FORTUNE — Jayshree Ullal made her career at networking leader Cisco Systems, before leaving in 2008 and shortly after that joining a new company started by Andy Bechtolsheim, a founder of Sun, and several others. In a recent interview, she discussed what she learned at Cisco—and how her new company, Arista Networks, competes against it. Below, her words as told to Fortune‘s Adam Lashinsky.

In 2008 Arista was 30 engineers and getting ready to launch product. I left Cisco in May of 2008, and I took the summer off to evaluate clean tech and social networking, and finally came back to my roots.

There is a lot of Cisco DNA in this company because Cisco is the biggest networking giant. People therefore assumed we were naturally going to be acquired by Cisco. The conviction with which we believed we were building an independent company wasn’t understood. I think it is today. But it wasn’t very clear then. Being acquired by Cisco wasn’t the goal or the intent. We were really looking to build a company with legs, and there’s a lot of Arista pride in building great technology, delivering a great customer experience, providing outstanding and exceptional service, and offering our customers the disrupted solution they were looking for.

There was no doubt in our minds that we would provide technology disruption. But I think what makes us really excited is that there’s a customer disruption in buying behaviors. Lots of startups come and go and build great technology, but we were able to catch the cloud wave. And there were times when Andy [Bechtolsheim] and I feared we were late to the market. The hallmark of a good company is not just execution but some set of customer acceptance which is defined by luck and timing as well. And I think we were able to get the confluence of all that.

I was at Cisco for 15 years. The equivalent of 105 — every year is 7 years. I came with their very first acquisition, Crescendo. This was in 1993, when the company was $600 million, $700 million in revenue, and mostly a routing company. And John Morgridge was the CEO. John Chambers was the head of sales. And this acquisition really put John [Chambers] on the map. Crescendo, because they acquired the company for $93 million, and we went on to do anywhere from, I don’t know, put the numbers at $10 billion to $15 billion in switching revenue over that period of time. All of which is not just credit to us. There was a significant investment.

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A side story there you’d be interested in. First of all, when they buy a company they ask all the key chief executives to sign up for two years. I agonized over two years. I said, “How can I ever stay in a big company for two years?” Two years felt like an eternity. I wept about that process. So I lived in Cisco two years at a time for 15 years. But I think part of why Cisco became an addiction for me was they really cultivated a startup and an entrepreneurial environment through that Crescendo acquisition as part of a larger company.

The company had T‑shirts at that time with an arrow that said, “path to a billion.” They were 600-something million, and their goal was to hit a billion [dollars in revenue; Cisco’s fiscal-year 2013 revenues were $48.6 billion]. And John Chambers came to me and said, “I want you to do switching, and that must be another billion.”

So I rolled my eyes like teenagers do and said, “What are these guys talking about? They haven’t hit a billion in their mainstream market.” Crescendo was all of 10 million in revenue when they bought us, and it seemed absurd to me that they would ask me to do a billion.

And I think I even made some flip comment to him like, “Just because you did it in routers doesn’t give you a right to do this in switches.” So that was John Chambers — very aspirational and very optimistic and “Yes we can do it.” It wasn’t Crescendo that made Cisco, it was the commitment, the vision, and the inspiration of investing in that acquisition.

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I think they’re a very tough competitor, and I think they’re doing a fine job of holding their own. Cisco still has very large market share. I would argue almost unnaturally high market share. It’s somewhere between 50% and 70% of the switching and datacenter market. We don’t participate in the entire switching market that Cisco has. Arista is only focused on the data center and the cloud piece of it. But I guess I would come back to you and say that no market is forever. All markets mature and what’s exciting for Cisco is to have some tough competitors that keep them nimble, and certainly, Arista’s an example of that.

But what’s most exciting for Arista is we don’t have to succeed because Cisco fails or vice versa. The market, the total available market, is so large that we both can succeed without Peter robbing Paul, or whatever. So in my view customers are looking for an alternative. The more conservative customers who have grown up with Cisco in their traditional enterprises certainly will stay with Cisco. Just like you don’t get fired for buying IBM, you won’t get fired for buying Cisco, and those are not the traditional technical customer community that comes to Arista first. They might come later.

We’re very much in the early adopter phase where the ones who come to us are the ones who are really looking to build this open modern network and know they need a multi-vendor solution to that.

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It’s really a tipping point moment because remember, the data center market right now is anticipated to be around $3 billion or $4 billion. And in the next three years, it’s supposed to get to $10 billion. Some even say $16 billion. But let’s take the low-end of this. So, the way we look at it is even if you say half or 70% of Cisco, because that’s the way life goes, even with the best technology people will go with old habits. We think that there is enough market, enough opportunity and enough customers who want a second vendor. And because we don’t have the legacy of having built an enterprise, we could start with a clean sheet of paper and only offer that. Cisco will come from their strength of legacy and Arista will come from its strength of novelty.

We have a great deal of respect for the company and in fact I think our approaches are entirely different. Since I helped build the enterprise, I would never compete with Cisco directly in the enterprise in a conventional way. It makes no sense. It would take me 15 years and 15,000 engineers, and that’s not a recipe for success.