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

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Presentation transcript:

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

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

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

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

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

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

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

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

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

t1 t2 tn-1 tn

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

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

at equilibrium (i.e steady state)

At steady state: