Package jline.api.pfqn.sens

Class Pfqn_hst

java.lang.Object

jline.api.pfqn.sens.Pfqn_hst

public final class Pfqn_hst
extends Object

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	Pfqn_hst.Result	HST sensitivity coefficients and the constrained worst case.

Method Summary

Modifier and Type	Method	Description
static Pfqn_hst.Result	pfqn_hst(Matrix L, double N, double Z)	Convenience overload analysing the bottleneck station.
static Pfqn_hst.Result	pfqn_hst(Matrix L, double N, double Z, int ist)	HST robustness certificate.

Methods inherited from class java.lang.Object

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

Method Details

pfqn_hst

public static Pfqn_hst.Result pfqn_hst(Matrix L,
 double N,
 double Z,
 int ist)

HST robustness certificate.

HST states that the mean service time at station i does not depend on the queue length there. Suri perturbs it to S_i(n) = S_i (1 + a_n), one relative deviation per queue-length level, and shows (eq. 3.11) that to first order c_n = P(n_i >= n+1)/u_i - P(n_i >= n), with u_i = L_i X0 and P(n_i >= n) = L_i^n G(N-n)/G(N). The naive certificate |dX0/X0| <= (sum_n |c_n|) d follows from |a_n| <= d alone, and by Lemma 3.1 that total equals Q_i(N) - Q_i(N-1).

That bound is loose because an operationally consistent perturbation must leave the observed mean service time unchanged, sum_n p_n a_n = 0. The constrained problem (P1) max |sum_n c_n a_n| subject to |a_n| <= d and sum_n p_n a_n = 0 is a one-constraint linear program, solved here exactly: its optimum sets a_n = +/-d according to whether c_n/p_n exceeds a threshold, with at most one fractional coordinate. The feasible set is symmetric, so the optimum comes in a +/- pair and only the magnitude is determined.

Parameters:

L - service demand vector (M x 1) of the queueing stations

N - population (integer, at least one job)

Z - think time

ist - 0-based station index the perturbation applies to

Returns:

the marginals, the sensitivity coefficients and the (P1) optimum

pfqn_hst

public static Pfqn_hst.Result pfqn_hst(Matrix L,
 double N,
 double Z)

Convenience overload analysing the bottleneck station.