Study on Steady-State Performance Measures of the Gt/Gt/1 Queue Model

2018 ◽  
Vol 08 (06) ◽  
pp. 706-711
Author(s):  
军霞 王
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Queue Model ◽  
Steady State Performance

Sensitivity analysis for stationary and ergodic queues

1992 ◽  
Vol 24 (03) ◽  
pp. 738-750 ◽  
Author(s):  
P. Konstantopoulos ◽  
Michael A. Zazanis
Keyword(s):  
Sensitivity Analysis ◽  
Steady State ◽  
Performance Measures ◽  
Perturbation Analysis ◽  
Service Process ◽  
Single Server ◽  
Stationary Version ◽  
Major Interest ◽  
Regenerative Approach ◽  
Steady State Performance

Starting with some mild assumptions on the parametrization of the service process, perturbation analysis (PA) estimates are obtained for stationary and ergodic single-server queues. Besides relaxing the stochastic assumptions, our approach solves some problems associated with the traditional regenerative approach taken in most of the previous work in this area. First, it avoids problems caused by perturbations interfering with the regenerative structure of the system. Second, given that the major interest is in steady-state performance measures, it examines directly the stationary version of the system, instead of considering performance measures expressed as Cesaro limits. Finally, it provides new estimators for general (possibly discontinuous) functions of the workload and other steady-state quantities.

Sensitivity analysis for stationary and ergodic queues

1992 ◽  
Vol 24 (3) ◽  
pp. 738-750 ◽  
Author(s):  
P. Konstantopoulos ◽  
Michael A. Zazanis
Keyword(s):  
Sensitivity Analysis ◽  
Steady State ◽  
Performance Measures ◽  
Perturbation Analysis ◽  
Service Process ◽  
Single Server ◽  
Stationary Version ◽  
Major Interest ◽  
Regenerative Approach ◽  
Steady State Performance

Starting with some mild assumptions on the parametrization of the service process, perturbation analysis (PA) estimates are obtained for stationary and ergodic single-server queues. Besides relaxing the stochastic assumptions, our approach solves some problems associated with the traditional regenerative approach taken in most of the previous work in this area. First, it avoids problems caused by perturbations interfering with the regenerative structure of the system. Second, given that the major interest is in steady-state performance measures, it examines directly the stationary version of the system, instead of considering performance measures expressed as Cesaro limits. Finally, it provides new estimators for general (possibly discontinuous) functions of the workload and other steady-state quantities.

scholarly journals Loss Systems with Slow Retrials in the Halfin–Whitt Regime

2013 ◽  
Vol 45 (01) ◽  
pp. 274-294 ◽  
Author(s):  
F. Avram ◽  
A. J. E. M. Janssen ◽  
J. S. H. Van Leeuwaarden
Keyword(s):  
Steady State ◽  
Critical Load ◽  
Performance Measures ◽  
System Performance ◽  
Economies Of Scale ◽  
Blocking Probability ◽  
Loss System ◽  
Qed Regime ◽  
Loss Systems ◽  
Steady State Performance

The Halfin–Whitt regime, or the quality-and-efficiency-driven (QED) regime, for multiserver systems refers to a situation with many servers, a critical load, and yet favorable system performance. We apply this regime to the classical multiserver loss system with slow retrials. We derive nondegenerate limiting expressions for the main steady-state performance measures, including the retrial rate and the blocking probability. It is shown that the economies of scale associated with the QED regime persist for systems with retrials, although in situations when the load becomes extremely critical the retrials cause deteriorated performance. Most of our results are obtained by a detailed analysis of Cohen's equation that defines the retrial rate in an implicit way. The limiting expressions are established by studying prelimit behavior and exploiting the connection between Cohen's equation and Mills' ratio for the Gaussian and Poisson distributions.

scholarly journals Loss Systems with Slow Retrials in the Halfin–Whitt Regime

2013 ◽  
Vol 45 (1) ◽  
pp. 274-294 ◽  
Author(s):  
F. Avram ◽  
A. J. E. M. Janssen ◽  
J. S. H. Van Leeuwaarden
Keyword(s):  
Steady State ◽  
Critical Load ◽  
Performance Measures ◽  
System Performance ◽  
Economies Of Scale ◽  
Blocking Probability ◽  
Loss System ◽  
Qed Regime ◽  
Loss Systems ◽  
Steady State Performance

The Halfin–Whitt regime, or the quality-and-efficiency-driven (QED) regime, for multiserver systems refers to a situation with many servers, a critical load, and yet favorable system performance. We apply this regime to the classical multiserver loss system with slow retrials. We derive nondegenerate limiting expressions for the main steady-state performance measures, including the retrial rate and the blocking probability. It is shown that the economies of scale associated with the QED regime persist for systems with retrials, although in situations when the load becomes extremely critical the retrials cause deteriorated performance. Most of our results are obtained by a detailed analysis of Cohen's equation that defines the retrial rate in an implicit way. The limiting expressions are established by studying prelimit behavior and exploiting the connection between Cohen's equation and Mills' ratio for the Gaussian and Poisson distributions.

Quasi-steady-state performance of a heat pipe subjected to transient acceleration loadings

10.2514/3.895 ◽  
1997 ◽  
Vol 11 ◽  
pp. 306-309 ◽  
Author(s):  
Edwin H. Olmstead ◽  
Edward S. Taylor ◽  
Meng Wang ◽  
Parviz Moin ◽  
Scott K. Thomas ◽  
...  
Keyword(s):  
Steady State ◽  
Heat Pipe ◽  
Quasi Steady State ◽  
Steady State Performance

A Novel Control Scheme for PWM Boost Converter based on Sliding Mode Control using Particle Swarm Optimization

2020 ◽  
Vol 14 ◽  
Author(s):  
Gang Liu ◽  
Dong Qiu ◽  
Xiuru Wang ◽  
Ke Zhang ◽  
Huafeng Huang ◽  
...  
Keyword(s):  
Particle Swarm Optimization ◽  
Steady State ◽  
Sliding Mode ◽  
Particle Swarm ◽  
Mathematic Model ◽  
Absolute Error ◽  
Boost Converter ◽  
Sliding Mode Controller ◽  
Swarm Optimization ◽  
Steady State Performance

Background: The PWM Boost converter is a strongly nonlinear discrete system, especially when the input voltage or load varies widely, therefore, tuning the control parameters of which is a challenge work. Objective: In order to overcome the issues, particle swarm optimization (PSO) is employed for tuning the parameters of a sliding mode controller of a boost converter. Methods: Based on the analysis of the Boost converter model and its non-linear characteristics, a mathematic model of a boost converter with a sliding mode controller is built firstly. Then, the parameters of the Boost controller are adjusted based on the integrated time and absolute error (ITAE), integral square error (ISE) and integrated absolute error (IAE) indexes by PSO. Results: Simulation verification was performed, and the results show that the controllers tuned by the three indexes all have excellent robust stability. Conclusion: The controllers tuned by ITAE and ISE indexes have excellent steady-state performance, but the overshoot is large during the startup. The controller tuned by IAE index has better startup performance and slightly worse steady-state performance.

scholarly journals Steady-State Analysis of the Join-the-Shortest-Queue Model in the Halfin–Whitt Regime

2020 ◽  
Vol 45 (3) ◽  
pp. 1069-1103
Author(s):  
Anton Braverman
Keyword(s):  
Steady State ◽  
Diffusion Limit ◽  
Fluid Limit ◽  
Time Intervals ◽  
Dimensional Diffusion ◽  
Queue Model ◽  
Join The Shortest Queue ◽  
Shortest Queue ◽  
Process Level ◽  
General Tool

This paper studies the steady-state properties of the join-the-shortest-queue model in the Halfin–Whitt regime. We focus on the process tracking the number of idle servers and the number of servers with nonempty buffers. Recently, Eschenfeldt and Gamarnik proved that a scaled version of this process converges, over finite time intervals, to a two-dimensional diffusion limit as the number of servers goes to infinity. In this paper, we prove that the diffusion limit is exponentially ergodic and that the diffusion scaled sequence of the steady-state number of idle servers and nonempty buffers is tight. Combined with the process-level convergence proved by Eschenfeldt and Gamarnik, our results imply convergence of steady-state distributions. The methodology used is the generator expansion framework based on Stein’s method, also referred to as the drift-based fluid limit Lyapunov function approach in Stolyar. One technical contribution to the framework is to show how it can be used as a general tool to establish exponential ergodicity.

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