fixit = Show[
    MapAt[# /.
       Line[d_] :> Line[Join @@ Most@SplitBy[d, Last@# == 0 &]] &, #,1], PlotRange -> Automatic] &;
    p = Plot[
    {f[p]},
    {p, 0, 1},
    AxesLabel -> {"p, АТС/метр", ""}, PlotStyle -> {Red, Thick}
    ];
     Show[
      ListPlot[Qp, PlotRange -> All,
      AxesLabel -> {"p, cars/m", "Q, cars/s"}],
     p // fixit,
     ImageSize -> plotWidth
     ]