A join the shorter queue model in heavy traffic

We prove a new heavy traffic limit result for a simple queueing network under a ‘join the shorter queue’ policy, with the amount of traffic which has a routeing choice tending to zero as heavy traffic is approached. In this limit, the system considered does not exhibit state space collapse as in previous work by Foschini and Salz, and Reiman, but there is nevertheless some resource pooling gain over a policy of random routeing.