Optimal control policies in service systems with limited information on the downstream stage

Existing models in multistage service systems assume full information on the state of downstream stages. In this paper, we investigate how much the lack of such information impacts jobs' waiting time in a two‐stage system with two types of jobs at the first stage. The goal is to find the optimal control policy for the server at the first stage to switch between type‐1 and type‐2 jobs, while minimizing the long‐run average number of jobs in the system. We identify control policies and corresponding conditions under which having no or partial information, the system can still capture the most benefit of having full information.