Package jline.api.snc

Class Snc_srv_exp

java.lang.Object
jline.api.snc.Snc_srv_exp
public final class Snc_srv_exp extends Object
MGF service envelope of an exponential server, in JOB units.

A single server with Exp(mu) service times completes jobs at the epochs of a Poisson process of rate mu while it is busy, so its cumulative service counted in JOBS is Poisson with mean mu*(t-s) and rho(theta) = mu*(1-exp(-theta))/theta with a zero burst.

THIS IS THE SERVICE ELEMENT TO USE WHENEVER THE WORK UNIT IS THE JOB. Pairing Snc_srv_rate with a job-counting arrival envelope would model a server that completes jobs at deterministic intervals, an M/D/1, and would UNDERSTATE the delay of an exponential server rather than bound it. The M/M/1 read with this element instead reproduces both exact decay rates: the backlog bound decays as (lambda/mu)^n in jobs and the delay bound as exp(-(mu-lambda)*d) in time, since the optimal theta tends to log(mu/lambda).

Job units also compose across hops: a departure envelope from Snc_output is a job count and is directly the arrival envelope of the next station, whereas service-time work units differ from station to station.

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

  • Method Details

    • snc_srv_exp

      public static double[] snc_srv_exp(double mu, double theta)
      Parameters:
      mu - service rate, jobs per slot
      theta - Chernoff parameter, theta > 0
      Returns:
      {0, rho}

    • of

      public static SncEnvelope of(double mu)
      Parameters:
      mu - service rate
      Returns:
      the envelope as a function of theta