Asked by Cassie Trucchio on Jun 09, 2024

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A queuing model which follows the M/M/1 assumptions has λ = 2 and μ = 8. The average number in the system Ls is ________ and the utilization of the system is ________.

A) 3; 100%
B) 0.33; 25%
C) 4; 33%
D) 6; 25%
E) 4; 25%

M/M/1 Assumptions

The basic hypotheses underpinning the M/M/1 queue model, including assumptions of a single server, Poisson arrival rates, and exponentially distributed service times.

Average Number

A mathematical concept representing the sum of values divided by the number of values.

Utilization

Refers to the extent to which a resource, such as equipment or workforce, is being used effectively in a production process.

  • Compute the average count of entities in the system when applying different queueing theories.
  • Assess service and utilization factors across finite and infinite demographic models.
  • Perceive the relationship between the rate of service and rate of arrival on the functionality of the system and the lengthiness of queues.
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KS
Katelynn SullawayJun 13, 2024
Final Answer :
B
Explanation :
The average number in the system (L) is calculated using the formula L = λ / (μ - λ), where λ = 2 and μ = 8. Substituting these values gives L = 2 / (8 - 2) = 2 / 6 = 0.33. The utilization of the system (ρ) is calculated using the formula ρ = λ / μ, which gives ρ = 2 / 8 = 0.25 or 25%.