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In this paper we present a self-consistent simulation model of colliding beams in high energy accelerators. The model, which is based on a particle-in-cell method, uses a new developed shifted-Green function algorithm for the efficient calculation of the beam-beam interaction. The model uses transfer maps to treat the external focusing elements and a stochastic map to treat radiation damping and quantum excitation of the beams. In the parallel implementation we studied various strategies to deal with the particular nature of the colliding beam system - a system in which there can be significant particle movement between beam-beam collisions. We chose a particle-field decomposition approach instead of the conventional domain decomposition or particle decomposition approach. The particle-field approach leads to good load balance, reduced communication cost, and shows the best scalability on an IBM SP3 among the three parallel implementations we studied. A performance test of the beam-beam model on a Cray T3E, IBM SP3, and a PC cluster is presented. As an application, we studied the effect of long-range collisions on antiproton lifetime in the Fermilab Tevatron.