Package jline.api.pfqn

Class Pfqn_mwrbb

java.lang.Object

jline.api.pfqn.Pfqn_mwrbb

public final class Pfqn_mwrbb
extends Object

Majumdar-Woodside robust box bounds on throughput for closed multiclass queueing networks with mixed scheduling disciplines.

Computes distribution-insensitive (NBUE) upper and lower bounds on the per-class system throughput of a closed multiclass queueing network, per S. Majumdar and C.M. Woodside, "Robust bounds and throughput guarantees for closed multiclass queueing networks", Performance Evaluation 32 (1998) 101-136. The upper bound intersects the no-contention bound (eq. 2) with the utilization-based bound (eq. 3) and is independent of the scheduling discipline. The lower bound is the multiclass throughput guarantee of Theorem 2 (eq. 15): X_c >= N_c / (Z_c + sum_k V_kc (S_kc + d_kc+)), where the per-visit queueing delay bound d_kc+ depends on the discipline at station k -- FIFO (Theorem 1 / eq. 6, via Lemma 1), processor sharing (Lemma 2), preemptive priority (Lemma 3) and non-preemptive priority (Lemmas 4-5). The coupled inequalities are resolved by the interval- narrowing fixed point reproducing the BNR-Prolog robust box bounds; for a single FIFO class it reduces to the Muntz-Wong asymptotic bounds.

Bounds are insensitive to the service-time distributions (only NBUE is assumed) and to routing dependencies. The think time Z aggregates the pure-delay (infinite-server) stations; only queueing stations are passed in V,S.

Since:

LINE 3.0

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	Pfqn_mwrbb.Result	Result holder for pfqn_mwrbb(jline.util.matrix.Matrix, jline.util.matrix.Matrix, jline.util.matrix.Matrix, jline.util.matrix.Matrix).

Field Summary

Fields

Modifier and Type	Field	Description
static final int	ABA
static final int	FIFO	Discipline codes for the sched argument.
static final int	NPPRIO
static final int	PPPRIO
static final int	PS

Method Summary

Modifier and Type	Method	Description
static Pfqn_mwrbb.Result	pfqn_mwrbb(Matrix V, Matrix S, Matrix N, Matrix Z)	FIFO, equal-priority convenience overload.
static Pfqn_mwrbb.Result	pfqn_mwrbb(Matrix V, Matrix S, Matrix N, Matrix Z, Matrix sched, Matrix prio)

Methods inherited from class java.lang.Object

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

Field Details

FIFO

public static final int FIFO

Discipline codes for the sched argument.

See Also:

• Constant Field Values

PS

public static final int PS

See Also:

• Constant Field Values

NPPRIO

public static final int NPPRIO

See Also:

• Constant Field Values

PPPRIO

public static final int PPPRIO

See Also:

• Constant Field Values

ABA

public static final int ABA

See Also:

• Constant Field Values

Method Details

pfqn_mwrbb

public static Pfqn_mwrbb.Result pfqn_mwrbb(Matrix V,
 Matrix S,
 Matrix N,
 Matrix Z)

FIFO, equal-priority convenience overload.

pfqn_mwrbb

public static Pfqn_mwrbb.Result pfqn_mwrbb(Matrix V,
 Matrix S,
 Matrix N,
 Matrix Z,
 Matrix sched,
 Matrix prio)

Parameters:

V - (K x C) mean visits of class c at queueing station k

S - (K x C) mean service demand per visit of class c at station k

N - (1 x C) or (C x 1) population of class c

Z - (1 x C) or (C x 1) think time of class c (may be null)

sched - (K x 1) discipline code per station (0=FIFO, 1=PS, 2=non-preemptive priority, 3=preemptive priority); null => all FIFO

prio - (1 x C) class priority, lower value = higher priority; null => all equal

Returns:

robust box bounds and per-visit residence times