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In this paper, we study the effect of users' traffic characteristics on the temporal behavior of total downlink interference in multi-service wireless CDMA networks. We show that under certain conditions on traffic characteristics that cover a range of practical situations, downlink interference follows an asymptotically self-similar process and thus is long-range dependent. We then obtain the asymptotic outage probability and show that in a network that is designed based on the Poisson assumptions the outage probability is degraded by the interference long-range dependent. Simulation results for actual cases confirm analytical results.