Package jline.api.mapqn

Class Mapqn_bnd_lr_mva

java.lang.Object

jline.api.mapqn.Mapqn_bnd_lr_mva

public final class Mapqn_bnd_lr_mva
extends Object

Implementation of bnd_mvaversion.mod linear program: the MAP-AMVA optimization program of G. Casale, E. Smirni, "MAP-AMVA: Approximate Mean Value Analysis of Bursty Systems", IEEE/IFIP DSN 2009, pp. 409-418.

The constraints assembled below are the paper's: the population constraint (1), the utilization bound (2), the MAP phase balance (3), the flow balance (4), the generalized horizontal cut (12), the vertical-cut MVA relation (13) in the linearized form (18)-(19) whose B(j,k,i) variables are the E_i^{j,k} of Theorem 4, and the two auxiliary families QN <= N*UN and sum_w QN >= N*UN.

Method Summary

Modifier and Type	Method	Description
static double	getQueueLengthMVA(Mapqn_solution sol, int i, int k)
static double	getUtilizationMVA(Mapqn_solution sol, int i, int k)
static Mapqn_solution	solve(MVAVersionParameters params, int objectiveQueue, int objectiveLevel)
static Mapqn_solution	solve(MVAVersionParameters params, int objectiveQueue, int objectiveLevel, String sense)	As above, optimizing in the requested direction.
static Mapqn_solution	solve(MVAVersionParameters params, int objectiveQueue, int objectiveLevel, String sense, String objectiveVar)	As above, over a chosen variable family and optionally over the SUM of the levels.

Methods inherited from class java.lang.Object

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

Method Details

solve

public static Mapqn_solution solve(MVAVersionParameters params,
 int objectiveQueue,
 int objectiveLevel)

solve

public static Mapqn_solution solve(MVAVersionParameters params,
 int objectiveQueue,
 int objectiveLevel,
 String sense)

As above, optimizing in the requested direction. The LP is a relaxation containing the exact solution, so "max" is a valid upper bound on the utilization at that population level and "min" the matching lower bound.

Parameters:

sense - "min" or "max"

solve

public static Mapqn_solution solve(MVAVersionParameters params,
 int objectiveQueue,
 int objectiveLevel,
 String sense,
 String objectiveVar)

As above, over a chosen variable family and optionally over the SUM of the levels.

objectiveLevel == 0 optimizes the aggregate sum_k X(queue, k), which is the quantity the paper's bounds are stated on: U_i(N) = sum_k U_i^k(N) is the utilization of station i, while U_i^k alone is its utilization while the MAP sits in phase k. Optimizing the K terms separately and adding them is also a bound but a strictly looser one, since the phases cannot all peak at once.

Parameters:

objectiveVar - "UN" or "QN", the variable family optimized over

getUtilizationMVA

public static double getUtilizationMVA(Mapqn_solution sol,
 int i,
 int k)

getQueueLengthMVA

public static double getQueueLengthMVA(Mapqn_solution sol,
 int i,
 int k)