Kelly and Jackson networks with interchangeable, cooperative servers

2021 ◽  
Vol 53 (2) ◽  
pp. 463-483
Author(s):  
Chia-Li Wang ◽  
Ronald W. Wolff
Keyword(s):  
Performance Improvement ◽  
Service Rate ◽  
Stability Conditions ◽  
Jackson Networks ◽  
Full Cooperation

AbstractIn open Kelly and Jackson networks, servers are assigned to individual stations, serving customers only where they are assigned. We investigate the performance of modified networks where servers cooperate. A server who would be idle at the assigned station will serve customers at another station, speeding up service there. We assume interchangeable servers: the service rate of a server at a station depends only on the station, not the server. This gives work conservation, which is used in various ways. We investigate three levels of server cooperation, from full cooperation, where all servers are busy when there is work to do anywhere in the network, to one-way cooperation, where a server assigned to one station may assist a server at another, but not the converse. We obtain the same stability conditions for each level and, in a series of examples, obtain substantial performance improvement with server cooperation, even when stations before modification are moderately loaded.

scholarly journals Computable Bounds on the Spectral Gap for Unreliable Jackson Networks

2015 ◽  
Vol 47 (02) ◽  
pp. 402-424 ◽  
Author(s):  
Paweł Lorek ◽  
Ryszard Szekli
Keyword(s):  
Convergence Rates ◽  
Spectral Gap ◽  
Service Rate ◽  
Spectral Gaps ◽  
Birth And Death Processes ◽  
Marginal Distributions ◽  
Hazard Functions ◽  
Jackson Networks ◽  
One Dimensional ◽  
The One

The goal of this paper is to identify exponential convergence rates and to find computable bounds for them for Markov processes representing unreliable Jackson networks. First, we use the bounds of Lawler and Sokal (1988) in order to show that, for unreliable Jackson networks, the spectral gap is strictly positive if and only if the spectral gaps for the corresponding coordinate birth and death processes are positive. Next, utilizing some results on birth and death processes, we find bounds on the spectral gap for network processes in terms of the hazard and equilibrium functions of the one-dimensional marginal distributions of the stationary distribution of the network. These distributions must be in this case strongly light-tailed, in the sense that their discrete hazard functions have to be separated from 0. We relate these hazard functions with the corresponding networks' service rate functions using the equilibrium rates of the stationary one-dimensional marginal distributions. We compare the obtained bounds on the spectral gap with some other known bounds.

scholarly journals Computable Bounds on the Spectral Gap for Unreliable Jackson Networks

2015 ◽  
Vol 47 (2) ◽  
pp. 402-424 ◽  
Author(s):  
Paweł Lorek ◽  
Ryszard Szekli
Keyword(s):  
Convergence Rates ◽  
Spectral Gap ◽  
Service Rate ◽  
Spectral Gaps ◽  
Birth And Death Processes ◽  
Marginal Distributions ◽  
Hazard Functions ◽  
Jackson Networks ◽  
One Dimensional ◽  
The One

The goal of this paper is to identify exponential convergence rates and to find computable bounds for them for Markov processes representing unreliable Jackson networks. First, we use the bounds of Lawler and Sokal (1988) in order to show that, for unreliable Jackson networks, the spectral gap is strictly positive if and only if the spectral gaps for the corresponding coordinate birth and death processes are positive. Next, utilizing some results on birth and death processes, we find bounds on the spectral gap for network processes in terms of the hazard and equilibrium functions of the one-dimensional marginal distributions of the stationary distribution of the network. These distributions must be in this case strongly light-tailed, in the sense that their discrete hazard functions have to be separated from 0. We relate these hazard functions with the corresponding networks' service rate functions using the equilibrium rates of the stationary one-dimensional marginal distributions. We compare the obtained bounds on the spectral gap with some other known bounds.

Stability Conditions Related to a Previously Unrecognized Form of Thrombin

1972 ◽  
Vol 27 (02) ◽  
pp. 361-362 ◽  
Author(s):  
Walter H. Seegers ◽  
Lowell E. McCoy
Keyword(s):  
Stability Conditions

Peningkatan kinerja guru dalam pembelajaran di kelas melalui supervisi edukatif Kolaboratif secara periodik MIS Lawe kongker Tahun pelajaran 2019/2020

2020 ◽  
Vol 1 (3) ◽  
pp. 316-324
Author(s):  
Syukrani Kadir
Keyword(s):  
Student Learning ◽  
Performance Improvement ◽  
Teacher Performance ◽  
Learning Cycle ◽  
Learning Achievement ◽  
Educational Supervision ◽  
Average Action ◽  
Learning Plans

periodically in preparing learning plans, implementing learning, assessing learning achievement, carrying out follow-up assessments of student learning achievement that can improve teacher performance. This performance improvement is through periodic collaborative educational supervision. Based on the results of educational supervision in cycle I and cycle II, teacher performance increased, namely in cycle I, teacher performance in preparing learning plans in cycle I reached 71.98%, while cycle II was 92.44%. Teacher performance in implementing learning cycle I reached 72.44% while cycle II reached 93.81%. Teacher performance in assessing learning achievement in cycle Im reached 81.30% while cycle II was 90.56%. Teacher performance in carrying out follow-up assessments of student learning achievement in the first cycle reached 59.76% while the second cycle was 83.00%. Thus, the average action cycle II was above 75.00%. Based on the results of this study, it can be concluded that the teacher's performance has increased in preparing learning plans, implementing learning, assessing learning achievement, carrying out follow-up assessments of student learning achievement.

Towards the digital land reclamation

2020 ◽  
pp. 5-9
Author(s):  
Sergey Vasil'ev ◽  
Vyacheslav Schedrin ◽  
Aleksandra Slabunova ◽  
Vladimir Slabunov
Keyword(s):  
Retrospective Analysis ◽  
Land Reclamation ◽  
Practical Experience ◽  
Maximum Effect ◽  
Optimal Management ◽  
Scientific Potential ◽  
History Of ◽  
Definition Of ◽  
Further Development ◽  
Full Cooperation

The aim of the research is a retrospective analysis of the history and stages of development of digital land reclamation in Russia, the definition of «Digital land reclamation» and trends in its further development. In the framework of the retrospective analysis the main stages of melioration formation are determined. To achieve the maximum effect of the «digital reclamation» requires full cooperation of practical experience and scientific potential accumulated throughout the history of the reclamation complex, and the latest achievements of science and technology, which is currently possible only through the full digitalization of reclamation activities. The introduction of «digital reclamation» will achieve greater potential and effect in the modernization of the reclamation industry in the «hightech industry», through the use of innovative developments and optimal management decisions.

CONVEYOR MODEL AND IMPLEMENTATION OF THE REAL NUMBERS ADDER ON FPGA

2020 ◽  
Vol 33 (109) ◽  
pp. 21-31
Author(s):  
І. Ya. Zeleneva ◽  
Т. V. Golub ◽  
T. S. Diachuk ◽  
А. Ye. Didenko
Keyword(s):  
Performance Improvement ◽  
Experimental Studies ◽  
Production Costs ◽  
Floating Point ◽  
Computing Device ◽  
Quartus Ii ◽  
Functional Blocks ◽  
Mental Testing ◽  
Processor Cores ◽  
Floating Point Numbers

The purpose of these studies is to develop an effective structure and internal functional blocks of a digital computing device – an adder, that performs addition and subtraction operations on floating- point numbers presented in IEEE Std 754TM-2008 format. To improve the characteristics of the adder, the circuit uses conveying, that is, division into levels, each of which performs a specific action on numbers. This allows you to perform addition / subtraction operations on several numbers at the same time, which increas- es the performance of calculations, and also makes the adder suitable for use in modern synchronous cir- cuits. Each block of the conveyor structure of the adder on FPGA is synthesized as a separate project of a digital functional unit, and thus, the overall task is divided into separate subtasks, which facilitates experi- mental testing and phased debugging of the entire device. Experimental studies were performed using EDA Quartus II. The developed circuit was modeled on FPGAs of the Stratix III and Cyclone III family. An ana- logue of the developed circuit was a functionally similar device from Altera. A comparative analysis is made and reasoned conclusions are drawn that the performance improvement is achieved due to the conveyor structure of the adder. Implementation of arithmetic over the floating-point numbers on programmable logic integrated cir- cuits, in particular on FPGA, has such advantages as flexibility of use and low production costs, and also provides the opportunity to solve problems for which there are no ready-made solutions in the form of stand- ard devices presented on the market. The developed adder has a wide scope, since most modern computing devices need to process floating-point numbers. The proposed conveyor model of the adder is quite simple to implement on the FPGA and can be an alternative to using built-in multipliers and processor cores in cases where the complex functionality of these devices is redundant for a specific task.

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