Package jline.solvers.mam.handlers

Class Mam_bgchain_env

java.lang.Object
jline.solvers.mam.handlers.Mam_bgchain_env
public final class Mam_bgchain_env extends Object
Lumps the background modulating chain onto the number of closed jobs held by one station, giving the Markovian environment that the open classes at that station see.

Station i does not observe the whole closed population vector, only how many closed jobs compete with the open ones for its server. The lumped generator is the stationary-weighted aggregation of the chain's generator over the level sets {s : totocc(s,i) = e},

A(e,e') = sum_{s in e} pi(s) sum_{s' in e'} Q(s,s') / sum_{s in e} pi(s),

which is exact when the partition is lumpable in the Kemeny-Snell sense and is the standard exact-aggregation approximation otherwise. The diagonal is set from the off-diagonal row sums, so A is a proper generator whatever the lumping error is. Environment states of zero stationary probability are unreachable and are dropped, so the support need not be 0..N.

See Also:

  • Method Details

    • mam_bgchain_env

      public static Mam_bgchain_env.Env mam_bgchain_env(Mam_bgchain_ctmc.Result bg, int i)
      Parameters:
      bg - the solved background chain
      i - index of the station within the chain's support
      Returns:
      the lumped environment