# Simple service time in M/M/1

I'm trying to understand queueing systems and I found some notes online. The define $\lambda$ as the mean arrival rate, and $\mu$ as the mean service rate (the average number of customers who can be served by a single service station per unit time). The example they give is

Customers arrive at a bank at a rate of 30 per hour. Arrivals are random and service time is exponential, so that the $M/M/1$ model applies. The clerk’s service time is 90 seconds. Therefore $\lambda = 30$ and $\mu = 45$, and $\rho = \lambda/\mu = 30/45$.

I don't understand where the $\mu = 45$ came from. Can some please explain. Thank you.

## 1 Answer

Since the clerk's service time is 90 seconds, this means that he has an average rate of 40 customers per hour. Therefore $\mu = 40$ and so the notes might have made a typo.

• If you want this to be an answer to your question, can you say more? Otherwise, this should be an addition to the question statement. – gung Dec 5 '15 at 12:27