Example $3-$ Queuing Theory in Court $($Based on an actual case$)$

A worker at the Unemployment Office is responsible for processing a company's

forms when it opens for business. The worker can process an average of $4$ forms

per week.

In $2011$ an average of $1\mathrm{.}8$ companies per week submitted forms for processing,

and the worker had an order flow time of $0\mathrm{.}45$ weeks.

In $2012$ an average of $3\mathrm{.}9$ companies per week submitted forms for processing

and the worker had a $5$ week order flow time.

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 also should 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. Assume $C{V}_A=1$ and $C{V}_P=1.$

Use the concepts and tools learned in OPIM $201$ to defend the worker.