  We consider a family of discrete time multihop switched queueing networks
where each packet moves along a fixed route. In this setting, BackPressure is
the canonical choice of scheduling policy; this policy has the virtues of
possessing a maximal stability region and not requiring explicit knowledge of
traffic arrival rates. BackPressure has certain structural weaknesses because
implementation requires information about each route, and queueing delays can
grow super-linearly with route length. For large networks, where packets over
many routes are processed by a queue, or where packets over a route are
processed by many queues, these limitations can be prohibitive. In this
article, we introduce a scheduling policy for FIFO networks, the Proportional
Scheduler, which is based on the proportional fairness criterion. We show that,
like BackPressure, the Proportional Scheduler has a maximal stability region
and does not require explicit knowledge of traffic arrival rates. The
Proportional Scheduler has the advantage that information about the network's
route structure is not required for scheduling, which substantially improves
the policy's performance for large networks. For instance, packets can be
routed with only next-hop information and new nodes can be added to the network
with only knowledge of the scheduling constraints.
