Traffic measurement provides fundamental statistics for network management functions. To implement the measurement modules on the data plane for real-time query response, modern sketches are designed to work with limited on-die memory allocation from network processors and collect traffic statistics in epochs of a preset length. To handle real-time queries at arbitrary times over traffic in a preceding period ${T}$ (called ${T}$-queries), the prior art sets the epoch length to ${T \over n}$ and keeps the measurement results in a window of $n - 1$ past epochs to support approximate ${T}$-queries. Such an approach however drastically increases the memory cost or decreases the accuracy in the query results if the memory allocation is fixed. In this paper, motivated by the concept of offloading in today's edge-cloud computing, we propose a collaborative edge-center traffic measurement model, where the traffic measurement modules at all network devices form the edge, which offloads the traffic measurement results to a measurement center possibly hosted in a datacenter. The center synthesizes the measurements from the past epochs and sends the aggregate results back to the measurement modules to support T-queries. We conduct experiments using real traffic traces to evaluate the performance of the proposed edge-center measurement model. The experimental results demonstrate that the proposed designs significantly outperform the prior art.