Package jline.api.snc

package jline.api.snc
Stochastic network calculus (SNC).

The only api domain in LINE whose deliverable is a TAIL QUANTILE with a certified violation probability rather than a mean. An envelope is the pair (sigma(theta), rho(theta)) in the exponential form

   E[exp(theta*A(s,t))] <= exp(theta*(rho*(t-s) + sigma)),   theta > 0,

and its service counterpart with the sign of theta reversed. The min-plus operations (Snc_leftover, Snc_conv, Snc_output) compose envelopes across a feed-forward network, and every bound is a Chernoff infimum over theta computed by Snc_thetaopt.

TIME IS SLOTTED with unit slot length, which is what makes the geometric sum over the start of the backlogged period converge to 1/(1-exp(-theta*(rhoS-rhoA))); the continuous-time formulation would give 1/(theta*(rhoS-rhoA)) instead. INFEASIBILITY IS SIGNALLED BY Infinity, never by an exception, so the theta search can discard the point.

Port of matlab/src/api/snc. Wired into SolverBA as the method snc.upper.

Reference: M. Fidler, A. Rizk, "A Guide to the Stochastic Network Calculus", IEEE Communications Surveys and Tutorials 17(1), 92-105, 2015.

  • Class
    Description
    Snc_bound_backlog
    Violation probability of a backlog level.
    Snc_bound_delay
    Violation probability of a delay target.
    Snc_conv
    Min-plus convolution of two service envelopes (tandem concatenation).
    Snc_env_cpoisson
    MGF arrival envelope of a compound Poisson flow with Exp job sizes.
    Snc_env_map
    MGF arrival envelope of a MAP/MMPP flow with unit-size jobs.
    Snc_env_poisson
    MGF arrival envelope of a Poisson flow with unit-size jobs.
    Snc_env_tokenbucket
    Deterministic token-bucket arrival envelope.
    Snc_leftover
    Leftover service envelope under blind (arbitrary) multiplexing.
    Snc_mean_backlog
    Upper bound on the mean backlog, from integrating the backlog tail bound.
    Snc_mean_delay
    Upper bound on the mean delay, from integrating the delay tail bound.
    Snc_output
    Output (departure) arrival envelope of a flow leaving a server.
    Snc_perc_backlog
    Backlog quantile at a prescribed violation probability.
    Snc_perc_delay
    Delay quantile at a prescribed violation probability.
    Snc_srv_exp
    MGF service envelope of an exponential server, in JOB units.
    Snc_srv_rate
    MGF service envelope of a constant-rate work-conserving server.
    Snc_thetaopt
    Minimizes a Chernoff bound over the free parameter theta.
    SncEnvelope
    An MGF envelope evaluated at a Chernoff parameter.
    SncResult
    The value of a Chernoff bound together with the theta that attains it.