Asynchronous text-based communication, secure messaging, has become one of the preferred modes of communication despite its potential to disrupt workflow and increase burden. Identifying peak communication can guide interventions to reduce communication overload among healthcare workers. The objective of this study is to predict future secure messaging volume among healthcare professionals utilizing a graph-based transformer model. The data consisted of secure messaging metadata from 14 inpatient hospitals and 381 outpatient clinics for the period February 1, 2023, through April 30, 2024. The model architecture consists of a multi-headed graph transformer to embedded hourly communication structures followed by transformer decoder architecture to predict the future messaging volume. Results show successful predictions across test sets, with improved performance using domain-specific time-dependent positional encoding. This approach integrates network topology, temporal patterns, and relational context (who is communicating and at what time) for accurate message traffic forecasting and underscore its novel design.