The Registration Area Has Just Opened at a Large Convention

question 120

Essay

The registration area has just opened at a large convention of building contractors in Banff. There are 300 people arriving per hour (Poisson distributed), and the cost of their waiting time in the queue is valued at $120 per person per hour. The local convention bureau provides servers to register guests at a fee of $20 per person per hour. It takes about 1.5 minutes to register an attendee (exponentially distributed). A single waiting line, with multiple servers, is set up.
a) What is the minimum number of servers for this system?
b) What is the optimal number of servers for this system?
c) What is the cost for the system, per hour, at the optimum number
of servers?
d) What is the server utilization rate with the minimum number of
servers?

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Definitions:

Stimulus Transduced

The conversion of a stimulus from the environment into a form that can be processed by the nervous system.

Sensory Adaptation

The process by which sensory receptors diminish their sensitivity to continuous stimuli, allowing organisms to focus on changes in their environment.

Action Potentials

Rapid, temporary changes in the electrical charge of a cell's membrane, crucial for nerve signal transmission.

Transduction

A process in genetics whereby foreign DNA is introduced into a cell by a virus or viral vector.