itten as A(1)= (8.33) The ratio between the up time and the total operation time of the system can also be inter- preted as the probability of founding the system working looking at it in a random instant. This is another possible definition of the availability of a system. Besides the instantaneous availability, depending generally from time due to the fact that old systems tend to go out of work more frequently than new systems, the average Convergent Network Management and Control Plane availability is widely used, which is the average probability that in a fixed a time interval the system works in an instant of this time interval. Mathematically it can be written as (8.34) where the total observation time has been identified with At, the up time is written as A t- Tdwi which is the difference between the total observation time and the downtime and the function Taw(T) is a function defined only in the observation interval and equal to one when the system is out of work and to zero when it is correctly working. Equation 8.34 can be read as the normalized average up time divided by the observation time, which is also the average probability to find the system working, observing it in a random instant during the observation time. In the analysis of failures affecting systems that does not deteriorate sensibly with time, it is often assumed that the system working stabilizes up to a steady state in which the system characteristics does not depends on time. In this case, that reflects sufficiently well what happens in communication systems, a steady-state availability is defined as A = =lim (8.35) In order to compare different survivability methods we will evaluate the corresponding value of the average steady state availability of the routed GLSPs using a simulation pro- gram. In order to evaluate the average GLSP availability, let us number the GLSPs (optical or MPLS depending on the case) that are routed through the network in an arbitrary order. Let us imagine that the simulation simulates NF failure events by 