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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:

Cash Inflows

The total amount of money being transferred into an entity, coming from various sources like sales, financing, or investments.

Financially Attractive

A term used to describe investments or opportunities that are likely to provide a good financial return.

Internal Rate

Often refers to the internal rate of return (IRR), which is a discount rate that makes the net present value of all cash flows from a particular project equal to zero.

Return

The amount of profit or loss gained from an investment relative to its initial cost.

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