  A new class of particle systems with sequential interaction is proposed to
approximate the McKean-Vlasov process that originally arises as the limit of
the mean-field interacting particle system. The weighted empirical measure of
this particle system is proved to converge to the law of the McKean-Vlasov
process as the system grows. Based on the Wasserstein metric, quantitative
propagation of chaos results are obtained for two cases: the finite time
estimates under the monotonicity condition and the uniform in time estimates
under the dissipation and the non-degenerate conditions. Numerical experiments
are implemented to demonstrate the theoretical results.
