Mathematics · Queueing Theory
Consider an M/M/1 queue with arrival rate λ and service rate μ. Let Q 0 = 0 and Q t denote the queue length at time t. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1The stationary distribution of the process (Q t ) is geometric, when it exists✓
- 2(Q t ) admits a stationary distribution if and only if λ ≤ μ
- 3lim t → ∞ P(Q t > k) = 2 -(k+1) for all k < ∞ if λ = μ 2
- 4lim t → ∞ P(Q t > k) = 1 for all k < ∞ if λ > μ
Correct answer
The stationary distribution of the process (Q t ) is geometric, when it exists
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