Page 232 - DCOM303_DMGT504_OPERATION_RESEARCH

Unit 11: Queuing Theory

2. The average queue length: Notes

    

    

      
 

= 1.04 customers
3. The average time a customer spends in the system:


  

=

= 0.11 × 60 = 6.66 minutes
4. The average time a customer waits before being served:


   

=

= 0.069 × 60
= 4.16 minutes

Example: Trucks at a single platform weigh-bridge arrive according to Poisson probability
distribution. The time required to weigh the truck follows an exponential probability distribution.
The mean arrival rate is 12 trucks per day, and the mean service rate is 18 trucks per day.
Determine the following:
1. What is the probability that no trucks are in the system?
2. What is the average number of trucks waiting for service?
3. What is the average time a truck waits for weighing service to begin?

4. What is the probability that an arriving truck will have to wait for service?
Solution:
Given  = 12 trucks per days,  = 18 trucks per day.
1. Probability that no trucks are waiting for service,


 


 

= 0.3333 or 33.33%

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