An Application of Queuing Theory to Waterfowl Migration

There has always been great interest in the migration of waterfowl and other birds. We have applied queuing theory to modelling waterfowl migration, beginning with a prototype system for the Rocky Mountain Population of trumpeter swans (Cygnus buccinator) in Western North America. The queuing model can be classified as a D/BB/28 system, and we describe the input sources, service mechanism, and network configuration of queues and servers. The intrinsic nature of queuing theory is to represent the spatial and temporal characteristics of entities and how they move, are placed in queues, and are serviced. The service mechanism in our system is an algorithm representing how swans move through the flyway based on seasonal life cycle events. The system uses an observed number of swans at each of 27 areas for a breeding season as input and simulates their distribution through four seasonal steps. The result is a simulated distribution of birds for the subsequent year’s breeding season. The model was built as a multiagent system with one agent handling movement algorithms, with one facilitating user interface, and with one to seven agents representing specific geographic areas for which swan management interventions can be implemented. The many parallels in queuing model servers and service mechanisms with waterfowl management areas and annual life cycle events made the transfer of the theory to practical application straightforward.