Package jline.api.sum

Class Sum_closed

java.lang.Object

jline.api.sum.Sum_closed

public class Sum_closed
extends Object

Summation method (SUM) for closed queueing networks, including the extended SUM (ESUM) node functions for non-product-form networks with generally distributed service times. The method expresses the mean queue length of each station as a function of its throughput, Ki = fi(lambdai), and solves the population constraint sum_i Ki = K. Single-class models are solved by bisection on the system throughput (Bolch et al., Sec. 9.2.1); multiclass models by Gauss-Seidel sweeps of per-class bisections on the population constraints, a robust alternative to the successive substitution of Sec. 9.2.2. Node functions: - Product-form stations (scv=1, or insensitive disciplines PS/LCFS-PR, for which the caller must pass scv=1): Eq. (9.15)/(9.19). - FCFS stations with general service (scv!=1): ESUM corrections, Eq. (10.88) for -/G/1 and Eq. (10.89) for -/G/m, with ai=(1+scv_i)/2 and Erlang-C waiting probability P_mi. - Infinite-server stations (mi=Inf) and think times Z: Ki = lambdai*Li. Reference: G. Bolch, S. Greiner, H. de Meer, K.S. Trivedi, Queueing Networks and Markov Chains, 2nd ed., Wiley, 2006, Secs. 9.2 and 10.1.4.4.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	Sum_closed.Result	Result of the summation method.

Constructor Summary

Constructors

Constructor	Description
Sum_closed()

Method Summary

Modifier and Type	Method	Description
static Sum_closed.Result	sum_closed(Matrix L, Matrix N, Matrix Z, Matrix mi, Matrix scv, double tol, int maxiter)	Summation method for closed queueing networks.

Methods inherited from class java.lang.Object

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

Constructor Details

Sum_closed

public Sum_closed()

Method Details

sum_closed

public static Sum_closed.Result sum_closed(Matrix L,
 Matrix N,
 Matrix Z,
 Matrix mi,
 Matrix scv,
 double tol,
 int maxiter)

Summation method for closed queueing networks.

Parameters:

L - MxR service demand matrix, L(i,r) = e(i,r)/mu(i,r)

N - 1xR population vector

Z - 1xR think times (aggregated as a delay term)

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

scv - MxR squared coefficient of variation of service times

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

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

Returns:

throughputs, queue lengths, utilizations, residence times