Page 230 - DCOM303_DMGT504_OPERATION_RESEARCH

Unit 11: Queuing Theory

The expected number of customers in the system is given by, Notes
 
L =  =       
s
 
 
  (2)
    
The expected number of customers in the queue is given by,


   

 
  
 
 
  (3)
     
With an average arrival rate , the average time between the arrivals is 1/. Therefore, the mean
waiting time in queue, w is the product of the average time between the arrivals and the
q
average queue length,

   
W =     (4)
q       
    
=    
       
   
Substituting   
       
Similarly the average waiting time in the system,

    
W =     (5)
s       
putting L = l (m - l),
s

we get W =
s   
Queuing Equations

The evaluation of Model I is listed below:
1. Expected number of customers in the system:

 
 
    
2. Expected number of customers in the queue:
 
 
     

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