I've been doing some reading on queueing theory, and one thing I don't understand is what exactly λ and μ are. Some definitions state that they are the arrival and service rate (customers arrived/departed per minute), while others say that λ is equal to the probability of going from a state with n customers to a state with n+1 customers. What I don't understand about this is that if the first definition were to be true, the value of λ could be greater than 1, while if the second definition were true, it could not be. So, can the values of λ and μ be greater than 1?
2026-03-25 01:23:50.1774401830
Can λ and μ be greater than 1?
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From what I recall of the only queueing theory course I have taken, $\mu$ and $\lambda$ are indeed rates per unit of time. Actually, $\frac{1}{\lambda}$ and $\frac{1}{\mu}$ are the mean expected values of service. They can be greater than one because they are not probabilities (they may be parameters for distribution, for instance when you use Poisson processes to model the situation).