Package jline.api.qsys

Class Qsys_mg1_breakdown

java.lang.Object

jline.api.qsys.Qsys_mg1_breakdown

public final class Qsys_mg1_breakdown
extends Object

M/G/1 FCFS queue whose server fails after an exponential up time of rate alpha, busy or idle, and is restored after a general repair time R, with preemptive resume and arrivals continuing while down: the semantics of Queue.setBreakdown without down service. Port of MATLAB qsys_mg1_breakdown.m.

The busy period opens with the residual repair time D met by a job arriving to an empty system, and each job then holds the server for its completion time C = S + repairs during S (Gaver 1962). The queue is an M/G/1 with exceptional first service C0 = D + C (Welch 1964; Avi-Itzhak and Naor 1963). Stable iff lambda E[S] (1 + alpha E[R]) < 1.

Method Summary

Modifier and Type	Method	Description
static QsysMeanValueResult	qsys_mg1_breakdown(double lambda, double mu, double cs, double alpha, double ER, double ER2, double rlst)

Methods inherited from class java.lang.Object

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

Method Details

qsys_mg1_breakdown

public static QsysMeanValueResult qsys_mg1_breakdown(double lambda,
 double mu,
 double cs,
 double alpha,
 double ER,
 double ER2,
 double rlst)

Parameters:

lambda - Poisson arrival rate

mu - service rate, E[S] = 1/mu

cs - coefficient of variation of the service time

alpha - failure rate of an up server (0: no failures, the M/G/1)

ER - mean repair time

ER2 - second raw moment of the repair time

rlst - repair LST at the arrival rate, R*(lambda), in (0,1)

Returns:

W, Wq = W - 1/mu, U = lambda/mu, Q = mean number in system