Optimal Routing to Parallel Servers in Heavy Traffic

Routing control is an important component in many engineering and management systems consisting of multiple and possibly heterogeneous servers. Imagine that upon the arrival of each job (or customer), a controller will evaluate the available (dynamic) state information and make a decision to dispatch the job to one of the servers. The state information can be queue length, arrival history, service history, and so on, depending on the nature of the application. How will the controller use the available state information to minimize the average waiting time an arriving job may experiences? In the paper, “Optimal Routing to Parallel Servers in Heavy Traffic,” Ye carries out the heavy traffic analysis to identify the routing policies that best use the available state information. For example, when there is no state information available for routing control, the best “blind” strategy is to dispatch the incoming jobs in a weighted round-robin fashion that exhibits certain form of the square-root rule. Although in the case that the job arrival history is available, the controller should use the information by closely chasing a kind of “arrival deviation,” which can reduce up to 50% of the waiting time compared with the best blind strategy. This study sheds new insights into the value of state information for routing control and provides new tools for engineering and service system design.