Package jline.solvers.fluid.analyzers

Class DdppAnalyzer

java.lang.Object

jline.solvers.fluid.analyzers.DdppAnalyzer

All Implemented Interfaces:

FluidAnalyzer

public class DdppAnalyzer
extends Object
implements FluidAnalyzer

Refined mean-field (O(1/N)) steady state of the matrix fluid drift, options.method="ddpp" (alias "fld.ddpp").

The model is read as a density-dependent population process whose size N is the total closed population: the state is the job count of every (station, class, phase) coordinate and a jump moving a job from a to b has rate theta_a(x)*W(a,b), with theta_a = x_a*min(1, c_i/X_i) (x_a at an infinite server). The family scales every population and finite server count together, so the fixed point x* and the correction V are N-independent in job counts. Gast and Van Houdt (POMACS 1(2), 2017) give E[X] = x* + V + O(1/N), with J*W + W*J' + Q = 0 and V = -J^{-1}*(1/2)*H:W, both solved on an orthonormal basis of the jump span. The rates are refined to the same order, so the corrected throughputs satisfy flow balance exactly.

The correction is nonzero only at a saturated MULTICLASS PS/FCFS share: a single-class network gives V = 0 (piecewise-linear drift for exponential service, vanishing Hessian contraction for phase-type service, so the result is insensitive beyond the mean). MATLAB twin: solver_fluid_ddpp.m and fluid_ddpp_admits.m; the fixed point is found by the same pseudo-transient continuation, so the codebases agree.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	DdppAnalyzer.Refusal	A refusal: the identifier and the message, or null when admitted.

Field Summary

Fields

Modifier and Type	Field	Description
double	N	Total closed population N.
Matrix	QNfluid	Fluid metrics at x*, for comparison with the refined result.
Matrix	TNfluid	Fluid metrics at x*, for comparison with the refined result.
Matrix	UNfluid	Fluid metrics at x*, for comparison with the refined result.
double[]	V	The O(1/N) correction V in job counts.
double[]	xFluid	The fluid fixed point x* (before the correction).

Constructor Summary

Constructors

Constructor	Description
DdppAnalyzer()

Method Summary

Modifier and Type	Method	Description
static DdppAnalyzer.Refusal	admits(NetworkStruct sn, SolverOptions options)	The model class of 'ddpp', decided statically.
void	analyze(NetworkStruct sn, SolverOptions options, SolverResult result)
Matrix	getXVecIt()
static DdppAnalyzer.Refusal	hyperbolic(NetworkStruct sn, SolverOptions options)	Does the fluid fixed point admit the 1/N expansion? admits(jline.lang.NetworkStruct, jline.solvers.SolverOptions) is static, but smoothness and exponential stability of the fixed point are a property of the numbers: a closed Delay -> FCFS repairman with N = 3, think rate 1 and service rate 2 puts exactly one job at the single server, on the kink of min(1, c/X).

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Details

xFluid

public double[] xFluid

The fluid fixed point x* (before the correction).

V

public double[] V

The O(1/N) correction V in job counts.

QNfluid

public Matrix QNfluid

Fluid metrics at x*, for comparison with the refined result.

UNfluid

public Matrix UNfluid

Fluid metrics at x*, for comparison with the refined result.

TNfluid

public Matrix TNfluid

Fluid metrics at x*, for comparison with the refined result.

N

public double N

Total closed population N.

Constructor Details

DdppAnalyzer

public DdppAnalyzer()

Method Details

admits

public static DdppAnalyzer.Refusal admits(NetworkStruct sn,
 SolverOptions options)

The model class of 'ddpp', decided statically. Mirrors fluid_ddpp_admits.m: closed classes only, INF/PS/FCFS stations (FCFS with exponential service at one rate for every class), renewal PH service, steady state, no load dependence, and the moment_maxstate cap.

Returns:

null when admitted, otherwise the refusal

hyperbolic

public static DdppAnalyzer.Refusal hyperbolic(NetworkStruct sn,
 SolverOptions options)

Does the fluid fixed point admit the 1/N expansion? admits(jline.lang.NetworkStruct, jline.solvers.SolverOptions) is static, but smoothness and exponential stability of the fixed point are a property of the numbers: a closed Delay -> FCFS repairman with N = 3, think rate 1 and service rate 2 puts exactly one job at the single server, on the kink of min(1, c/X). The support gate asks this after the static predicate, so findSolver does not offer a run that would refuse. Runs the analysis up to its hyperbolicity checks. Call it only once admits(jline.lang.NetworkStruct, jline.solvers.SolverOptions) has accepted the model. MATLAB twin: fluid_ddpp_hyperbolic.m.

Returns:

null when the fixed point is hyperbolic, otherwise the refusal

analyze

public void analyze(NetworkStruct sn,
 SolverOptions options,
 SolverResult result)

Specified by:

analyze in interface FluidAnalyzer

getXVecIt

public Matrix getXVecIt()

Specified by:

getXVecIt in interface FluidAnalyzer