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:

Discriminatory Manner

Involves treatment or consideration based on class or category rather than individual merit; in ways that are unfair or prejudicial.

Employment Management

The practice of overseeing and directing all aspects of an individual's work life within an organization, including hiring, training, and evaluating.

Trade Union

An organization formed by workers to protect their rights and interests through collective bargaining.

Bargaining Unit

A group of employees with a common interest, often related to job function or workforce sector, represented collectively in negotiations with employers.