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In a previous paper, hereafter referred to as I, we have analyzed the 7 TeVLHC data on W + jets events from the standpoint of IR-improved DGLAP partonshower effects, using the IR-improved Herwiri1.031 parton shower MC incomparison with the Herwig6.5 parton shower MC in the context of the exact$O(\alpha_s)$ matrix element matched parton shower framework provided byMG5\_aMC@NLO. In the current paper, we extend this analysis to the LHC 8 and 13TeV data to investigate the energy dependence of the results obtained in I.Specifically, W~+ jet events are generated in the MADGRAPH5\_aMC@NLO frameworkand showered by HERWIG6.521 and HERWIRI1.031 with $\mathtt{PTRMS}=2.2$ and 0GeV, respectively. The differential cross sections are reported as functions ofjet multiplicity, transverse linear momenta ($P_{T}$), the jet pesudo-rapidity($\eta$) and the scalar sum of jet transverse momenta ($H_{T}$) for differentjet multiplicities 1--3. The dijet cross sections as functions of transverselinear momenta, invariant mass of the dijet and the jet separation are shown aswell. Distributions of angular correlations between the jets and the muon areexamined as well and the corresponding cross sections are presented. Therespective measured cross sections are compared with the exactnext-to-leading-order (NLO) matrix element matched parton shower theoreticalpredictions provided by MADGRAPH5\_aMC@NLO/HERWIRI1.031~($\mathtt{PTRMS}=0)$and MADGRAPH5\_aMC@NLO/HERWIG6.521~($\mathtt{PTRMS}=2.2~\mathrm{GeV})$ and thephenomenological consequences are discussed with an eye toward their energydependence.

IR-improved DGLAP parton shower effects for associated production of a W boson and jets in pp collisions at $\sqrt{s}=$8 and 13 TeV