Question
Download Solution PDFArrival 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
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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