This work is concerned with the atomistic simulation of the volumetric, conformational and structural properties of monodisperse polyethylene (PE) melts of molecular length ranging from C-78 up to C-1000. In the past, polydisperse models of these melts have been simulated in atomistic detail with the end-bridging Monte Carlo algorithm [Pant and Theodorou, Macromolecules 28, 7224 (1995); Mavrantzas , Macromolecules 32, 5072 (1999)]. In the present work, strictly monodisperse as well as polydisperse PE melts are simulated using the recently introduced double bridging and intramolecular double rebridging chain connectivity-altering Monte Carlo moves [Karayiannis , Phys. Rev. Lett. 88, 105503 (2002)]. These algorithms constitute generalizations of the EB move, since they entail the construction of two trimer bridges between two properly chosen pairs of dimers along the backbones of two different chains or along the same chain. In the simulations, a new molecular model is employed which is a hybrid of the united-atom TraPPE model [Martin and Siepmann, J. Phys. Chem. B 102, 2569 (1998)] and the anisotropic united-atom model [Toxvaerd, J. Chem. Phys. 107, 5197 (1997)]. Results are first presented documenting the efficiency of the algorithm in equilibrating long-chain PE melts and its dependence on chain length and polydispersity. Simulation data concerning the volumetric, conformational and structural properties of the monodisperse PE melts, obtained with the new simulation algorithm, are found to be in excellent agreement with available experimental data.