Package jline.api.sum

Class Sum_closing

java.lang.Object

jline.api.sum.Sum_closing

public class Sum_closing
extends Object

Closing method for open and mixed non-product-form queueing networks (Bolch et al., Sec. 10.1.5), solved with the summation method. The external world of each open class is replaced by an additional -/G/1 station with service rate mu_inf,r = Ropen*lambda0(r), where Ropen is the number of open classes, service SCV equal to the interarrival time SCV of the open class, and unit visit ratio. The resulting closed network is then solved by Sum_closed with a large population Kclosed for the open classes (5000 is recommended for the summation method). Closed classes are passed through unchanged, which makes the method applicable to mixed networks. Reference: G. Bolch, S. Greiner, H. de Meer, K.S. Trivedi, Queueing Networks and Markov Chains, 2nd ed., Wiley, 2006, Sec. 10.1.5.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	Sum_closing.Result	Result of the closing method.

Constructor Summary

Constructors

Constructor	Description
Sum_closing()

Method Summary

Modifier and Type	Method	Description
static Sum_closing.Result	sum_closing(Matrix lambda0, Matrix scva, Matrix L, Matrix mi, Matrix scv, Matrix N, Matrix Z, double Kclosed, double tol, int maxiter)	Closing method for open and mixed networks solved with SUM.

Methods inherited from class java.lang.Object

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

Constructor Details

Sum_closing

public Sum_closing()

Method Details

sum_closing

public static Sum_closing.Result sum_closing(Matrix lambda0,
 Matrix scva,
 Matrix L,
 Matrix mi,
 Matrix scv,
 Matrix N,
 Matrix Z,
 double Kclosed,
 double tol,
 int maxiter)

Closing method for open and mixed networks solved with SUM.

Parameters:

lambda0 - 1xR external arrival rates (0 for closed classes)

scva - 1xR interarrival time SCVs of the open classes (1 if Poisson)

L - MxR service demand matrix of the original network, with visit ratios of open classes normalized per external arrival

mi - Mx1 number of servers (Double.POSITIVE_INFINITY for IS)

scv - MxR service time SCVs (pass 1 for insensitive stations)

N - 1xR populations: Double.POSITIVE_INFINITY for open classes, finite integers for closed classes

Z - 1xR think times

Kclosed - closing population for the open classes (e.g. 5000)

tol - convergence tolerance (e.g. 1e-6)

maxiter - maximum number of iterations (e.g. 10000)

Returns:

throughputs and original-station metrics