Competitive non-preemptive call control

We deal with randomized competitive algorithms for non-preemptive call control on tree-like switching networks. We give an optimal O(log n) competitive algorithm for non-preemptive call scheduling on trees. We then extend the problem to include variable call rates, call durations, and arbitrary call benefits, and obtain a polylog competitive algorithm. We also show that many similar algorithms for different problems that can deal with constant values of parameters such as rates and benefits can be transformed into randomized algorithms that can deal with varying values of the parameters. Using randomization, this extends the work of Garay et al. on call control for the line network [GGKMY] to tree networks, while avoiding the preemption requirement, and while allowing arbitrary benefits and arbitrary rates. Alternately, this can be viewed as a generalization of the work of Awerbuch, Azar and Plotkin for throughput competitive routing [AAP], limited to trees, but without the limitation of requiring communication rates to be a small fraction of the link bandwidth. In common to all our results is an algorithmic paradigm - `Classify and Randomly Select'. This algorithmic tool seems useful for a variety of on-line problems in addition to those presented in this paper.