In this paper, the reliability and MTTF (Mean Time to Failure) for multi-ring RPR (Resilient Packet Ring) are calculated
on the conditions of single-link failures, double-link failures and no failure, respectively. The parameters such as the total
number of stations N, the number of the sub-rings R, and the distribution of Niwhich represents the number of the
stations in the i-th sub-ring (1≤i≤R) are contained in the formulas. The relationship between the value of the
reliability/MTTF and the parameters N, R and Ni is analyzed. The result shows that reliability/MTTF of the RPR
multi-rings is increasing while the variance of Ni is decreasing. It is also proved that the value of the reliability/MTTF is
maximum when Ni=Nj ( i ≠j and 1≤i, j≤R) by using Lagrange multipliers method, i.e. the condition of the optimal
reliability of multi-ring RPR is satisfied when var(Ni) =0.
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