Arrival to a system follows poisson's distribution with mean rate of 8 per hour and mean service time is 3 minutes, What will be the expected queue length?

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Concept:

The given problem follows the M/M/1 queuing model, where arrivals follow a Poisson distribution, and the service times are exponentially distributed.

The expected queue length Lq is given by:

where:

  • = Mean arrival rate (customers per hour)
  • = Mean service rate (customers per hour)

Calculation:

Step 1: Compute the Service Rate \( \mu \)

Given that the mean service time per customer is **3 minutes**, we convert it to an hourly rate:

Step 2: Compute the Expected Queue Length

Substituting values into the formula:

 

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