Optimization via trunk reservation in single resource loss systems under heavy traffic

Trunk reservation is a simple, robust and extremely effective mechanism for controlling loss systems which allows priority to be given to chosen traffic streams. We consider the control of a single resource under a limiting regime in which capacity and arrival rates increase together. We obtain trunk reservation control policies which are asymptotically optimal when calls have differing capacity requirements, holding times, arrival rates and reward rates. The priority levels associated with these trunk reservation policies arise from an attainable bound on the performance of any control policy.