opt.+opt.+sens

opt.sens.ctmcSensitivities(model, options)

ctmcSensitivities d(metric)/d(rate) for an arbitrary Markovian model, via the generator-derivative equation of Trivedi and Bobbio (2017), Eq. (9.81).

This is the fallback for the cases the differentiated-MVA primitive cannot reach: open, multiserver, and non-unit-visit networks, for which opt.sens.openSensitivities and opt.sens.closedSensitivities return []. It is exact wherever SolverCTMC is exact, and correspondingly it is limited by the state-space size rather than by the product-form assumptions.

Only queue-length sensitivities are produced. Utilization, response time, and throughput are reward rates whose definition involves the solved metrics themselves, so they need the reward-derivative term of Eq. (9.83) and are not covered here.

Returns [] if the model has no CTMC representation of tractable size.

opt.sens.computeModelSensitivities(model, useCTMC)

computeModelSensitivities Analytic d(metric)/d(rate) for a model as an opt.SensitivityData, mirroring native-Python compute_model_sensitivities. Returns [] when unavailable (the optimizer then falls back to finite differences).

The open and closed product-form branches are implemented in opt.sens.openSensitivities and opt.sens.closedSensitivities. Both are fast but narrow: they return [] for open, multiserver, or non-unit-visit networks. When they do, and USECTMC is true, the generator-derivative fallback opt.sens.ctmcSensitivities is tried instead, which is exact but pays for state-space generation.

@param model Network model @param useCTMC Enable the CTMC fallback, default false @return sens opt.SensitivityData or []

opt.sens.openSensitivities(model)

openSensitivities Analytic d(metric)/d(rate) for open product-form networks (single-server queueing and infinite-server delay stations, which decouple), mirroring native-Python _open_sensitivities. Returns [] for closed, mixed, or multiserver networks (finite-difference fallback).

Reference: Z. Liu and P. Nain, INRIA RR-1144 (1989), Thm 3.2 (open BCMP).

opt.sens.closedSensitivities(model): closedSensitivities Analytic d(metric)/d(rate) for closed single-server product-form networks with unit visit ratios, via the differentiated-MVA primitive pfqn_sens. Mirrors native-Python _closed_sensitivities. Returns [] for open, multiserver, or non-unit-visit networks.