In this study, we developed a real-time connected vehicle (CV) speed advisory application that uses public cloud services and tested it on a simulated signalized corridor for different roadway traffic conditions. First, we developed a scalable serverless cloud computing architecture leveraging public cloud services offered by Amazon Web Services (AWS) to support the requirements of a real-time CV application. Second, we developed an optimization-based real-time CV speed advisory algorithm by taking a modular design approach, which makes the application automatically scalable and deployable in the cloud using the serverless architecture. Third, we developed a cloud-in-the-loop simulation testbed using AWS and an open-source microscopic roadway traffic simulator called Simulation of Urban Mobility (SUMO). Our analyses based on different roadway traffic conditions showed that the serverless CV speed advisory application meets the latency requirement of real-time CV mobility applications. Besides, our serverless CV speed advisory application reduced the average stopped delay (by 77%) and the aggregated risk of collision (by 21%) at signalized intersection of a corridor. These prove the feasibility as well as the efficacy of utilizing public cloud infrastructure to implement real-time roadway traffic management applications in a CV environment.