Package jline.api.mam

Class Qbd_setupdelayoff_mmk

java.lang.Object

jline.api.mam.Qbd_setupdelayoff_mmk

public final class Qbd_setupdelayoff_mmk
extends Object

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	Qbd_setupdelayoff_mmk.Result	Mean number present and throughput of the setup/delayed-off pool.

Method Summary

Modifier and Type	Method	Description
static Qbd_setupdelayoff_mmk.Result	qbd_setupdelayoff_mmk(int k, double N, double arv, double mu, double alpharate, double alphascv, double betarate, double betascv)	Mean number present and throughput of a k-SERVER queue whose servers each pay a setup when woken from off and count down a delay-off when idle.

Methods inherited from class java.lang.Object

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

Method Details

qbd_setupdelayoff_mmk

public static Qbd_setupdelayoff_mmk.Result qbd_setupdelayoff_mmk(int k,
 double N,
 double arv,
 double mu,
 double alpharate,
 double alphascv,
 double betarate,
 double betascv)

Mean number present and throughput of a k-SERVER queue whose servers each pay a setup when woken from off and count down a delay-off when idle.

The M/M/k/setup/delayedoff model of Gandhi, Harchol-Balter and Adan (Performance Evaluation 67(11), 2010), solved exactly as a finite CTMC over its REACHABLE states, under the admission rules of the LDES engine (Solver_ssj_ln.admitWithSetup), which are what a SetupTask means:

• an arrival takes an ACTIVE idle server if one exists, else one still counting down its delay-off (the countdown is cancelled and it pays nothing), else it queues and wakes ONE off server, if any is off;
• a server that completes takes the head of the queue, or starts its delay-off when the queue is empty, and powers off when that expires;
• a setup is never cancelled: a server finishing it takes the head of the queue, or stays ACTIVE and idle with no countdown when the queue is empty.

A state is (queued, busy, active-idle, setup phase counts, delay-off phase counts), the remaining servers being off. Both phases are taken in canonical Coxian form, entered at phase 1 for every SCV; servers in a phase are exchangeable, so an arrival that catches a delay-off server catches one in phase j with probability proportional to the count there, which is exact whenever the delay-off is exponential. With k = 1 the chain is the one Qbd_setupdelayoff_closed solves.

With N finite the population is closed and ARV is the complementary delay Z, so lambda(n) = (N-n)/Z. With N infinite ARV is the Poisson rate and the level is truncated where the probability of the top level falls below GlobalConstants.Zero, doubling the truncation until it does; the queue must then be stable, arv < k*mu.

Parameters:

k - number of servers

N - closed population, or infinity for an open queue

arv - complementary delay Z when N is finite, arrival rate when it is not

mu - service rate of one server

alpharate - rate of the setup phase

alphascv - squared coefficient of variation of the setup phase

betarate - rate of the delay-off phase

betascv - squared coefficient of variation of the delay-off phase

Returns:

the mean number present and the throughput