Package jline.api.qsys

Class Qsys_mapphc

java.lang.Object

jline.api.qsys.Qsys_mapphc

public final class Qsys_mapphc
extends Object

The MAP/PH/c FCFS queue, solved exactly. THE STATE SPACE. With c identical servers the server identities carry no information, so the service phases are held as a MULTISET: a configuration is n = (n_1..n_ms) with sum(n) = k servers busy in phase i. There are binomial(ms+k-1,k) of them, the count of Asmussen and Moller (2001), against ms^k for the ordered space. Levels 0..c-1 are the boundary (level = servers busy), levels >= c repeat and carry the queue. THE WAITING TIME. An arrival that finds j customers waiting ahead of it waits for j+1 service completions, so Wq is the (j+1)-st event time of the configuration MAP (Lc, Cdep) started at the arrival-epoch configuration. Folding the matrix-geometric level distribution over j gives the LINEAR matrix ODE G'(t) = G Lj + R G Cj with G(0) = (I-R)^-1 kron(D1,I)/lambda and P(Wq > t) = pi_c G(t) e, so Wq is matrix-exponential. Its transform obeys the generalized Sylvester equation g(sI-Lj) - R g Cj = G(0), and every moment reuses that one operator with a different right-hand side. References: S. Asmussen and J.R. Moller, "Calculation of the steady state waiting time distribution in GI/PH/c and MAP/PH/c queues", Queueing Systems 37(1):9-29, 2001. D.P. Gaver, P.A. Jacobs, G. Latouche, "Finite birth-and-death models in randomly changing environments", Adv. Appl. Probab. 16:715-731, 1984.

Method Summary

Modifier and Type	Method	Description
static QsysMapPhcResult	qsys_mapphc(Matrix D0, Matrix D1, Matrix alpha, Matrix S, int c)
static QsysMapPhcResult	qsys_mapphc(Matrix D0, Matrix D1, Matrix alpha, Matrix S, int c, int maxNumComp, int numWMoms, Matrix wPoints)

Methods inherited from class java.lang.Object

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

Method Details

qsys_mapphc

public static QsysMapPhcResult qsys_mapphc(Matrix D0,
 Matrix D1,
 Matrix alpha,
 Matrix S,
 int c)

qsys_mapphc

public static QsysMapPhcResult qsys_mapphc(Matrix D0,
 Matrix D1,
 Matrix alpha,
 Matrix S,
 int c,
 int maxNumComp,
 int numWMoms,
 Matrix wPoints)

Parameters:

D0 - arrival MAP hidden block, order ma

D1 - arrival MAP arrival block, order ma

alpha - PH service initial vector, order ms

S - PH service sub-generator, order ms

c - number of servers

maxNumComp - cap on the queue length probabilities returned

numWMoms - how many waiting-time moments to return

wPoints - times at which to evaluate P(Wq > t), or null

Returns:

the exact solution