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# Waiting time in a single server queue

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Using a single-server queuing system with Poisson arrivals of 10 units per hour and a constant service time of 2 minutes per unit. How do I go about calculating how long the customer waiting time will be in seconds, on average?

https://brainmass.com/statistics/poisson/waiting-time-in-a-single-server-queue-580689

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See attached file. Thanks
M/M/m/ queueing computations
Arrival rate (l) 10 per hour Assumes Poisson process ...

#### Solution Summary

Shows how to calculate waiting time in a single server queue

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## Queuing problem: Single server

(a) Consider a coffee counter with a single server at which tired students arrive according to a Poisson process. Let the mean arrival rate be two students per ten minutes and assume the serving time is exponentially distributed with an average of 180 seconds per student.

1. What is the average queue length?
2. How long does a student have to wait in the queue?
3. Find the average queue length and waiting time in the queue if the service time
decreases to 120 seconds per student.

(b) The owner of a shop observes that on average 18 customers per hour arrive and
there are typically 8 customers in the shop. What is the average length of time each
customer spends in the shop?

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