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Chapter 4: Unequal Erasure Protection (UEP) in Network Coding 53
of GEK allocation, e.g., if R 1 is allowed to allocate only one GEK, it will choose the best
one and assign it to T 4 . If two allotments are allowed, R 1 will assign two GEKs to T 4
and T 3 . The preference order relates to the erasure probability of each edge-disjoint path
discussed in earlier sections. Each sink’s main preference is to allocate the GEKs with
lower UEP levels to the paths with lower erasure probability. This means, according to
Table 4.4, the path from the source that reaches R 1 via T 4 has lower erasure probability
than those reaching R 1 via T 3 and T 1 .
Let each receiver’s estimate of its marginal values θ 1 , θ 2 , and θ 3 , as defined in Definition
4.8 be shown below.
Θ R 1 R 2 R 3 R 4
θ 1 123 75 85 45
θ 2 113 5 65 25
θ 3 40 3 7 5
Now, let the auction start with the initial price of 10.
At this price, R 1 is happy
to buy three allotments, while R 2 will buy only one, since the price exceeds the second
marginal value. Accordingly, the response from each receiver is shown in the first row of
Table 4.5.
Table 4.5: The sinks’ responses to the increasing price
.
Sinks R 1 R 2 R 3 R 4
Responses to 10 3 1 2 2
Responses to 25 3 1 2 1
Responses to 25+ɛ 3 1 1 1
Responses to 40 2 1 1 1
Since nobody clinches anything at this point, the source node raises the price. When
the price reaches 25, R 4 has no profit to be gained from the second allotment, and therefore
changes its response, as shown in the second row of Table 4.5.
From R 1 ’s perspective, the demand of all other bidders is four, while five allotments
are available. If other sinks bid monotonically, R 1 is now guaranteed to win at least one
allotment. Thus, according to our rule, R 1 clinches one allotment at the price of 25. It