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184 T. Abdullah et al.<br />

% Matchmak<strong>in</strong>g Efficiency<br />

100<br />

80<br />

60<br />

40<br />

20<br />

0<br />

0 1 2 3 4 5 6<br />

Number <strong>of</strong> Matchmakers<br />

(a)<br />

Matchmak<strong>in</strong>g Efficiency<br />

% Matchmak<strong>in</strong>g Efficiency<br />

50<br />

40<br />

30<br />

20<br />

10<br />

0<br />

0 10 20 30 40 50 60 70 80 90 100 110<br />

Degree <strong>of</strong> Neighborhood<br />

(b)<br />

Matchmak<strong>in</strong>g Efficiency<br />

Fig. 4. (a) Matchmak<strong>in</strong>g efficiency <strong>of</strong> centralized and multiple adaptive matchmakers<br />

approach. (b) Matchmak<strong>in</strong>g efficiency with vary<strong>in</strong>g the degree <strong>of</strong> neighborhood <strong>in</strong><br />

completely decentralized (P2P).<br />

more matchmaker(s) when needed by an overloaded matchmaker(s). Hence, the<br />

matchmak<strong>in</strong>g efficiency rema<strong>in</strong>s the same with the <strong>in</strong>creased number <strong>of</strong> matchmakers.<br />

The matchmak<strong>in</strong>g efficiency <strong>of</strong> completely centralized resource discovery<br />

approach is slightly higher than that <strong>of</strong> multiple adaptive matchmakers approach<br />

(Figure 4a). The matchmakers <strong>in</strong> multiple adaptive matchmakers approach communicate<br />

with other matchmakers <strong>in</strong> order to promote/demote matchmakers and<br />

for shar<strong>in</strong>g their access workload with the other matchmakers [12]. Some <strong>of</strong> the<br />

request/<strong>of</strong>fer messages expire dur<strong>in</strong>g this process. S<strong>in</strong>ce, there is no communication<br />

or work load shar<strong>in</strong>g with other matchmakers <strong>in</strong> the completely centralized<br />

approach, the maximum matchmak<strong>in</strong>g efficiency <strong>of</strong> the completely centralized system<br />

is slightly higher than that <strong>of</strong> the multiple adaptive matchmakers system.<br />

However, the completely centralized approach is not scalable and can have a s<strong>in</strong>gle<br />

po<strong>in</strong>t <strong>of</strong> failure [12,13].<br />

Figure 4b shows the matchmak<strong>in</strong>g efficiency <strong>of</strong> the resource discovery approach<br />

with vary<strong>in</strong>g the degree <strong>of</strong> neighborhood <strong>in</strong> a completely decentralized<br />

(P2P) ad hoc grid. The matchmak<strong>in</strong>g efficiency <strong>in</strong>itially <strong>in</strong>creases with<br />

an <strong>in</strong>creased degree <strong>of</strong> neighborhood. This seems logical as with an <strong>in</strong>creased<br />

degree <strong>of</strong> neighborhood, the chances for f<strong>in</strong>d<strong>in</strong>g a required resource/<strong>of</strong>fer also <strong>in</strong>crease.<br />

However, this trend starts decreas<strong>in</strong>g with further <strong>in</strong>crease <strong>in</strong> the degree<br />

<strong>of</strong> neighborhood due to the <strong>in</strong>creased number <strong>of</strong> request/<strong>of</strong>fer messages (refer to<br />

Figure 3a). The matchmaker agent <strong>of</strong> each node has to process more messages.<br />

The <strong>in</strong>creased process<strong>in</strong>g time results <strong>in</strong> TTL expiry <strong>of</strong> request/<strong>of</strong>fer messages<br />

and consequently a drop <strong>in</strong> the matchmak<strong>in</strong>g efficiency. The experiments were<br />

repeated for n = 100, 250 and d was varied from d =2, 4, 6, 8, ..., n. Thesame<br />

matchmak<strong>in</strong>g pattern as <strong>in</strong> Figure 4b was observed.<br />

An alternative view <strong>of</strong> the above discussed phenomenon is to consider the<br />

average response time. Figure 5a shows the average response time to f<strong>in</strong>d a<br />

match with vary<strong>in</strong>g the degree <strong>of</strong> neighborhood <strong>in</strong> a completely decentralized<br />

(P2P) ad hoc grid. Inourexperiments,theresponsetimestaysstableupto<br />

50 hops <strong>in</strong> the P2P case. The response time <strong>in</strong>creases more than proportional

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