Uniformization coefficients of a service-time descriptor, shared by the qsys functions that take the law exactly rather than as a PH fit (qsys_mapg1k, qsys_mgck_sync). More...

#include "line/api/qsys/qsys_mapg1k.h"

Include dependency graph for qsys_svclaw_coeffs.h:

Detailed Description

Uniformization coefficients of a service-time descriptor, shared by the qsys functions that take the law exactly rather than as a PH fit (qsys_mapg1k, qsys_mgck_sync).

Port of matlab/src/api/qsys/qsys_svclaw_coeffs.m. For any matrix M with I + M/theta nonnegative, E[exp(M S)] = sum_n cn[n] (I + M/theta)^n, where c_n = E[e^{-theta S}(theta S)^n/n!]. sum_n c_n = 1 exactly, which both sets the truncation order and certifies it. A residual above 1e-6 warns (unless the session is SILENT) and the coefficients are returned anyway, as in the reference.

The coefficients come from mapg1k_detail::service_coefficients, which builds them by recursion rather than log-gamma (see qsys_mapg1k.h); they agree with the reference to rounding. As in the reference, cn holds nmax+1 terms when the initial order guess reaches the cap nmax, and at most nmax otherwise.

Definition in file qsys_svclaw_coeffs.h.