Proof We thus have β(t 「Mor=∑ n+∑ 1 β(t)+1 Dividing by t on both sides, we obtain N(r)dr∑e (0T;+∑(,(t N β(t)+1 λ×T a(t)t re Nt, nt and lt are the average number of customs in the system, the average arrival rate and the average sojourn time during[0,t」. Suppose there is a steady state,ie,Nt→N,λt→λ, and Tt>T when t>o. The above equation immediately yields N=nTCommunication Networks Proof 10 We thus have න 0 𝑡 𝑁 𝜏 𝑑𝜏 = ෍𝑖=1 𝛽 𝑡 𝑇𝑖 +෍𝛽 𝑡 +1 𝛼 𝑡 𝑡 − 𝑡𝑖 Dividing by 𝑡 on both sides, we obtain 𝑁𝑡 = 0׬ 𝑡 𝑁 𝜏 𝑑𝜏 𝑡 = σ𝑖=1 𝛽 𝑡 𝑇𝑖 + σ𝛽 𝑡 +1 𝛼 𝑡 𝑡 − 𝑡𝑖 𝑡 𝛼 𝑡 𝛼 𝑡 = 𝜆𝑡 × 𝑇𝑡 where 𝑁𝑡 , 𝜆𝑡 and 𝑇𝑡 are the average number of customs in the system, the average arrival rate and the average sojourn time during 0,𝑡 . Suppose there is a steady state, i.e., 𝑁𝑡 → 𝑁, 𝜆𝑡 → 𝜆, and 𝑇𝑡 → 𝑇 when 𝑡 → ∞. The above equation immediately yields 𝑁 = 𝜆𝑇