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Home > Operation Research calculators > Queuing Theory M/M/1 Queuing Model example
1. Queuing Theory, M/M/1 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
2. Example-1: `lambda=8,mu=9`
(Next example)

1. Formula


Queuing Model : M/M/1

Arrival Rate `lambda,` Service Rate `mu`


1. Traffic Intensity
`rho=lambda/mu`


2. Probability of no customers in the system
`P_0=1-rho`


3. Average number of customers in the system
`L_s=lambda/(mu-lambda)`


4. Average number of customers in the queue
`L_q=L_s-rho`

Or
`L_q=(lambda^2)/(mu(mu-lambda))`


5. Average time spent in the system
`W_s=L_s/lambda`

Or
`W_s=1/(mu-lambda)`


6. Average Time spent in the queue
`W_q=L_q/lambda`

Or
`W_q=(lambda)/(mu(mu-lambda))`


7. Utilization factor
`U=L_s-L_q`


8. Probability that there are n customers in the system
`P_n=rho^n*P_0`


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


2. Example-1: `lambda=8,mu=9`
(Next example)


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