Package jline.api.qsys

Class Qsys_mmc_prio_tardiness

java.lang.Object

jline.api.qsys.Qsys_mmc_prio_tardiness

public final class Qsys_mmc_prio_tardiness
extends Object

Exact stationary expected tardiness E[(T_i - d_i)^+] and tardiness probability P(T_i > d_i) of each class of a multiclass M/M/c queue with a common exponential service rate, FCFS within a class and static priorities (class 1 highest), under head-of-line ("np") or preemptive-resume ("pr") priority (Hafizoglu, Gel and Keskinocak, INFORMS J. Comput. 25(2), 2013).

A class-i order that finds all servers busy waits q+1 busy periods of an M/M/1 queue with the higher-priority rate and service rate c mu (Theorem 2); under preemption the in-service states solve the tridiagonal system of Theorem 4. Mixing over the stationary state seen on arrival gives the response-time transform f(s); tardiness and its probability are the inverses at d of (s E[T] - 1 + f(s))/s^2 and (1 - f(s))/s. Classes with no higher-priority traffic use a closed form.

Java twin of matlab/src/api/qsys/qsys_mmc_prio_tardiness.m.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	Qsys_mmc_prio_tardiness.Result	Per-class results, in the order of the input rates.

Method Summary

Modifier and Type	Method	Description
static Qsys_mmc_prio_tardiness.Result	qsys_mmc_prio_tardiness(double[] lambda, double mu, int c, double[] d)
static Qsys_mmc_prio_tardiness.Result	qsys_mmc_prio_tardiness(double[] lambda, double mu, int c, double[] d, String type, String method)
static Qsys_mmc_prio_tardiness.Result	qsys_mmc_prio_tardiness(double[] lambda, double mu, int c, double d, String type, String method)

Methods inherited from class java.lang.Object

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

Method Details

qsys_mmc_prio_tardiness

public static Qsys_mmc_prio_tardiness.Result qsys_mmc_prio_tardiness(double[] lambda,
 double mu,
 int c,
 double[] d)

qsys_mmc_prio_tardiness

public static Qsys_mmc_prio_tardiness.Result qsys_mmc_prio_tardiness(double[] lambda,
 double mu,
 int c,
 double d,
 String type,
 String method)

qsys_mmc_prio_tardiness

public static Qsys_mmc_prio_tardiness.Result qsys_mmc_prio_tardiness(double[] lambda,
 double mu,
 int c,
 double[] d,
 String type,
 String method)

Parameters:

lambda - per-class arrival rates in priority order (class 1 highest)

mu - common service rate

c - number of servers

d - one due date, or one per class; infinity means none

type - "np" head-of-line or "pr" preemptive resume

method - Laplace inversion method of Laplace_invert.laplace_invert(java.util.function.UnaryOperator<org.apache.commons.math3.complex.Complex>, double, java.lang.String, int)