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In this paper, spatiotemporal relaxation of a neon glow discharge plasma is theoretically investigated. The study concerns the positive column and the adjacent anode region. The relaxation is initiated by a short laser pulse that disturbs the column plasma by depopulating the metastable atoms near the cathode-sided boundary of the considered region. The resulting decrease of the ionization rate initiates a spatiotemporal relaxation of the plasma in the downstream region, which is similar to ionization waves. In accordance with the chosen discharge parameters, ionization waves of p-type are generated. After about 3-4 ms, relaxation is finished, and the undisturbed state is reached. The theoretical investigations are based on a self-consistent hybrid model comprising a fluid description of all relevant plasma components, the solution of the Poisson equation, and a spatially resolved kinetic treatment of the electrons.