Package jline.api.polling

Class Polling_pcl

java.lang.Object

jline.api.polling.Polling_pcl

public final class Polling_pcl
extends Object

Pseudo-conservation law of a cyclic polling system with Poisson arrivals (Boxma and Groenendijk 1987; Takagi, "Queuing Analysis of Polling Models", ACM Computing Surveys 20(1), 1988, eq. (10)). The law is exact for any mix of exhaustive (E), gated (G), 1-limited (L) and decrementing (D) queues:

   SUM_i w_i E[W_i] = rhs

   w_i = rho_i                                   (E, G)
       = rho_i (1 - lambda_i R/(1-rho))           (L)
       = rho_i (1 - lambda_i (1-rho_i) R/(1-rho)) (D)

   rhs = rho SUM_i lambda_i b2_i/(2(1-rho)) + rho Delta2/(2R)
       + R (rho - SUM_i rho_i^2)/(2(1-rho)) + R/(1-rho) SUM_{G,L} rho_i^2
       - R/(2(1-rho)) SUM_D rho_i lambda_i^2 b2_i
 

where R and Delta2 are the mean and variance of the total switchover time per cycle. Port of MATLAB polling_pcl.m.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	Polling_pcl.Result	Weights and right-hand side of the law; pcl = rhs / SUM(w).

Method Summary

Modifier and Type	Method	Description
static Polling_pcl.Result	polling_pcl(double[] lambda, double[] b, double[] b2, double[] r1, double[] delta2, char[] code)	Pseudo-conservation law for a per-queue mix of disciplines.
static Polling_pcl.Result	polling_pcl(double[] lambda, double[] b, double[] b2, double[] r1, double[] delta2, PollingType type)	Pseudo-conservation law for one discipline at every queue.

Methods inherited from class java.lang.Object

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

Method Details

polling_pcl

public static Polling_pcl.Result polling_pcl(double[] lambda,
 double[] b,
 double[] b2,
 double[] r1,
 double[] delta2,
 PollingType type)

Pseudo-conservation law for one discipline at every queue.

Parameters:

lambda - per-queue Poisson arrival rate

b - per-queue mean service time

b2 - per-queue second service moment

r1 - mean switchover out of each queue

delta2 - variance of the switchover out of each queue

type - polling discipline; K-limited and G-limited mean K=1

polling_pcl

public static Polling_pcl.Result polling_pcl(double[] lambda,
 double[] b,
 double[] b2,
 double[] r1,
 double[] delta2,
 char[] code)

Pseudo-conservation law for a per-queue mix of disciplines.

Parameters:

code - per-queue class: 'E', 'G', 'L' (1-limited) or 'D'