A Multiple-Server Queuing Model Has Three Servers with a Mean

question 23

Essay

A multiple-server queuing model has three servers with a mean service time of five customers per server per hour. It has been determined that arrivals will average 12 per hour. Arrivals follow a Poisson distribution and service times follow an exponential distribution.
a. Calculate the probability that all three service channels are idle.
b. Determine the probability of five customers in the system.
c. Determine the average number of customers waiting for service.
d. Determine the average number of customers in the system.
e. Determine the average time a customer spends waiting for service.
f. Determine the average time a customer spends in the system.
g. Determine the probability an arriving customer will wait for service.

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Definitions:

Capital Expenditures Budget

A plan for a company’s expenditures on large physical assets like property, plant, and equipment that are expected to last more than one year.

Budgeted Balance Sheet

A projection of a company's financial position at a specific future date, showing expected assets, liabilities, and equity.

Operating Budgets

Detailed projections that outline expected income and expenses related to the day-to-day operations of an organization over a specific period.

Budgeted Income Statement

A financial statement that projects income and expenses for a future period, typically used for planning and budgeting purposes.