Rapid Bank always has three tellers on duty. Customers arrive to receive service from a teller...
Rapid Bank always has three tellers on duty. Customers arrive to receive service from a teller at a mean rate of 45 per hour. A teller requires an average of 3 minutes to serve a customer. When both tellers are busy, an arriving customer joins a single line to wait for service. Experience has shown that customers wait in line an average of 1.5 minutes before service begins.Determine the basic measures of performance – ??, ?, ??, and ? – for this queueing system. We don’t know the probability distributions of interarrival times and service times for this queueing system, so you will need to use the relationships between these measures of performance to help answer the question.
Homework Answers
The average waiting time is given which is Wq = 1.5 minutes
For any queuing system, the corresponding value of average time in the system i.e. W = Wq + average service time = 1.5+3 = 4.5 minutes.
We can use Little's law for any queuing system without having known the probability distribution:
Little's law states that WIP (L) = Flow time (W) * Flow rate (Arrival rate)
So,
Lq = Wq * Arrival rate = 1.5 minutes * (45/60) customers per hr. = 1.125 customers
L = W * Arrival rate = 4.5 minutes * (45/60) customers per hr. = 3.375 customers
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Rapid Bank always has three tellers on duty. Customers arrive to
receive service from a teller...
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