The Registration Area Has Just Opened at a Large Convention

question 141

Essay

The registration area has just opened at a large convention of building contractors in Banff. There are 200 people arriving per hour (Poisson distributed), and the cost of their waiting time in the queue is valued at $100 per person per hour. The local convention bureau provides servers to register guests at a fee of $15 per person per hour. It takes about 0.8 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:

Breaching Party

The entity or individual that fails to fulfill their contractual obligations, thereby violating the contract.

Technical Injury

A legal injury claimed in a lawsuit, often without tangible harm, based on a technical violation of a statute or regulation.

Actual Damage

Financial loss or harm that can be quantified or specifically identified, resulting from the breach of a legal duty or infringement of rights.

Wrongfully Terminated

Refers to a situation where an employee's dismissal from a job violates legal statutes, contractual terms, or workplace policies.