Package jline.api.pfqn.mva

Class Pfqn_mvasjn

java.lang.Object

jline.api.pfqn.mva.Pfqn_mvasjn

public final class Pfqn_mvasjn
extends Object

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	Pfqn_mvasjn.Profile	Conditional waiting time profile of one SJN station at the target population.
static final class	Pfqn_mvasjn.Result	Mean performance measures of the network.

Method Summary

Modifier and Type	Method	Description
static Pfqn_mvasjn.Result	pfqn_mvasjn(Matrix L, Matrix N, Matrix Z, Matrix scv, int[] sjnset, Matrix V, SjnOptions options)	Mean value analysis with shortest-job-next stations, over the whole population lattice.

Methods inherited from class java.lang.Object

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

Method Details

pfqn_mvasjn

public static Pfqn_mvasjn.Result pfqn_mvasjn(Matrix L,
 Matrix N,
 Matrix Z,
 Matrix scv,
 int[] sjnset,
 Matrix V,
 SjnOptions options)

Mean value analysis with shortest-job-next stations, over the whole population lattice.

The SJN station is modelled by the conditional waiting time W(x,n) of a tagged customer whose service requirement is x, obtained from the arrival theorem as the sum of the residual life of the job in service, the work of the queued jobs that will be served before the tagged one, and the work of the jobs that overtake it while it waits:

   W(x,n) = [ (1+CV^2) s U(n-1)/2 + X(n-1) phi(x,n-1) ] / [ 1 - X(n-1) theta(x) ]
   theta(x) = int_0^x t f(t) dt,   phi(x,n) = int_0^x W(t,n) t f(t) dt
   R(n) = s + int_0^inf W(x,n) f(x) dx
 

The recursion is explicit: W(.,n) needs only phi(.,n-1), so it is carried alongside the population recursion of exact MVA. This costs prod(N+1) steps; Pfqn_amvasjn is the fixed-point counterpart that trades the lattice for a Schweitzer closure on the same profile.

The service time density is not an input: only its mean and squared coefficient of variation are, and the density is reconstructed by the two-moment Erlang-mixture fit the reference prescribes. The x-integrals run on a fixed grid by composite Simpson, W(.,n) being needed at the next population so that quadrature rules sampling at arbitrary abscissae cannot be used; beyond the grid the profile is closed by the analytic tail W(x,n) = a - b exp(-c (x - Lx)).

Parameters:

L - service demand matrix (M x R) of the queueing stations

N - population vector (1 x R)

Z - think time vector (1 x R), may be null

scv - squared coefficients of variation of the service times (M x R), may be null

sjnset - zero-based indices of the stations scheduling by SJN, may be null

V - visit ratios (M x R), so that the per-visit service time is L./V, may be null

options - grid, priority and cap options, may be null

Returns:

mean performance measures and the conditional waiting time profiles