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The paper argues that some counting processes contain what it calls “multiple randomness,” where the inter-event time depends on the state of the system at that event. It develops this idea through M/M/1 queues and tandem/Jackson networks, and uses it to argue that some queues may be “properly sub-stable” rather than stable.

I read this as a stochastic-process paper that is trying to challenge how some familiar queueing results are interpreted, rather than simply introducing another queueing model. I found the idea of “multiple randomness” interesting, especially the distinction between the two types of inter-departure times in the M/M/1 setting. My comments below are mainly about making the proposed interpretation easier to compare with the standard queueing formulation.

1. The main distinction needs to be made more concrete. The paper argues that the inter-departure time in an M/M/1 queue should not simply be treated as one random variable because it depends on whether the queue is empty or non-empty. I think this is the key idea of the paper, but it takes some work to see exactly where this differs from the usual formulation. A small worked example showing the same sequence under both interpretations would help.

2. The Jackson theorem claim needs a very clear example. The paper describes the tandem M/M/1 case as a counterexample to Jackson’s theorem and argues that the downstream queue can become “properly sub-stable.” That is a strong claim, and I think one concrete numerical example would make it much easier to evaluate. In particular, it would help to show where the standard analysis and the proposed interpretation actually produce different conclusions.

3. I was not always sure what the simulations are actually demonstrating. The paper shows agreement with simulation results while arguing that the usual interpretation of those results is not correct. It would help to state more explicitly what quantity the simulation is estimating and how that quantity should be interpreted under the paper’s definition of multiple randomness.

4. The terminology could use a more intuitive introduction. “Multiple randomness” and “properly sub-stable” are important to the paper, but I had to go back through the queueing examples to understand what they mean operationally. A short step-by-step example of a few departures, showing when the two types of randomness occur, would make the rest of the paper much easier to follow.

Competing interests

The author declares that they have no competing interests.

Use of Artificial Intelligence (AI)

The author declares that they did not use generative AI to come up with new ideas for their review.