Convergence complexity of optimistic rate based flow control algorithms (brief announcement)
This paper studies basic properties of rate based flowcontrol algorithms and the max-min fairness criteria. We suggest a new approach for modeling and analysis of such algorithms, which may be considered more “optimistic” and realistic than traditional approaches. For the max-min fairness criteria we show that under certain circumstances it may be very sensitive to small changes in the flows. Furthermore, we show that it may be hard to locally estimate in a given state how close a session is to its max-min fair allocation. Our abstraction separates the flow control algorithm into two parts. The scheduler, that in each state selects the next session to be considered for an increase, and the update rule by which the algorithm decides whether to perform the update or not. The convergence cornpleml~ of each algorithm is the total number of update operations applied until the algorithm quiesces. Three different schedulers are considered, depending on the selection in each state, of the next session to be improved: (1) global rnin scheduler that selects the globally smallest rate session that could still be improved. (2) Joccd min scheduler that selects any session whose rate may be improved, and which is smaller than all the sessions it shares an edge with. (3) arbitrary scheduler that selects an arbitrarily session. Note that the local min is more appropriate for a distributed environment than the global rein, and the arbitrary gives the highest degree of flexibility. Two variants are considered for the update decision: (1) a selected session rate is increased as long as it may be increased, and (2) approximate algorithms, in which the rate of a session is increased only if the increase is by more than 6. The approximate algorithms reach quiescence when no session may be increased by more than 6. The main results presented in this paper are: