202. Markov Chains
202.1. Checkout Counter Model
- Discrete time ()
-
Custommer arrivals: Benoulli()
- Geometric arrival times
- Custommer service times: Geometric()
- State : Number of cusommers at time
Where:
- : Probability of having an arrival
- : Probability of having an departure
- : Probability of having an arrival and a departure simultaneously
- : Probability of not having a custommer arrival
- : Probability of not having a custommer departure
- : Probability of custommer arrival without a custommer departure
- : Probability of custommer departure without a custommer arrival
202.2. -Step Transition Probabilities
State occupance probabilities given initial state :
202.3. Key Recursion
The total probability of ending at with state is the sum of probabilities of the different paths to get to state