due to each peer being equal with each other in terms
of relative neighbours and functionalities. In this doc-
ument, only the experiments with one and three hops
will be discussed; discussions on hops two and four
as well as how our mechanism differs from a pure ex-
haustive search are available in (Gibson et al., 2012).
To calculate the divergence of a peer, we calcu-
late the difference between the peer’s knowledge of
each opponent with the opponent’s actual knowledge
at each game tick. For each graph, the higher the di-
vergence, the more different the perceived and actual
values are, leading to inaccurate gameplay.
In Figure 2(a), each message only lasts one hop,
meaning only the immediate neighbours of D (peers
C and E) will receive messages. The graph shows that
peers C and E mostly have a low divergence, mean-
ing the perceived knowledge peer D has of C and E
are close to C and E’s actual knowledge respectively.
However for the remaining peers (A, B, F, G and H)
divergence is high because D is never able to commu-
nicate with them. Peers A, B, G and H appear to flat-
line around the 5000 game tick point because in all in-
stances (peer D’s perception and the actual peers con-
trolling the players), the players seem to have “lost”
(ran out of fuel) at the same time. The divergence is
still high because the perceived and actual player po-
sitions will be at different locations around the track.
Figure 2(b) shows that since messages can arrive
at more distant peers, the divergence among these
peers will be smaller. For three hops, peers A and
G can be reached. Since peer H is never in reach, it
always has a high divergence. There are some spikes
in divergence in the reachable peers. We believe this
is caused when peer D tries to overtake the reachable
peers in its copy of the game, but failing to complete
the overtake. This may affect the peer’s closest oppo-
nents, leading to fluctuating thresholds for the oppo-
nents and affecting queries being sent.
By looking at Figures 2(a) and 2(b), total diver-
gence among the peers decreases as the number of
hops increases. This should be obvious because as
messages are able to reach more peers, information
retrieved will be more accurate and hence lower di-
vergence. To show how much hop count improves
information accuracy, Figure 3 shows how peer D’s
convergence with all peers combined improves over
time with increasing hop count and how all peers ben-
efit from increased hop count for their convergences.
In Figure 3(a), the graph shows that as the num-
ber of hops increases per message, the divergence is
generally lower at each point in game time. Each
line represents the average of each opponent percep-
tions from each experiment. For hops one and two
though, hop two’s divergence spikes over hop one’s
divergence at some points. This is also present in hops
three and four where hop three’s divergence spikes
over hop four’s divergence at some points. These
spikes are likely caused by the spikes seen in Figures
2(a) and 2(b), resulting in some errors being carried
over. To smooth out the errors, we averaged each
peer’s total divergences (each peer’s version of the
graph in Figure 3(a)) and applied weighting to the
closest players of each peer at each game tick to high-
light divergences in the closest opponents are more
important than divergences in distant players since
closer opponents are in the player’s interest set. This
combination of peer divergences and weightings led
to Figure 3(b) which clearly shows that as hop count
increases for messages, all peers improve because of
lower divergence, leading to more accurate applica-
tion performance and gameplay.
6 CONCLUSIONS, DISCUSSION
AND FUTURE WORK
In this paper, we have discussed an alternative ap-
proach to exchanging information over P2P networks
through the use of timestamps. We have also showed
how we approach this using rule-based applications
(specifically, but not limited to, computer games) by
evaluating the age of its knowledge base and gener-
ating queries to a peer who will be able to update
the information. Finally, we showed and explained
our experiment results to show how our approach per-
forms in varying configurations. Using the experi-
ment results will allow us to further refine our pro-
posed approach for other types of applications, specif-
ically data-intensive applications.
Although the results may be obvious in showing
that as message hops increases, a peer’s perception of
other peers improves, it confirms that our mechanism
of reducing queries based on certain times throughout
an application’s life leads to similar results compared
with an exhaustive querying to all peers.
We will use the results to develop our research to
focus on data-intensive applications as well as im-
prove our simulator’s performance to minimise di-
vergence spikes. This will mean looking at other
means of creating queries depending on the state of
the player instead of just time. One area that will
be focussed on more in the future is security. Whilst
running our experiment, we assume that all peers are
trustworthy and have no devious intentions. This is
not a reasonable approach for real-world applications
though. One area that should be focussed on is rogue
messages. Peers may be able to “lie” by sending
wrong information about itself or even other peers so
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