We study call admission rates in a linear communication
network with each call identified by an arrival time, duration,
bandwidth requirement, and origin-destination pair. Network
links all have the same bandwidth capacity, and a call
can be admitted only if there is sufficient bandwidth available
on every link along the call's path. Calls not admitted
are held in a queue, in contrast to the protocol of loss
networks. We determine maximum admission rates (capacities)
under greedy call allocation rules such as First Fit and
Best Fit for several baseline models and prove that the
natural necessary condition for stability is sufficient.
We establish the close connections between our new problems
and the classic problems of bin packing and interval packing.
In view of these connections, it is surprising to find
that Best Fit allocation policies are inferior to First
Fit policies in the models studied.
Biased Random Walks, Lyapunov Functions, and Stochastic Analysis of Best Fit Bin Packing