  The influence of the medium dependent finite width of QGP bags on their
equation of state is analyzed within an exactly solvable model. It is argued
that the large width of the QGP bags not only explains the observed deficit in
the number of hadronic resonances, but also clarifies the reason why the heavy
QGP bags cannot be directly observed as metastable states in a hadronic phase.
The model allows us to estimate the minimal value of the width of QGP bags from
a variety of the lattice QCD data and get that the minimal resonance width at
zero temperature is about 600 MeV, whereas the minimal resonance width at the
Hagedorn temperature is about 2000 MeV. As shown these estimates are almost
insensitive to the number of the elementary degrees of freedom. The recent
lattice QCD data are analyzed and it is found that besides sigma T**4 term the
lattice QCD pressure contains T-linear and T**4 ln T terms in the range of
temperatures between 240 MeV and 420 MeV. The presence of the last term in the
pressure bears almost no effect on the width estimates. Our analysis shows that
at hight temperatures the average mass and width of the QGP bags behave in
accordance with the upper bound of the Regge trajectory asymptotics (the linear
asymptotics), whereas at low temperatures they obey the lower bound of the
Regge trajectory asymptotics (the square root one). Since the model explicitly
contains the Hagedorn mass spectrum, it allows us to remove an existing
contradiction between the finite number of hadronic Regge families and the
Hagedorn idea of the exponentially growing mass spectrum of hadronic bags.
