Package jline.examples.java.basic

Class OpenBMMAPtModel

java.lang.Object
jline.examples.java.basic.OpenBMMAPtModel
public class OpenBMMAPtModel extends Object
Open queueing network whose arrival stream is a BATCH, MARKED, time-inhomogeneous MAP.

BMMAPt crosses the three axes LINE models for an arrival stream. A block is indexed by segment, mark and batch size: D1kb[c][b][j] holds the rates that, in segment j, release a batch of b+1 jobs ALL carrying mark c+1, and D0[j] plus the sum of every block is a generator in each segment. At a Source the mark selects the CLASS of the arriving jobs and the batch size says HOW MANY of them arrive at that instant.

Two derived levels come for free and are what keep the family legible: summing over b gives the MMAPt of the marks alone, and summing over c as well gives the MAPt of the epochs alone. So a consumer that ignores batches sees exactly the marked schedule, and one that ignores marks too sees exactly the unmarked one.

The schedule below moves BOTH the class mix and the batch size, which is the point: it is the combination no existing family expresses. Every segment fires epochs at rate 4, so the epoch stream is statistically identical throughout; what changes is which class the batch carries and how big it is. In the morning segment the Premium class arrives in PAIRS and Economy singly; in the evening segment that reverses. The JOB rate therefore differs from the EPOCH rate, and differs per class within a segment even though the epoch rate does not.

Reductions worth knowing: with every batch size 1 a BMMAPt IS the MMAPt with the same blocks, sample path for sample path on one seed; with K = 1 it is the unmarked batch schedule; with both it is the MAPt; and with identical segments it is the stationary BMAP.

References: Q.-M. He, "The versatility of MMAP[K] and the MMAP[K]/G[K]/1 queue", Queueing Systems 38(4), 2001, for the marked structure; D. M. Lucantoni, "New results on the single server queue with a batch Markovian arrival process", Stochastic Models 7(1), 1991, for the batch structure; Y. M. Ko and J. Pender, "Diffusion limits for the (MAP_t/Ph_t/inf)^N queueing network", Oper. Res. Lett. 45(3), 2017, for the time-inhomogeneous one.

  • Constructor Details

    • OpenBMMAPtModel

      public OpenBMMAPtModel()

  • Method Details

    • example

      public static Network example()
      Builds a Source -> Queue -> Sink model whose arrivals follow a two-segment BMMAPt.

    • main

      public static void main(String[] args)