Abstract In this paper, we deal with the lumpability approach to cope state space explosion problem inherent computation of stationary performance indices large stochastic models. The method is based on a aggregation technique and applies Markov chains exhibiting some structural regularity. Moreover, it allows one efficiently compute exact values when model actually lumpable. notion quasi-lumpa...

This paper suggests to replace PIs and PIDs, which play a key role in control engineering, by intelligent Proportional-Derivative feedback loops, or iPDs, are derived from model-free control. standpoint is enhanced laboratory experiment.

Abstract The main goal of this paper is estimating certain new fractional integral inequalities for the extended Chebyshev functional in sense synchronous functions by employing proportional (PFI) and Hadamard integral. We establish concerning one- two-parameter integrals. also discuss particular cases.

Proportional odds models are commonly used to model ordinal responses, but the proportional assumption may not hold in practice, leading biased inference. Tests such as score, Wald and likelihood ratio (LR) have been proposed evaluate based on without assumption. Brant has an independent binary model-based Wald-type test, Wolfe Gould extended idea propose LR-type test. This paper provides a bri...