A worker at the State Unemployment Office is responsible for processing a company’s forms when it opens for business. The worker can process an average of four forms per week. In 2010, an average of 1.8 companies per week submitted forms for processing, and the worker had a backlog of 0.45 week. In 2011, an average of 3.9 companies per week submitted forms for processing, and the worker had a five-week backlog.

The poor worker was fired but later sued to get her job back. The court said that because the amount of work submitted to the worker had approximately doubled, the worker’s backlog should also have doubled.

Because her backlog increased by more than a factor of 10, she must have been slacking off, so the state was justified in firing her. Use queueing theory to defend the worker. (This is based on an actual case.)