Service systems which involves waiting is of crucial importance in our daily lives. In a single server queueing system in which the types of customers are mixed and random like Starbucks, those types of customers who are expected to be slow are likely to block customers behind him, making the overall waiting time unnecessarily long. Hence it is plausible that by splitting the server with
properly allocated service resources, each restricting to serve certain types of customers, one can increase the overall service quality. In this project we built a model describing this phenomenon and discuss the optimal scheme for allocating of service resources. It turns out that there is actually a trade-o between reducing
the idle times of both servers and keeping waiting time for the fast-typed customers low. We find that when different types of customers di ffer significantly in the expected service time, it is good to separate the queue. Moreover, we need some structures in the optimal solution which might reduce the searching complexity into polynomial time.