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1) The inter arrival time at a counter is an exponential random variable with mean 10 minutes. The service time at the counter is also an exponential variable with mean 3 minutes. What is the probability that the counter is idle? The department will set up a second counter when the expected waiting time of a customer will be at least 3 minutes. What should be the average inter arrival time to justify a second counter?

1) The inter arrival time at a counter is an exponential random variable with mean 10 minutes. The service time at the counter is also an exponential variable with mean 3 minutes. What is the probability that the counter is idle? The department will set up a second counter when the expected waiting time of a customer will be at least 3 minutes. What should be the average inter arrival time to justify a second counter?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1) The inter arrival time at a counter is an exponential random variable with mean 10 minutes. The service time at the counter is also an exponential variable with mean 3 minutes. What is the probability that the counter is idle? The department will set up a second counter when the expected waiting time of a customer will be at least 3 minutes. What should be the average inter arrival time to justify a second counter?
Transcribed Image Text:1) The inter arrival time at a counter is an exponential random variable with mean 10 minutes. The service time at the counter is also an exponential variable with mean 3 minutes. What is the probability that the counter is idle? The department will set up a second counter when the expected waiting time of a customer will be at least 3 minutes. What should be the average inter arrival time to justify a second counter?
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