For a M/M/I/∞/∞/FCFS queue model, the mean arrival rate is equal to 10 per hour and the mean service rate is 15 per hour. The expected queue length is

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  1. 1.33
  2. 1.53
  3. 2.75
  4. 3.20

Answer (Detailed Solution Below)

Option 1 : 1.33
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Concept:

Queuing Theory

Given:

Mean arrival rate (λ) = 10/hr, Mean service rate (μ) = 15/hr

∴ Traffic intensity, \(\rho = \frac{\lambda }{\mu } = \frac{2}{3}\)

Queue length = \(\frac{{{\rho ^2}}}{{1 - \rho }}\)

Calculation:

Queue length = \(\frac{{4/9}}{{1/3}}\) = 4/3

∴ Queue length = 1.33
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