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:

Income Summary

An account in the ledger used to summarize revenues and expenses for a period, helping to determine the net income or loss.

Income Summary Account

A temporary ledger account used to summarize a period’s revenues and expenses before transferring the net result to the company's equity account(s).

Net Income

Net income is the total earnings of a company after subtracting all expenses, including taxes, interest, and operating expenses, from its total revenues.

Capital

Financial assets or the financial value of assets, such as cash and securities, owned by a business or individual, used for creating wealth or to engage in further production.