When \( k = 1 \), the single-server queue, the exponential parameter in state \( x \in \N_+ \) is \( \mu + \nu \) and the transition probabilities for the jump chain are \[ Q(x, x - 1) = \frac{\nu}{\m...When \( k = 1 \), the single-server queue, the exponential parameter in state \( x \in \N_+ \) is \( \mu + \nu \) and the transition probabilities for the jump chain are \[ Q(x, x - 1) = \frac{\nu}{\mu + \nu}, \; Q(x, x + 1) = \frac{\mu}{\mu + \nu} \] When \( k = \infty \), the infinite server queue, the cases above for \( x \ge k \) are vacuous, so the exponential parameter in state \( x \in \N \) is \( \mu + x \nu \) and the transition probabilities are \[ Q(x, x - 1) = \frac{\nu x}{\mu + \nu…
