First Passage Time -
f = p f p
First Return Probabilities -
f = p f kiip(nk)
Mean First Passage Time -
mij =E [ N ij ]= nf (ijn) for all i j
Mean Recurrence Time -
mii =E [ N ii ]= nf (iin) for
Birth Death Process:^
N(t): # of arrivals
(T): arr. time of 1st cust.
Infinite Queue Capacity: M/M/1
Limited Queue Capacity: M/M/1/N
Multiple servers with infinite queue capacity: M/M/s
Basics Economic Order Quantity: Items withdrawn from stock continuously at a constant demand rate. Items are produced or
ordered Q units at a time and all Q units arrive instantaneously (no lead time). This is a continuous review process
Continuous Time Markov Chains- The system can change state at any point.
pij ( t )=P cfw_ X ( t ) = j| X ( 0 ) =ifor any i, j s
pij ( t )= pik ( v ) p kj ( tv ) , for any i , j s , t 0,0<v <t .
Classification of States States I and j communicate if t1