Modeling P2P Grid Information Services with Colored Petri Nets - Grid Computing: Infrastructure, Service, and Applications - page 335

number of initial requests, we obtain the total cost of messages being sent
using formula (13.3).
Let D be the average delay incurred at each PG, X the total number of
PGs, R the range per section, N the initial number of requests sent, S the
number of splitting requests sent within a PG, and Z the number of hops
per section.

Total delay = ( R - 1) ¥ D (13.2)

Total messages sent = N ¥ R (13.3)

In a case where avalanching (dynamic sectioning) is permitted, we assume
that all sections are equal in range and each PG sends S splitting requests.
The total time it takes to execute a request can be computed using formula
(13.4). Similar to formula (13.2), the range is now replaced with Z hops per
section, which can be calculated using formula (13.6). Since every parallel
hop produces multiple requests, the total messages sent at every hop can
be computed using formula (13.5).

Total delay = Z ¥ D (13.4)

z

Total messages sent = N ¥ S
n =1

S n (13.5)

Ê ˆ

Ê 1 ˆ 1

ʈ ʈ

Z = ln 1 + ∏ ( X / N ) ∏ ln (13.6)

Á˜ Á˜

Á ˜

Á ˜

˯ ˯

Ë ¯

Ë S ¯ S

13.4
Since PIndex is designed for large-scale grid information networks, simu-
lations are required to observe its features as proposed. A simulator or a
model that can be used to simulate a PIndex network should have the fol-
lowing features:

Modeling PIndex with Colored Petri Nets

• Performing the specii c algorithms used by PIndex

• Performing parallel PG operations

• Prioritizing tasks within PIndex

• Modeling many thousands of nodes

• Modeling time intervals of around 100 m

• Supporting different types of probability distributions of events.