Re: Another problem, little difficult
From: neale (neale_rs_at_yahoo.com)
Date: 08/30/04
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Date: Mon, 30 Aug 2004 20:51:03 +0000 (UTC)
This is also a Markov chain but the states will need to be defined
with information about the last c states.
On Mon, 30 Aug 2004 11:39:21 -0500, Sailesh Kumar wrote:
>Hi,
> I need to do some computation for a cache architecture. I have
arrived at
>a simplified model and I need help to get it solved. Here is the
problem.
>
> Balls are being put into and removed from a bucket, one arrival and
one
>departure in each unit time.
>Arivals:
> Balls that are arriving have equal probability that they can have
any
>color from b different colors.
>Departure:
> Balls from the bucket are departing in following way, a) All colors
are
>selected, whose balls haven't been departed in last c unit times. b)
Then
>from selected colors, a ball is departed of the color which has
maximum
>number of balls. Thus, in every window of c unit time, balls of c
different
>colors need to be sent. (c < b)
>
> The bucket has N balls initially, with equal number of balls of
every b
>color.
>
> Now, when this process is carried out for very long time say T (T
is
>trillions), how many times will the bucket be having balls of only c
colors
>(c < b).
> In other words, after a long time and in steady state, whats is the
>probability that the bucket will have balls of only c colors (c < b).
>
>Thanks in advance,
>Regards,
>Sailesh
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