finalexamformulas

finalexamformulas - Formula Sheet Markov Chains...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Formula Sheet Markov Chains Chapman–Kolmogorov Equations: p ( n ) ij = M X k =0 p ( m ) ik p ( n - m ) kj for any m < n . Steady-State Probabilities: π j = M X i =0 π i p ij j = 0 , 1 ,...,M M X j =0 π j = 1 Queueing Theory M/M/ 1 M/M/s M/G/ 1 P n = C n P 0 = C n ˆ X n =0 C n ! - 1 C n = ± λ μ n = ρ n ( λ/μ ) n n ! , for n = 1 , 2 ,...,s ( λ/μ ) n s ! s n - s , for n = s + 1 ,s + 2 ,... ± λ μ n = ρ n P 0 = 1 - ρ " s - 1 X n =0 ( λ/μ ) n n ! + ( λ/μ ) s s ! 1 1 - λ/ ( ) # - 1 1 - ρ L q = λ 2 μ ( μ - λ ) P 0 ( λ/μ )
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

This homework help was uploaded on 04/07/2008 for the course IE 220 taught by Professor Storer during the Spring '07 term at Lehigh University .

Ask a homework question - tutors are online