2. Counting Process:
State of the system is given by the total number of customers in the system .

3. N(t)=state of system at time t . (1) N(0)=0
c ont..
N(t)=state of system at time t .
(1) N(0)=0
(2) events are independant if they relate to non-overlapping intervals .
4pm
5pm
6pm

4. (3) stationary process :
i.e Pdf depends only on the interval length , not starting point .

5. (4) probablity that one event occurs in an interval of length h is

7. 5) probablity that more than one event occurs in an interval of length h is 0(h) .

8. example :
for h5/2
h5/2 /h = h3/2 --->0 as h---> 0

9. (5) probablity that more than one event occurs in an interval of length h is 0(h) .

10. Set up a Differential Differency Equation :
Let :
Pn(t) = the probability that N(t)=n

12. P0 (h)=prob no event occurs in an interval of length h.

14. t1 t2
tn-1 tn

18. M i s
used : [ ] E t l = 1 2 20 P n ( ) p r o b . a v c u e f g h

19. L e t l n b m : B i r h R a w s y d
BIRTH & DEATH PROCESS

22. at equilibrium (i.e steady state)

24. At steady state: