Package jline.api.qsys

Class Qsys_mapmapc

java.lang.Object
jline.api.qsys.Qsys_mapmapc
public final class Qsys_mapmapc extends Object
The MAP/MAP/c FCFS queue whose service MAP is CARRIED in service-start order. THE SERVICE LAW. The service MAP is one station-level process whose successive draws are chained in service-START order, idle periods included: each job starts in the phase the previous draw ENDED in, which is how JMT and both LDES engines sample a MAP service and the law SolverCTMC follows through its pair form. A renewal reading of the marginal (qsys_mapphc, or the single-fast-server surrogate) discards the autocorrelation of the service times. THE STATE SPACE. With V = (-S0)^-1 S1, a draw started in h lands in j with probability V(h,j); a busy server is a PAIR (i,j) of current phase i and landing j, run under S0 conditioned on ending in j. A level holds the MULTISET of busy pairs and the landing phase of the draw started last. LdqbdMphc with carry=true builds those blocks; this class lifts them to a MAP arrival stream and solves the level-independent QBD above level c matrix-geometrically, as Qsys_mapphc does for a renewal service. At c = 1 the chain is the frozen-phase MAP/MAP/1 queue. 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. M.F. Neuts, "Matrix-geometric solutions in stochastic models", Johns Hopkins University Press, 1981.

  • Method Details

    • qsys_mapmapc

      public static QsysMapPhcResult qsys_mapmapc(Matrix D0, Matrix D1, Matrix S0, Matrix S1, int c)

    • qsys_mapmapc

      public static QsysMapPhcResult qsys_mapmapc(Matrix D0, Matrix D1, Matrix S0, Matrix S1, int c, int maxNumComp, int numWMoms)
      Parameters:
      D0 - arrival MAP hidden block, order ma
      D1 - arrival MAP arrival block, order ma
      S0 - service MAP hidden block, order p
      S1 - service MAP completion block, order p
      c - number of servers
      maxNumComp - cap on the queue length probabilities returned
      numWMoms - how many waiting-time moments to return
      Returns:
      the exact solution