... 6- 2 Topics Time-Reversal of Markov Chains Reversibility Truncating a Reversible Markov Chain Burke’s Theorem Queues in Tandem 6- 3 Time-Reversed Markov Chains {Xn: ... π j Pji πi = π j ∑ i =0 Pji = π j ∞ 6- 6 Reversibility Stochastic process {X(t)} is called reversible if (X(t1), X(t2),…, X(tn)) and (X(τ-t1), X(τ-t2),…, X(τ-tn)) have the same probability distribution, ... Example: Discrete-time birth-death processes are reversible, since they satisfy the DBE 6- 8 Example: Birth-Death Process Pn −1,n P01 Sc Pn ,n +1 n Pn ,n −1 P 10 P00 S Pn ,n n+1 Pn +1,n One-dimensional...