A Multistep Extending Truncation Method towards Model Construction of Infinite-State Markov Chains

Algorithm 1

An advanced truncation algorithm towards construction of CTMC.

(1)  procedure TRANSIENTTRUNCADVANCED𝒞,𝑆₀,𝑡,𝜀

(2)   𝐼=𝑆₀

(3)   𝐵=𝑆₀

(4)   compute 𝒫_𝐼◊^[0,𝑡]𝐵

(5)   while   max𝒫_𝐼◊^[0,𝑡]𝐵≥𝜀   do

(6)    𝑠^′=𝑠∣𝒫_𝑠◊^[0,𝑡]𝐵=max𝒫_𝐼◊^[0,𝑡]𝐵

(7)    compute 𝒫_𝑠′◊^[0,𝑡]𝑠^′′∣𝑠^′′∈𝐵

(8)    while   _𝑠′∑_′∈𝐵𝒫_𝑠′◊^[0,𝑡]𝑠^′′≥𝜀   do

(9)     𝐸=𝐵⧵𝑠₀^′′,𝑠₁^′′,𝑠₂^′′,…,𝑠_𝑛^′′ such that

(10)    𝒫_𝑠′◊^[0,𝑡]𝑠₀^′′≤𝒫_𝑠′◊^[0,𝑡]𝑠₁^′′≤𝒫_𝑠′◊^[0,𝑡]𝑠₂^′′≤⋯≤𝒫_𝑠′◊^[0,𝑡]𝑠_𝑛^′′ and

      ∑𝒫_𝑠′◊^[0,𝑡]𝑠_𝑖^′′<𝜀

(11)    𝐵={𝑠𝑢𝑐𝑐𝑒𝑠𝑠𝑜𝑟𝑠(𝑠)∣𝑠∈𝐸}

(12)    compute 𝒫_𝑠′◊^[0,𝑡]𝑠^′′∣𝑠^′′∈𝐵

(13)   end while

(14)   compute 𝒫_𝐼◊^[0,𝑡]𝐵

(15)  end while

(16) end procedure