We describe how the amount of work in the network becomes large in the simple case of two servers, with one arrival stream for each server and a third, routeable arrival stream. If the proportion of routeable jobs is large enough then the waiting times at the servers become large in tandem when the total workload becomes large, thus delaying overload as long as possible. The fact that this resource pooling can be attained with a local routing policy not dependent on the state of the network has engineering significance for load sharing among distributed call centres.
We also compare this `join the shorter actual waiting time' policy (JSAW) with a join the shorter expected waiting time policy and join the shorter queue. For some overflow events, we find that the performance of all three policies is roughly the same in the sense that the probability of an overflow has the same exponential decay rate under any policy. Although the JSAW policy is the best, in these cases its probability of overflow is only the lowest by a subexponential factor. However, for other overflow events we find that the JSAW policy is substantially better.