Package jline.api.mdd

package jline.api.mdd
Decision-diagram state-space storage and Miner-Ciardo-Donatelli aggregation.

MDD stores a CTMC reachable set in a quasi-reduced ordered multi-valued decision diagram instead of an explicit state list, and Mdd_mcd solves the chain by level aggregation without ever forming the |S|-state generator. Mdd_rec is the exact counterpart for a model that already has a product form: one memoised walk of the same diagram returns its normalising constant, and the same walk under a per-level mask returns the marginals.

References:

  • A.S. Miner, G. Ciardo, "Efficient Reachability Set Generation and Storage Using Decision Diagrams", ICATPN 1999, LNCS 1639, pp.6-25.
  • A.S. Miner, G. Ciardo, S. Donatelli, "Using the exact state space of a Markov model to compute approximate stationary measures", ACM SIGMETRICS 2000, pp.207-216.
  • S. Balsamo, A. Marin, I. Stojic, "Computation of the normalising constant for product-form models of distributed systems with synchronisation", Future Generation Computer Systems 111 (2020) 475-490.

MATLAB twin: matlab/src/api/mdd/. Python twin: python/line_solver/api/mdd/.

  • Class
    Description
    MDD
    Quasi-reduced ordered Multi-valued Decision Diagram.
    Mdd_closedqn
    Exact solve of a single-class closed exponential queueing network whose CTMC state space (reachable occupancy vectors) is stored in a Multi-valued Decision Diagram instead of an explicit state list.
    Mdd_descriptor
    Kronecker rate descriptor of a single-class closed queueing network.
    Mdd_mcd
    Miner-Ciardo-Donatelli approximate stationary analysis.
    Mdd_ps
    Kronecker rate descriptor for shared-server stations with phase-type service.
    Mdd_reachset
    Reachability set generation into a decision diagram.
    Mdd_rec
    MDD-rec: the normalising constant of a product-form model whose reachable set is held in a decision diagram.
    MddClosedQnResult
    Result of the MDD-stored exact closed-network solve of Mdd_closedqn.
    MddDescriptor
    Kronecker rate descriptor of a structured model, the input of Mdd_mcd.
    MddEvent
    One event of the Kronecker rate descriptor.
    MddLocalMatrix
    A local rate matrix W_k^e of the Kronecker descriptor, held row-compressed.
    MddLocalMatrix.Builder
    Incremental triplet builder; duplicate entries are accumulated.
    MddMcdOptions
    Knobs of the level iteration in Mdd_mcd.
    MddMcdResult
    Result of the Miner-Ciardo-Donatelli level aggregation.
    MddNextState
    Next-state function of a structured model, over local-index tuples.
    MddServiceLaw
    Phase-type service law of one station, as a Markovian (D0,D1) pair.
    MddStats
    Storage description of the set held in an MDD.
    MddStruct
    Plain-array export of an MDD, the input contract of Mdd_mcd.