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Bandwidth for High Speed Networks

The probability of dropping a packet as it arrives to

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Unformatted text preview: ring to the absence of per- ow state. algorithm in which only edge routers maintain per ow state, while core non-edge routers do not maintain per ow state but instead utilize the per- ow information carried via a label in each packet's header. This label contains an estimate of the ow's rate; it is initialized by the edge router based on per- ow information, and then updated at each router along the path based only on aggregate information at that router. Second, to avoid per ow bu ering and scheduling, as required by Fair Queueing, we use FIFO queueing with probabilistic dropping on input. The probability of dropping a packet as it arrives to the queue is a function of the rate estimate carried in the label and of the fair share rate at that router, which is estimated based on measurements of the aggregate tra c. Thus, our approach avoids both the need to maintain per- ow state and the need to use complicated packet scheduling and bu ering algorithms at core routers. To give a better intuition about how this works, we rst present the idealized bit-by-bit or uid version of the probabilistic dropping algorithm, and then extend the algorithm to a practical packetby-packet version. 2.1 Fluid Model Algorithm We rst consider a bu erless uid model of a router with output link speed C , where the ows are modelled as a continuous stream of bits. We assume each ow's arrival rate ri t is known precisely. Max-min fair bandwidth allocations are characterized by the fact that all ows that are bottlenecked i.e., have bits dropped by this router have the same output rate. We call this rate the fair share rate of the server; let t be the fair share rate at time t. In general, if max-min bandwidth allocations are achieved, each ow i receives service at a rate given by minri t; t. P Let At denote the total arrival rate: At = n=1 ri t. If i At C then the fair share t is the unique solution to C= n X i=1 minri t; t; 1 If At  C then no bits are dropped and we will, by convention, set t = maxi ri t. If ri t  t, i.e., ow i sends no more than the server's fair share rate, all of its tra c will be forwarded. If ri t t, then a fraction ri ti,t t of its bits will be dropped, so r it will have an output r...
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