Key Equations

Structure of Waiting-Line Problems

  1. 1. Customer arrival Poisson distribution:

    P n = ( λT ) n n! e λT
  2. 2. Service time exponential distribution:

    P(tT)=1 e μT

Using Waiting-Line Models to Analyze Operations

  1. 3. Average utilization of the system:

    ρ= λ μ
  2. 4. Probability that n customers are in the system:

    P n =( 1ρ ) ρ n
  3. 5. Probability that zero customers are in the system:

    P 0 =1ρ
  4. 6. Average number of customers in the service system:

    L= λ μ  λ
  5. 7. Average number of customers in the waiting line:

    L q =ρL
  6. 8. Average time spent in the system, including service:

    W= 1 μ  λ
  7. 9. Average waiting time in line:

    W q =ρW
  8. 10. Little’s law:

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