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There is a rich theory and plethora of algorithms in the literature aiming at the efficient scheduling of stochastic networks. These solutions are predominantly designed under the assumption of traffic demands that are independently generated at network nodes, without any requirement for synchronization among their received services. In this work, we note that many applications, including cloud computing, virtual reality, gaming, autonomous vehicular networks and collaborative design, generate traffic simultaneously at multiple nodes when they arrive, with possibly non-uniform file sizes, whose performance relies on the synchronous completion of the traffic across the network. This calls for the design of new scheduling algorithms that aims to coordinate the service of packets of the same traffic across the network. Towards this end, we propose a novel scheduling algorithm that not only accounts for the heterogeneity of the file size distributions, but also works towards synchronizing the completion time of the same traffic stream across the network. This is achieved by employing two insights that emanate from key motivating examples we develop: (1) the normalization of traffic load with respect to the non-uniform file sizes; and (2) the incorporation of deviation of normalized loads across network nodes that serve synchronized traffic. After establishing the throughput-optimality of our algorithm in general stochastic networks, we perform extensive simulations under various (spanning both wired and wireless) settings to reveal the potential completion time gains that it yields over other throughput-optimal strategies designed under the assumption of independent traffic generation.