We show that there is a curious connection between circular colorings of edge-weighted digraphs and periodic schedules of timed marked graphs. Circular coloring of an edge-weighted digraph was introduced by Mohar [B. Mohar, Circular colorings of edge-weighted graphs, J. Graph Theory 43 (2003) 107–116]. This kind of coloring is a very natural generalization of several well-known graph coloring problems including the usual circular coloring [X. Zhu, Circular chromatic number: A survey, Discrete Math. 229 (2001) 371–410] and the circular coloring of vertex-weighted graphs [W. Deuber, X. Zhu, Circular coloring of weighted graphs, J. Graph Theory 23 (1996) 365–376]. Timed marked graphs G → [R.M. Karp, R.E. Miller, Properties of a model for parallel computations: Determinancy, termination, queuing, SIAM J. Appl. Math. 14 (1966) 1390–1411] are used, in computer science, to model the data movement in parallel computations, where a vertex represents a task, an arc u v with weight c u v represents a data channel with communication cost, and tokens on arc u v represent the input data of task vertex v . Dynamically, if vertex u operates at time t , then u removes one token from each of its in-arc; if u v is an out-arc of u , then at time t + c u v vertex u places one token on arc u v . Computer scientists are interested in designing, for each vertex u , a sequence of time instants { f u ( 1 ) , f u ( 2 ) , f u ( 3 ) , … } such that vertex u starts its k th operation at time f u ( k ) and each in-arc of u contains at least one token at that time. The set of functions { f u : u ∈ V ( G → ) } is called a schedule of G → . Computer scientists are particularly interested in periodic schedules. Given a timed marked graph G → , they ask if there exist a period p > 0 and real numbers x u such that G → has a periodic schedule of the form f u ( k ) = x u + p ( k − 1 ) for each vertex u and any positive integer k . In this note we demonstrate an unexpected connection between circular colorings and periodic schedules. The aim of this note is to provide a possibility of translating problems and methods from one area of graph coloring to another area of computer science.