A markov/probability question
From: Sailesh Kumar (sailesh_at_arl.wustl.edu)
Date: 09/21/04
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Date: Tue, 21 Sep 2004 05:22:08 -0500
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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