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Home > Operation Research calculators > Queuing Theory M/M/Infinity Queuing Model example
7. Queuing Theory, M/M/infinity Queuing Model example ( Enter your problem )
( Enter your problem )
Algorithm and examples
  1. Formula
  2. Example-1: `lambda=8,mu=9`
  3. Example-2: `lambda=6,mu=7`
  4. Example-3: `lambda=10` per 8 hr, `mu=1` per 30 min
  5. Example-4: `lambda=4` per 1 hr, `mu=1` per 10 min
  6. Example-5: `lambda=30` per 1 day, `mu=1` per 36 min
  7. Example-6: `lambda=96` per 1 day, `mu=1` per 10 min
 		Other related methods
  1. M/M/1 Model
  2. M/M/1/N Model (M/M/1/K Model)
  3. M/M/1/N/N Model (M/M/1/K/K Model)
  4. M/M/s Model (M/M/c Model)
  5. M/M/s/N Model (M/M/c/K Model)
  6. M/M/s/N/N Model (M/M/c/K/K Model)
  7. M/M/Infinity Model
6. M/M/s/N/N Model (M/M/c/K/K Model)
(Previous method)		2. Example-1: `lambda=8,mu=9`
(Next example)

1. Formula


Queuing Model : M/M/`oo`

Arrival Rate `lambda,` Service Rate `mu`


1. Traffic Intensity
`rho=lambda/mu`


2. Probability of no customers in the system
`P_0=e^(-rho)`


3. Probability that there are n customers in the system
`P_n=rho^n/(n!)*P_0`


4. Average number of customers in the system
`L_s=rho`


5. Average number of customers in the queue
`L_q=0`


6. Average time spent in the system
`W_s=1/mu`


7. Average Time spent in the queue
`W_q=0`


This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then Submit Here


6. M/M/s/N/N Model (M/M/c/K/K Model)
(Previous method)		2. Example-1: `lambda=8,mu=9`
(Next example)


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