Package jline.api.npfqn

Class Npfqn_gtmtst_fluid

java.lang.Object

jline.api.npfqn.Npfqn_gtmtst_fluid

public final class Npfqn_gtmtst_fluid
extends Object

Time-varying open network of many-server fluid queues with abandonment.

Each queue is the Gt/Mt/st+GI fluid queue of Qsys_gtmtst_fluid; the departure flow of queue i is routed to queue j with the proportion P[i][j], and whatever is left leaves the network.

THE NETWORK IS A FIXED POINT. The total arrival rate of queue j is lambda_j(t) = lambda_j^0(t) + sum_i sigma_i(t)P_ij(t) with sigma_i = mu_i B_i the service completion rate (eqs. 23-24), and sigma_i itself depends on lambda_i. The iteration starts from the external rates alone and adds one more traversal of the network per round, so the nth iterate is the fluid that has made n transitions; the map is a monotone contraction, so the rates increase to the fixed point rather than oscillating.

Only the SERVICE COMPLETION flow is routed. Abandoning fluid leaves the network, which is what makes the traffic equations linear in sigma.

Port of MATLAB npfqn_gtmtst_fluid.m.

Reference: Y. Liu, W. Whitt (2014). Algorithms for time-varying networks of many-server fluid queues. INFORMS Journal on Computing 26(1), 59-73.

Since:

LINE 3.1.0

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	Npfqn_gtmtst_fluid.Result	Result of the network solve.

Method Summary

Modifier and Type	Method	Description
static Npfqn_gtmtst_fluid.Result	npfqn_gtmtst_fluid(DoubleUnaryOperator[] lambdaFuns, DoubleUnaryOperator[] sFuns, DoubleUnaryOperator[] muFuns, DoubleUnaryOperator[] patienceCcdfs, double[][] P, double T, double dt, double[] B0, double[] w0, double tol, int maxIter)

Methods inherited from class java.lang.Object

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

Method Details

npfqn_gtmtst_fluid

public static Npfqn_gtmtst_fluid.Result npfqn_gtmtst_fluid(DoubleUnaryOperator[] lambdaFuns,
 DoubleUnaryOperator[] sFuns,
 DoubleUnaryOperator[] muFuns,
 DoubleUnaryOperator[] patienceCcdfs,
 double[][] P,
 double T,
 double dt,
 double[] B0,
 double[] w0,
 double tol,
 int maxIter)

Parameters:

lambdaFuns - external arrival rate of each queue

sFuns - staffing of each queue

muFuns - service rate of each queue

patienceCcdfs - patience ccdf of each queue

P - routing proportions, substochastic

T - horizon

dt - grid step; non-positive takes T/2000

B0 - initial fluid in service, or null for empty

w0 - initial boundary waiting times, or null for empty

tol - sup-norm tolerance on the arrival-rate iteration

maxIter - cap on the iterations

Returns:

the network solution