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At a train station, people entering a single line to buy their ticket for their journey are served at an average rate equal to the average rate that new customers enter in. How will the length of the que evolve in time?

Answer: The process is a stochastic process and can be thought of a bounded random walk with p=q. If the problem was unbounded then on average the length of the que remains the same. However we are not allowed to have a negative number of people waiting in the line so the problem is bounded. Since the variance of a random walk increases with time and due to the boundary we should expect the average length of the que to growth with time.

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