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MSO Week10 - Coggle Diagram

- - - - lambda could also refer to failure rate, and 1/lambda refers to average lifetime of the product
    - - smaller average waiting time = 1/(lambda + miu) < 1/lambda
  - - - note lambda 1 and lambda 2 must follow the same time scale
  - - - PP(lambda1 + lambda2)
    - - split based on probability, so new lambda = lambda*p
    - - one is about the unit time with mean lambda
        while the other is about t with mean lambda * t
      - PP(lambda) = Poisson(lambda*t)
    - - arrival rate = lambda, mean of inter arrival time = 1/lambda
- - - - row sum must be equal to 0
      - differential of the transition probability matrix where you set t = 0
      - the values of lambda and miu in the diagram dont have to be between 0 and 1
      - diagonals (downward right) must be less than or equal to 0
- - - - pi * Q = 0
        sum of pis = 1
        
        remember they sum to 0 AND NOT 1
      - remember, one equation will be useless
      - take incremental steps: always express pi 1 in terms of pi 0 ... express pi 2 in terms of pi 1 --> then sub in
      - limiting distribution --> find pi i and pi nought (rmbr to express pi i fully , not with the pi nought term)
    - - pi lambda = pi miu
      - N many states: N-1 many cuts
      - flow in mean rate = flow out mean rate