Page 131 - DCAP601_SIMULATION_AND_MODELING

Unit 8: Simulation of Queuing System (II)

Proof Notes

For each job i = 1, 2, . . ., define an indicator function
t
 1 a   c i
i
t
 i ( )  
 0 otherwise
Then
n
t
l ( )   i ( ) 0 t  c n
t

i 1
and so
n n n n
n c n c n c
i 
)
t
c
 l ( )dt     i ( )dt    i ( )dt   ( – a  w i
t
t
i
0
0
i 1 i 1 0 i 1 i 1
The other two equations can be derived similarly.
Example

10
376
 l ( )dt   w  614
t
i
0
i 1

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