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I am new to Queuing systems. There is an independent assumption made for the interarrival time. Can someone please explain to me why this assumption is true, can you provide me with an example?

"In modeling the arrival process, we assume that the Ti’s are independent, continuous random variables"

This image is from the textbook: Operations research

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  • $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    Commented May 6 at 21:37

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You have to keep in mind the separation between a physical process and a model. We observe some process in the real world (customers arriving at a server) and want to construct a model that helps us answer questions about the process.

We are free to design such a model however we want. For starters, we might invent a model that says a new customer arrives deterministically every 1 minute. Of course, this is very simplistic. A more complex model would allow customers to arrive randomly but with independent inter-arrival times. If this is still too simplistic and we feel it doesn't capture the physical process effectively, we can relax that assumption too (see Hawke's process).

In short, the assumption of independent inter-arrival times is mathematically convenient but still allows the model to capture many important features of the physical process.

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  • $\begingroup$ Thank you for the explanation and for sharing the Hawke's process. I will look into it. It makes sense now why independent assumption works for inter-arrival times. $\endgroup$ Commented May 6 at 23:40
  • $\begingroup$ @romeshprasad : I think you misunderstood the above answer (which I have +1d). It was not explaining why independence "works." It was explaining that independence is a modeling assumption that is more general and useful than deterministic arrivals (while also being simple enough to analyze). The idea behind a mathematical model is that you state your assumptions and then analyze the system subject to those assumptions. To suggest that independence "works" or "is true," you would need to clarify what you mean by "works" and "is true." What system are you comparing this model against? $\endgroup$
    – Michael
    Commented May 7 at 3:43
  • $\begingroup$ @Michael thank you for the response. I used the word "work" casually. I will be careful in my choice of words. $\endgroup$ Commented Jun 14 at 22:21

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