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The paper considers a network with many apparently-independent periodic processes and discusses one method by which these processes can inadvertently become synchronized. In particular, we study the synchronization of periodic routing messages. We give examples of the harmful effect of these synchronized updates on other network traffic, and offer guidelines on how to avoid inadvertent synchronization. Using simulations and analysis, we study the process of synchronization and show that the transition from unsynchronized to synchronized traffic is not one of gradual degradation but is instead a very abrupt 'phase transition': in general, the addition of a single router will convert a completely unsynchronized traffic stream into a completely synchronized one. We show that synchronization can be avoided by the addition of randomization to the traffic sources and quantify how much randomization is necessary. In addition, we argue that the inadvertent synchronization of periodic processes is likely to become an increasing problem in computer networks.