Shortest Queue Policy for the Tandem Parallel Queue

摘要

The authors consider two nodes in tandem. At each node or service centre there are two servers present with the same service rate mu and each with its own queue. Customers arrive at the first node according to a Poisson process with arrival rate lambde. At their arrival, they have to be assigned to one of the servers, so they are routed to one of the queues at node 1. Customers leaving centre 1 enter node 2 and are routed to one of the queues at node 2. The goal of our analysis is to find a policy which stochastically minimizes the number of customers in the system at any time point. In the communication model which motivated the research, the information on which an arriving customer has to be routed to one of the queues consists of the lengths of the queues in that node. So at any node there is no information available about the queue lengths of the other node. The paper considers two cases. One is the model described above, which is called the tandem parallel queue with Partial Information (PI). The other is the case where the routing decisions in a node may also depend on the queue lengths at the other node. This is called the Full Information (FI) case.