Package jline.api.pfqn.mva

Class Pfqn_tay

java.lang.Object

jline.api.pfqn.mva.Pfqn_tay

public final class Pfqn_tay
extends Object

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	Pfqn_tay.Result	Mean performance measures plus the arrival-instant queue lengths.

Method Summary

Modifier and Type	Method	Description
static Pfqn_tay.Result	pfqn_tay(Matrix L, Matrix N, Matrix Z)	Convenience overload with the default tolerance and iteration budget.
static Pfqn_tay.Result	pfqn_tay(Matrix L, Matrix N, Matrix Z, double tol, int maxiter, Matrix QN0)	Tay's arrival-instant AMVA.

Methods inherited from class java.lang.Object

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

Method Details

pfqn_tay

public static Pfqn_tay.Result pfqn_tay(Matrix L,
 Matrix N,
 Matrix Z,
 double tol,
 int maxiter,
 Matrix QN0)

Tay's arrival-instant AMVA.

Let E_mkc = (D_mk/X_c) dX_c/dD_mk be the elasticity of the class-c throughput with respect to the class-k demand at station m. Tay shows that the elasticities satisfy the R linear equations

 E_mkj sum_t B_tj Q_jt (1+Q_jt) =
     -[(delta_jk + Q_jm) B_mk Q_km + sum_{c!=j} E_mkc sum_t B_tc Q_jt Q_ct]
 

with B_ir = 1/(1 + D_ir X_r/N_r), and that the arrival-instant queue length is then simply Q_km^(r) = Q_km + E_mkr, which closes the MVA recursion R_rm = D_rm (1 + sum_k Q_km^(r)). One R x R solve per (station, class) pair per iteration.

Delay stations enter through Z only. They are "AS" servers in the survey's notation (d_t = 0), so they contribute Z_j X_j to the denominator of the elasticity equations but nothing to its numerator.

Parameters:

L - service demand matrix (M x R)

N - population vector (1 x R)

Z - think time vector (1 x R)

tol - convergence tolerance on the queue lengths

maxiter - maximum number of iterations

QN0 - initial guess for the queue lengths (M x R), or null

Returns:

throughputs, queue lengths, utilizations, residence times, iteration count and the arrival-instant queue lengths

pfqn_tay

public static Pfqn_tay.Result pfqn_tay(Matrix L,
 Matrix N,
 Matrix Z)

Convenience overload with the default tolerance and iteration budget.