Package jline.api.mam

Class Qbd_setupdelayoff_closed

java.lang.Object

jline.api.mam.Qbd_setupdelayoff_closed

public final class Qbd_setupdelayoff_closed
extends Object

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	Qbd_setupdelayoff_closed.Result	Mean queue length and throughput of the closed setup/delay-off queue.

Method Summary

Modifier and Type	Method	Description
static Qbd_setupdelayoff_closed.Result	qbd_setupdelayoff_closed(double N, double Z, double mu, double alpharate, double alphascv, double betarate, double betascv)	Mean queue length and throughput of a FINITE-POPULATION queue with setup delay and delay-off.

Methods inherited from class java.lang.Object

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

Method Details

qbd_setupdelayoff_closed

public static Qbd_setupdelayoff_closed.Result qbd_setupdelayoff_closed(double N,
 double Z,
 double mu,
 double alpharate,
 double alphascv,
 double betarate,
 double betascv)

Mean queue length and throughput of a FINITE-POPULATION queue with setup delay and delay-off.

The closed twin of Qbd_setupdelayoff. The population N is finite and Z is the complementary delay, the mean time a customer spends away from this station, so the arrival rate is state dependent, lambda(n) = (N - n)/Z, and the level index is bounded by N. That makes the chain a LEVEL-DEPENDENT QBD over finitely many levels, i.e. a finite CTMC, and it is solved exactly rather than by a matrix-geometric tail.

THE SEMANTICS ARE THE SIMULATOR'S, not the mean-value shortcut's. When the queue empties the server begins a delay-off period; an arrival DURING it finds the server still warm and resumes without setup (Solver_ssj's cancelDelayoff), and only an arrival after the delay-off has expired pays the setup. That is an M/M/1 with setup time AND close-down time. The per-instance cold-start race p_cold*E[setup] + S this replaces raced the delay-off against the per-instance idle time and carried NO queueing term, so it described a serverless instance pool rather than a single-server vacation queue and left the reported response time byte-identical across a tenfold change in the setup mean.

The phase index is overloaded by level exactly as in the open twin: at level 0 phase 1 is the OFF server and the rest are the delay-off; above level 0 the phases are the setup and the last one is the busy server. Only the REACHABLE states are enumerated, because a finite chain cannot carry an unreachable row: it would be absorbing and the stationary solve singular.

Parameters:

N - population of the closed chain

Z - complementary delay, the mean time a customer spends away

mu - service rate of the station

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 queue length and the throughput