Asked by Bryson Winder on Jun 26, 2024

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A queuing model which follows the M/M/1 assumptions has λ = 3 and μ = 2. The average number in the system is

A) -3.
B) 3.
C) 0.667.
D) 150%.
E) growing without limit, since λ is larger than μ.

M/M/1 Assumptions

A set of conditions that underlie the M/M/1 queue model, including that arrivals occur according to a Poisson process, service times have an exponential distribution, there is a single server, and the queue has infinite capacity.

Average Number

A statistical measure representing the central or typical value in a set of numbers, often calculated as the sum of all numbers divided by the count of numbers.

μ

The symbol commonly used to represent the mean or average in statistics and mathematics.

  • Assess the average amount of entities in the system under various waiting line configurations.
  • Understand the impact of the service rate and arrival rate on system utilization and queue lengths.
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Verified Answer

PK
Prateek kadambandeJun 28, 2024
Final Answer :
E
Explanation :
In an M/M/1 queue, the average number in the system (L) is given by L = λ / (μ - λ) when λ < μ. However, if λ ≥ μ, the queue will grow without limit. Since λ = 3 and μ = 2, λ is larger than μ, meaning the system cannot reach a steady state and the number in the system grows without limit.