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absence of per ow state. algorithm in which only edge routers maintain per ow state,
while core nonedge 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
bitbybit or uid version of the probabilistic dropping algorithm, and then extend the algorithm to a practical packetbypacket 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. Maxmin 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 maxmin 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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This document was uploaded on 03/04/2014 for the course ENG 531 at Rice.
 Fall '10
 Eugene Ng

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