Sensitivity analysis over a random horizon: the maximal coupling rate perturbation analysis

2005 ◽  
Author(s):  
P. Bremaud ◽  
L. Massoulie
Keyword(s):  
Sensitivity Analysis ◽  
Perturbation Analysis ◽  
Random Horizon ◽  
Maximal Coupling ◽  
Coupling Rate

Maximal coupling Rare Perturbation Analysis with a random horizon

1995 ◽  
Vol 5 (4) ◽  
pp. 319-342 ◽  
Author(s):  
Pierre Br�maud ◽  
Laurent Massouli�
Keyword(s):  
Perturbation Analysis ◽  
Random Horizon ◽  
Maximal Coupling

Local Perturbation Analysis of Linear Programming with Functional Relation Among Parameters

2013 ◽  
pp. 1-24
Author(s):  
Payam Hanafizadeh ◽  
Abolfazl Ghaemi ◽  
Madjid Tavana
Keyword(s):  
Sensitivity Analysis ◽  
Linear Programming ◽  
Objective Function ◽  
Perturbation Analysis ◽  
Functional Relation ◽  
Local Perturbation ◽  
Nonlinear Functional ◽  
Functional Relations ◽  
Software Packages ◽  
The Right

In this paper, the authors study the sensitivity analysis for a class of linear programming (LP) problems with a functional relation among the objective function parameters or those of the right-hand side (RHS). The classical methods and standard sensitivity analysis software packages fail to function when a functional relation among the LP parameters prevail. In order to overcome this deficiency, the authors derive a series of sensitivity analysis formulae and devise corresponding algorithms for different groups of homogenous LP parameters. The validity of the derived formulae and devised algorithms is corroborated by open literature examples having linear as well as nonlinear functional relations between their vector b or vector c components.

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: additional results

1994 ◽  
Vol 26 (02) ◽  
pp. 556-560 ◽  
Author(s):  
P. Konstantopoulos ◽  
M. Zazanis
Keyword(s):  
Sensitivity Analysis ◽  
Stationary Distribution ◽  
Perturbation Analysis ◽  
Additional Condition ◽  
Approximation Scheme ◽  
Discontinuous Functions ◽  
Stationary Workload ◽  
The Right

Perturbation analysis estimators for expectations of possibly discontinuous functions of the time-stationary workload were derived in [2]. The expressions obtained may, however, not be valid if the customer-stationary distribution of the workload has atoms (at points other than zero). This was pointed out by Brémaud and Lasgouttes in [1]. In this note we clearly state the additional condition required for the validity of the expressions in [2]. We furthermore show how our approximation scheme can also be used to obtain the correct expressions for the right and left derivatives given in [1].

Sensitivity Analysis of Dissipative Reversible and Hamiltonian Systems: A Survey

2009 ◽  
Author(s):  
Oleg N. Kirillov ◽  
Ferdinand Verhulst
Keyword(s):  
Sensitivity Analysis ◽  
Hopf Bifurcation ◽  
Structural Stability ◽  
Hamiltonian Systems ◽  
Perturbation Analysis ◽  
Stability Boundary ◽  
Conservative System ◽  
Small Dissipation ◽  
Whitney Umbrella ◽  
The Stability

The paradox of destabilization of a conservative or non-conservative system by small dissipation, or Ziegler’s paradox (1952), has stimulated an ever growing interest in the sensitivity of reversible and Hamiltonian systems with respect to dissipative perturbations. Since the last decade it has been widely accepted that dissipation-induced instabilities are closely related to singularities arising on the stability boundary. What is less known is that the first complete explanation of Ziegler’s paradox by means of the Whitney umbrella singularity dates back to 1956. We revisit this undeservedly forgotten pioneering result by Oene Bottema that outstripped later findings for about half a century. We discuss subsequent developments of the perturbation analysis of dissipation-induced instabilities and applications over this period, involving structural stability of matrices, Krein collision, Hamilton-Hopf bifurcation and related bifurcations.

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.

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