Page 231 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes 3. Average waiting time in the system:


  
4. Average waiting time in the queue:


   
5. Average waiting time for a customer:

 
     
6. Expected length of non-empty queue:

 
  
7. Probability that there are n customers in the system:

      


       


      
8. Probability that there is nobody in the system:

 

9. Probability that there is at least one customer or queue is busy,
 
10. Traffic intensity, or utilization factor,


 


Example: Consider a situation where the mean arrival rate (l) is one customer every
4 minutes and the mean service time (m) is 2½ minutes. Calculate the average number of
customers in the system, the average queue length and the time taken by a customer in the
system and the average time a customer waits before being served.
Solution:

Given, Average Arrival Rate  = 1 customer every 4 minutes or 15 customers per hour
Average Service -Rate  = 1 customer every 2½ minutes or 24 customers per hour
1. The average number of customers in the system:



  

  customers


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