Re: Some comments on the draft of 3448/TFRC.bis (Feb 2007)

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Quoting Sally Floyd:
|        * Open issue: Add possible mechanisms for limited the maximum
|          burst size?  Using a token bucket size based on the
|          current rate?  Or not?  Email from Eddie Kohler and Gerrit
|          Renker.
Ouch. Didn't read that one. The token bucket question is actually a
phantom, the only possible logical conclusion here is that the bucket
size is zero. Below is the copy from the patch which has the details
if anyone is interested; the short conclusion is that the bucket size
must be zero. And this agrees with Eddie's answer to the token bucket
question.


[CCID 3]: Avoid accumulating of large send credit

Problem:
--------
 Large backlogs of packets which can be sent immediately currently accumulate
 when (i) the application idles, or (ii) the application emits at a rate slower
 than the allowed rate X/s, or (iii) due to scheduling inaccuracy (resolution
 only up to HZ). The consequence is that a huge burst of packets can be sent
 immediately, which violates the allowed sending rate and can (worst case)
 choke the network.

Fix:
----
 Avoid any backlog of sending time which is greater than one whole t_ipi. This
 permits the coarse-granularity bursts mentioned in [RFC 3448, 4.6], but disallows
 the disproportionally large bursts.


 D e t a i l e d   J u s t i f i c a t i o n   [not commit message]
 ------------------------------------------------------------------
 Let t_nom < t_now be such that t_now = t_nom + n*t_ipi + t_r, where
 n is a natural number and t_r < t_ipi. Then 
 
 	t_nom - t_now = - (n*t_ipi + t_r)
 
 First consider n=0: the current packet is sent immediately, and for
 the next one the send time is
 	
 	t_nom'  =  t_nom + t_ipi  =  t_now + (t_ipi - t_r)
 
 Thus the next packet is sent t_r time units earlier. The result is
 burstier traffic, as the inter-packet spacing is reduced; this 
 burstiness is mentioned by [RFC 3448, 4.6]. 
 
 Now consider n=1. This case is illustrated below
 
 	|<----- t_ipi -------->|<-- t_r -->|
 
 	|----------------------|-----------|
 	t_nom                              t_now
 
 Not only can the next packet be sent t_r time units earlier, a third
 packet can additionally be sent at the same time. 
 
 This case can be generalised in that the packet scheduling mechanism
 now acts as a Token Bucket Filter whose bucket size equals n: when
 n=0, a packet can only be sent when the next token arrives. When n>0,
 a burst of n packets can be sent immediately in addition to the tokens
 which arrive with rate rho = 1/t_ipi.
 
 The aim of CCID 3 is an on average smooth traffic with allowed sending
 rate X. The following determines the required bucket size n for the 
 purpose of achieving, over the period of one RTT R, an average allowed
 sending rate X.
 The number of bytes sent during this period is X*R. Tokens arrive with
 rate rho at the bucket, whose size n shall be determined now. Over the
 period of R, the TBF allows s * (n + R * rho) bytes to be sent, since
 each token represents a packet of size s. Hence we have the equation
 
 		s * (n + R * rho) = X * R
 	<=>	n + R/t_ipi	  = X/s * R = R / t_ipi
 
 which shows that n must be 0. Hence we can not allow a `credit' of
 t_nom - t_now > t_ipi time units to accrue in the packet scheduling.



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