semi-product-form for a pair of queues with finite batches: Equilibrium state probabilities and response time densities

A product form solution for the optimal fractions of divisible load to distribute to processors in a multi-level tree network is described. Here optimality involves parallel processing the load in a minimal amount of time. This tractable solution is similar to the product form solution for equilibrium state probabilities arising in Markovian queueing networks. The existence of this product form solution answers a long standing open question for divisible load scheduling.

Download Full-text

Response Time Distribution in a Tandem Pair of Queues with Batch Processing

Journal of the ACM ◽

10.1145/3448973 ◽

2021 ◽

Vol 68 (4) ◽

pp. 1-41

Author(s):

P. G. Harrison ◽

J. Bor

Keyword(s):

Response Time ◽

Laplace Transform ◽

Recurrence Formula ◽

Response Time Distribution ◽

Product Form ◽

Batch Arrivals ◽

The Laplace Transform ◽

Batch Sizes ◽

First Four Moments ◽

Time Density

Response time density is obtained in a tandem pair of Markovian queues with both batch arrivals and batch departures. The method uses conditional forward and reversed node sojourn times and derives the Laplace transform of the response time probability density function in the case that batch sizes are finite. The result is derived by a generating function method that takes into account that the path is not overtake-free in the sense that the tagged task being tracked is affected by later arrivals at the second queue. A novel aspect of the method is that a vector of generating functions is solved for, rather than a single scalar-valued function, which requires investigation of the singularities of a certain matrix. A recurrence formula is derived to obtain arbitrary moments of response time by differentiation of the Laplace transform at the origin, and these can be computed rapidly by iteration. Numerical results for the first four moments of response time are displayed for some sample networks that have product-form solutions for their equilibrium queue length probabilities, along with the densities themselves by numerical inversion of the Laplace transform. Corresponding approximations are also obtained for (non-product-form) pairs of “raw” batch-queues—with no special arrivals—and validated against regenerative simulation, which indicates good accuracy. The methods are appropriate for modeling bursty internet and cloud traffic and a possible role in energy-saving is considered.

Download Full-text

Response time distributions and network perturbation into product-form

Proceedings of the 4th International ICST Conference on Performance Evaluation Methodologies and Tools ◽

10.4108/icst.valuetools2009.7776 ◽

2009 ◽

Cited By ~ 1

Author(s):

Peter G. Harrison ◽

Maria G. Vigliotti

Keyword(s):

Response Time ◽

Product Form ◽

Response Time Distributions

Download Full-text

Research on Cognitive Matching of Biological Morphological Features and Images for Profiling Design

E3S Web of Conferences ◽

10.1051/e3sconf/202017901015 ◽

2020 ◽

Vol 179 ◽

pp. 01015

Author(s):

Bin Zhou ◽

Li Lin

Keyword(s):

Response Time ◽

Product Form ◽

Time Data ◽

Bionic Design ◽

Feature Group ◽

Biological Form ◽

Compatibility Group ◽

Form Features ◽

Cognitive Measurement ◽

Shape Characteristics

To obtain high-quality bionic design scheme of product form, this paper explores the matching relationship between users’ biological form features and their images from the level of implicit cognition, providing objective basis for effective selection of ideographic biological form features in bionic design of product form. The eye movement experiment was used to screen the biomorphic feature group that was focused on. Questionnaire survey and cluster analysis were used to obtain the main image phrases of the morphological feature group. The two collected materials were combined with implicit cognitive measurement (IAT) to obtain the response time data of the subjects in the classification task. According to Greenwald’s method to verify the effectiveness of the data as a whole, the response time of the combination of various features and images in the compatibility group is sorted to obtain the design guidance conclusion. Taking the white shouldered eagle as an example, the experimental data showed high validity by t-test, and the implicit effect value of the compatibility group was 0.68. According to the analysis of the data, the main image that most matches the head shape characteristics of the white shouldered eagle is “Ferocious”, and the main image that most matches the wing shape characteristics is “Lightsome”, and there is no difference in the implicit cognitive attitude between men and women. The designer takes this as the design reference to improve the effectiveness of the design output. This study can provide more objective suggestions for the bionic design of the related product shape.

Download Full-text

A semi-product-form for the equilibrium state probabilities in a pair of queues with finite batches

Proceedings of the 12th EAI International Conference on Performance Evaluation Methodologies and Tools - VALUETOOLS 2019 ◽

10.1145/3306309.3306316 ◽

2019 ◽

Author(s):

P. G. Harrison

Keyword(s):

Equilibrium State ◽

Product Form

Download Full-text

Temporal Prediction Errors Affect Short-Term Memory Scanning Response Time

Experimental Psychology (formerly Zeitschrift für Experimentelle Psychologie) ◽

10.1027/1618-3169/a000339 ◽

2016 ◽

Vol 63 (6) ◽

pp. 333-342

Author(s):

Roberto Limongi ◽

Angélica M. Silva

Keyword(s):

Response Time ◽

Short Term Memory ◽

Estimation Error ◽

Predictive Coding ◽

Time Estimation ◽

Prediction Errors ◽

Memory Scanning ◽

Short Term ◽

Term Memory ◽

Temporal Prediction

Abstract. The Sternberg short-term memory scanning task has been used to unveil cognitive operations involved in time perception. Participants produce time intervals during the task, and the researcher explores how task performance affects interval production – where time estimation error is the dependent variable of interest. The perspective of predictive behavior regards time estimation error as a temporal prediction error (PE), an independent variable that controls cognition, behavior, and learning. Based on this perspective, we investigated whether temporal PEs affect short-term memory scanning. Participants performed temporal predictions while they maintained information in memory. Model inference revealed that PEs affected memory scanning response time independently of the memory-set size effect. We discuss the results within the context of formal and mechanistic models of short-term memory scanning and predictive coding, a Bayes-based theory of brain function. We state the hypothesis that our finding could be associated with weak frontostriatal connections and weak striatal activity.

Download Full-text