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module, applications choose the transport layer protocol according to the scenarios.
The topology routing module provides lookup service, finds the best suitable host for
a given key, and also includes ID management and topology maintenance. Subscriber
data such as storage, consistency verification are taken charge of by the data storage
module. Application layer takes topology routing module and data storage module as
substruction, specifies logical function of the system despite the underlying details.
Modularized designs simplifies the system implementation.
In addition, a mathematical model is presented for system verification. Previous
work parameterized the workload of a P2P system by a tuple
< > [16], which
means n nodes in the system with an average node lifetime l, each node process f
lookups per second on average. Corresponding to Comb's topology, our work splits f
to fl and fg representing the average lookup times of intra-domain and inter-domain
per second. Suppose the whole overlay is divided into k domains, then each domain
has n/k nodes, in a system with a node lifetime l, on average n/(kl) nodes join and
leave each second in one domain. When a node joins or leaves, at least one message
will be sent to all its neighbors for informing, Comb maintenances all nodes within
the domain as its neighbors, i.e., at least n/k messages are sent during the joining or
leaving procedure. Assuming that all messages get unit size s and each request is ac-
knowledged by a response, then the traffic for nodes arrivals and departures B1 in one
domain is:
nfl
,,
nn nn
B
=+ • × +×
(1
1)
s
(
)
(1)
1
k lk l
Each node process l f intra-domain lookups with one hop and f inter-domain
lookups with two hops per second, resulting in traffic for lookups with one domain
B 2 is:
n
n
B
=+ •
(1
1)
s
(
f
+
2
f
)
(2)
2
l
g
k
k
As a result, without regard to the inter-domain maintenance and keep-alive traffic,
the minimum traffic demand in Comb B 3 is:
2
4
snf
4
sn
2
snf
4
sn
2
g
l
(3)
BBBk
=
(
+
)
•=
(
+
+
)
•=
k
+
2
snf
+
4
snf
min
1
2
l
g
kl
2
k
k
kl
4
The Base Protocol
Comb provides protocol for key based resources location, how nodes join and leave
the system and how to recover from the failures. This section gives a simplified ver-
sion of description of the Comb protocol.
4.1
Overview
As in Figure 2, Comb organizes all the nodes in a circular ring like Chord [6].
 
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