Rapid advancement of distributed computing systems enables complex services in remote computing clusters. Massive applications with large-scale and disparate characteristics also create high requirements for computing systems. Cloud computing provides a series of novel approaches to meet new trends and demands. However, some scalability issues have to be addressed in the request scheduling process and few studies have been conducted to solve these problems. Thus, this study investigates the scalability of the request scheduling process in cloud computing. We provide a theoretical definition of the scalability of this process. By modeling the scheduling server as a stochastic preemptive priority queue, we conduct a comprehensive theoretical and numerical analysis of the scalability metric under different structures and various environment configurations. The comparison and conclusion are expected to shed light on the future design and deployment of the request scheduling process in cloud computing.