Package jline.api.pfqn

Class Pfqn_marie

java.lang.Object

jline.api.pfqn.Pfqn_marie

public final class Pfqn_marie
extends Object

Marie's iterative aggregation-decomposition (Marie 1979/1980) for closed queueing networks with FCFS non-exponential (Coxian) service.

Single class only: each station is analyzed in isolation as a lambda(n)/Cox/1 queue whose state-dependent arrival rate is the complementary network throughput; the resulting conditional throughputs mu_i(n) drive an exact load-dependent product-form solve (Pfqn_mvald), iterated to a fixed point. The method reduces to exact product form for exponential service.

Multiclass (R > 1) is handled by pfqn_marie_multi(jline.util.matrix.Matrix, jline.util.matrix.Matrix, jline.util.matrix.Matrix, jline.util.matrix.Matrix): a QD-AMVA aggregate with class-dependent (cd) scaling beta_{i,r}(nvec) supplied by a multiclass lambda_r/Cox/1 FCFS isolation sub-model, iterated to a fixed point on the per-class throughput. beta==1 recovers standard FCFS AMVA, so the cd-scaling carries only the non-exponential correction; exponential class-independent service dispatches to exact MVA. Ported from matlab/src/api/pfqn/pfqn_marie.m (both single- and multiclass).

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	Pfqn_marie.MultiResult	Result of pfqn_marie_multi(jline.util.matrix.Matrix, jline.util.matrix.Matrix, jline.util.matrix.Matrix, jline.util.matrix.Matrix).
static class	Pfqn_marie.Result	Result of pfqn_marie(jline.util.matrix.Matrix, double, double, jline.util.matrix.Matrix).

Method Summary

Modifier and Type	Method	Description
static Pfqn_marie.Result	pfqn_marie(Matrix L, double N, double Z, Matrix scv)
static Pfqn_marie.Result	pfqn_marie(Matrix L, double N, double Z, Matrix scv, double tol, int maxiter, Matrix nservers)
static Pfqn_marie.MultiResult	pfqn_marie_multi(Matrix L, Matrix N, Matrix Z, Matrix scv)
static Pfqn_marie.MultiResult	pfqn_marie_multi(Matrix L, Matrix N, Matrix Z, Matrix scv, double tol, int maxiter)	Marie's method for multiclass FCFS Coxian closed networks.

Methods inherited from class java.lang.Object

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

Method Details

pfqn_marie

public static Pfqn_marie.Result pfqn_marie(Matrix L,
 double N,
 double Z,
 Matrix scv)

pfqn_marie

public static Pfqn_marie.Result pfqn_marie(Matrix L,
 double N,
 double Z,
 Matrix scv,
 double tol,
 int maxiter,
 Matrix nservers)

Parameters:

L - service demand column vector (M x 1)

N - total population (scalar)

Z - think time (total delay demand)

scv - per-station squared coefficient of variation (M x 1); null => all 1

tol - convergence tolerance on mu

maxiter - maximum iterations

nservers - per-station server count (M x 1); null => all 1

pfqn_marie_multi

public static Pfqn_marie.MultiResult pfqn_marie_multi(Matrix L,
 Matrix N,
 Matrix Z,
 Matrix scv)

pfqn_marie_multi

public static Pfqn_marie.MultiResult pfqn_marie_multi(Matrix L,
 Matrix N,
 Matrix Z,
 Matrix scv,
 double tol,
 int maxiter)

Marie's method for multiclass FCFS Coxian closed networks. The aggregate is QD-AMVA with class-dependent scaling beta_{i,r}(nvec) = (Coxian isolation conditional throughput)/(exponential isolation conditional throughput), iterated to a fixed point on the per-class throughput X.

Parameters:

L - M x R service demand matrix

N - 1 x R (or R x 1) per-class population

Z - 1 x R (or R x 1) per-class think time; null => zeros

scv - M x R per-station per-class SCV; null => all 1