Cell-to-cell communication networks have critical roles in diverse organismal processes, such as coordinating tissue development or immune cell response. However, compared to intracellular signal transduction networks, the function and engineering principles of cell-to-cell communication networks are far less understood. Here, we study cell-to-cell communication networks using a framework that models the input-to-output relationship of intracellular signal transduction networks with a single function-the response-time distribution. We identify a prototypic response-time distribution-the gamma distribution-arising in both experimental data sets and mathematical models of signal-transduction pathways. We find that simple cell-to-cell communication circuits can generate bimodal response-time distributions, and can control synchronization and delay of cell-population responses independently. We apply our modeling approach to explain otherwise puzzling data on cytokine secretion onset times in T cells. Our approach can be used to predict communication network structure using experimentally accessible input-to-output measurements and without detailed knowledge of intermediate steps.