Package jline.api.snc

Class Snc_bound_delay

java.lang.Object
jline.api.snc.Snc_bound_delay
public final class Snc_bound_delay extends Object
Violation probability of a delay target.

For a flow with arrival envelope (sigmaA,rhoA) served by an element with service envelope (sigmaS,rhoS), the virtual delay of the stable station obeys, for every theta > 0,

   P{D(t) > d} <= exp(-theta*(rhoS*d-sigmaA-sigmaS)) / (1-exp(-theta*(rhoS-rhoA))),

the horizontal rather than vertical deviation between the arrival and service envelopes. On the M/M/1 read in job units (Snc_env_poisson with Snc_srv_exp) the optimal theta tends to log(mu/lambda), so the bound reproduces the exact asymptotic decay rate exp(-(mu-lambda)*d).

Port of matlab/src/api/snc/snc_bound_delay.m.

  • Method Details

    • snc_bound_delay

      public static SncResult snc_bound_delay(SncEnvelope arv, SncEnvelope srv, double d)
      Parameters:
      arv - arrival envelope
      srv - service envelope
      d - delay target, slots
      Returns:
      the bound on P{D > d} in [0,1], and the minimizing theta

    • snc_bound_delay

      public static SncResult snc_bound_delay(SncEnvelope arv, SncEnvelope srv, double d, double thetamax)
      Parameters:
      arv - arrival envelope
      srv - service envelope
      d - delay target
      thetamax - upper end of the theta search
      Returns:
      the bound on P{D > d} in [0,1], and the minimizing theta