Dispersion-managed soliton interaction is investigated in an optical time-division multiplexed system with random dispersion map by the variational approach and the numerical simulation. It is found that the perturbation caused by random dispersion map enhances the interaction between neighboring solitons, and results in fluctuations of amplitude and separation which submerge solitons. The interaction distance relates to the standard deviation, the initial relative phases, the pulse width and the relative amplitude.