China Grid and Related Dependability Research - Grid Computing: Infrastructure, Service, and Applications - page 100

the index service and gets the location of the producer; the failure detector
is a producer that gives the status of the monitored objects.

4.5.3.2 Adaptive Model

A grid fault-detection service should stress two things: i rst, how to satisfy
the QoS between two processes; and second, how to satisfy the grid
dynamic nature. The QoS between the monitored process and the detec-
tor can be donated in a tuple ( T U D , T L

M ) , where T U D is an upper bound on

MR , T U

the detection time, T L

MR is a lower bound on the average mistake recur-

M is the upper bound on the average mistake duration. The
QoS requirement can be expressed as in Equation 4.1:

rence time, T U

T D £ T U D , T

MR ≥ T L

T M £ T U

M

MR ,

(4.1)

It is clear that the heartbeat interval Δ interval is a very important factor that
contributes to the detection time:

T U D ≥ Δ interval + Δ tr (4.2)

where Δ tr is a safety margin. A recursive method has been used to get
Δ interval , as depicted in algorithm 1, which is adopted from [56,58]. After
getting Δ interval , a sliding window algorithm is taken, and this sliding
method records the message behaviors, thus the Δ interval will change adap-
tively to the system conditions. Another problem for failure detection is
when to suspect failure. The details are presented in Algorithm 4.1.

Algorithm 4.1
Assumption: The inter-arrival of the “I'm alive” message follows a
Gaussian distribution. The parameters of the distribution are estimated
from a sample window. The probability of a given message arriving more
that t time unit is given as

+•

1

2 2

sp Ú

- m [( x ) /2 s ]

pt () = e dx

(4.3)

2

t

Step 1: [i nd Δ intervalmax ]
Compute

U 2

(1 - PT

T

)( )
()

g=

L D

U (4.4)

2

D+

tr D

UU

D = max( g TT , ) (4.5)

intervalmax M D