a minimal mean (57.5 msgs/round) and quite a low
standard deviation (35.27).
With write intensive loads (see Table 2) a TTL-
based propagation strategy (with 3 forwarding steps)
combined with a randomly generated topology pro-
vides a minimal mean amount of propagated mes-
sages with a moderate standard deviation.
5.2 Coverage
Tables 3 and 4 contain information about how many
rounds the algorithm needs on average to reach a cer-
tain coverage threshold. Such threshold is given as
the percentage of nodes that have received the new
values being propagated, in our case 50% and 90% of
the total nodes.
Table 3: Coverage - Read Intensive Workload.
GRAPH PROPAGATION ROUNDS
TYPE PROTOCOL 50% 90%
Complete simple, k=3 1 1
Random simple, k=3 2 3
Complete push,fbk,count,k=3 5 8
Complete pull,fbk,count,k=3 6 8
Complete p&p,fbk,count,k=3 4 5
Complete p&p,fbk,coin,k=3 4 5
Complete p&p,nof,coin,k=3, 4 7
Random p&p,fbk,count,k=3 3 5
Proposed 4/3 push,fbk,count,k=3 5 8
Proposed 4/3 pull,fbk,count,k=3 6 11
Proposed 4/3 p&p,fbk,count,k=3 3 5
Proposed 4/3 p&p,fbk,count,k=5 3 5
Proposed 4/3 p&p,nof,count,k=3 4 8
Proposed 4/5 p&p,fbk,count,k=3 3 5
Proposed 5/3 p&p,fbk,count,k=3 5 11
Table 3 shows that the TTL-based propagation
strategy with a randomly (Berab´asi-Albert) generated
topology is, among the best combinations obtained
in the traffic analysis of the previous section, the one
needing a minimal number of rounds to reach an ac-
ceptable coverage. It only needs 2 rounds to reach
50% of the nodes and 3 rounds to reach 90% of the
nodes. In order to reach these minimal values we
are assuming that the node that initially served each
update transaction was that with the maximal degree
(i.e., with the maximum number of connected neigh-
bor nodes). If an application chooses another node as
its delegate replica the number of propagation rounds
will be slightly higher.
Our best proposed configuration considering traf-
fic (5 partitions with 3 tiers, push-and-pull propaga-
tion with feedback and 3-round forwarding) needs a
high amount of communication rounds to achieve this
analyzed coverage (5 and 11 rounds, respectively).
This is not a serious drawback since our replication
strategy still provides a consistent view of the updated
nodes, even they do not maintain the latest version.
Table 4: Coverage - Update Intensive Workload.
GRAPH PROPAGATION ROUNDS
TYPE PROTOCOL 50% 90%
Full simple, k=3 1 1
Random simple, k=3 2 3
Full p&p,fbk,count,k=3 4 5
Random p&p,fbk,count,k=3 3 5
Proposed 4/3 p&p,fbk,count,k=3 3 5
The usage of write intensive loads (as shown in
Table 4) does not introduce any modification to the
values presented in Table 3 since the coverage does
not depend on the workload being considered but only
on the topology and propagation strategy.
5.3 Load
Tables 5 and 6 contain the number of messages re-
ceived by certain nodes in each turn. We check the
average of nodes that are in the core tier and nodes
that are in the read tiers.
Table 5: Load in the Nodes - Read Intensive Workload.
GRAPH PROPAGATION WRITE LOAD READ LOAD
TYPE PROTOCOL MEAN DEV. MEAN DEV.
Complete simple, k=3 18.546 8.918 18.546 8.918
Random simple, k=3 1.191 1.815 1.191 1.815
Complete push,fbk,count,k=3 1.573 1.109 1.573 1.109
Complete pull,fbk,count,k=3 1.799 0.675 1.799 0.675
Complete p&p,fbk,count,k=3 2.097 1.137 2.097 1.137
Complete p&p,fbk,coin,k=3 2.355 1.256 2.355 1.256
Complete p&p,nof,coin,k=3 1.622 0.571 1.622 0.571
Random p&p,fbk,count,k=3 2.015 1.105 2.015 1.105
Prop.4/3 push,fbk,count,k=3 1.006 0.728 1.257 0.882
Prop.4/3 pull,fbk,count,k=3 1.337 0.786 1.813 0.610
Prop.4/3 p&p,fbk,count,k=3 1.762 1.086 1.981 0.888
Prop.4/3 p&p,fbk,count,k=5 1.682 1.062 1.956 0.915
Prop.4/3 p&p,nof,count,k=3 1.021 0.620 1.344 0.481
Prop.4/5 p&p,fbk,count,k=3 1.524 0.792 1.933 0.819
Prop.5/3 p&p,fbk,count,k=3 0.788 0.607 1.147 0.827
As already shown in the traffic analysis, a com-
plete graph with a TTL-based propagation is unable
to scale. This fact is also clearly shown here, in both
tables. Thus, with a read intensive load each node
manages around 19 messages per round (with a stan-
dard deviation of 9), while this value grows up to 44
with a write intensive load.
With a read intensive load, a randomly generated
graph with TTL-based propagation provides excel-
lent values for both reading and writing operations on
nodes with a low standard deviation (1.8). However,
the best values are provided by our 5/3 topology pro-
posal (i.e., using 5 partitions and 3 tiers) that only re-
quires on average 0.8 messages on updated nodes and
1.1 messages on read nodes with a standard deviation
lower than in the random topology.
Considering write intensive loads, the random
topology with TTL-based propagation provides the
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