Avaya Application Solutions Deployment Manual page 258

Reliability and Recovery
B. Markov State Modeling for Redundant Components
For measuring the failure rate of the components that are working in parallel, either in active/
standby mode or active/active mode, the Markov Chain Model is used.
diagram of the Markov model displays the possible combinations of "up" and "down" states for
each component. Evaluation of the model along with the failure rates and repair/recovery rate
leads to the estimation of the individual steady-state probabilities and failure rates.
Example: - Consider an Avaya solution that features duplex Avaya S8700 Media Servers,
which are operating in an active/standby mode. The corresponding Markov state-transition
diagram is presented in
Figure 74: Markov State Transition Diagram for Duplicated Server
In Figure 74, State 2 represents both servers operating while State 1 represents one server
operating and State 0 represents no operating servers. The parameter represents the average
failure rate expressed in failures per hour of individual server, and it is the reciprocal of MTBF (
= 1/MTBF). The parameter
of an individual server, and it is the reciprocal of MTTR ( = 1/MTTR). A critical outage only
occurs when both servers are down, and thus the failure arrival rate for the pair of servers as a
whole is the rate at which transition from "State 1" to "State 0" occurs. The failure rate is
calculated according to the following formula:
P1 is the probability of being in "State 1".
5 This Model is also known as the State-Space Model.
258 Avaya Application Solutions IP Telephony Deployment Guide
Figure 74.
2
2 1
represents the average repair rate, expressed in repairs per hour
F =
----------------------------------------------
P =
1
2
2
P
1
2
2
+ 2 +
5
The state-transition
0