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The Mathematics of Complexity: You Can’t Just Mask It, You Must Eliminate It

by Juniper Employee on ‎04-15-2010 09:59 AM - last edited on ‎04-15-2010 04:21 PM by

Cloud computing promises increased efficiency for service providers and  enterprise IT, and greater agility for users. To realize those promises, the cloud needs to be made up of large, shared pools of standardized and virtualized resources (including server, storage, and network elements). The larger the resource pool, the greater the efficiency, so scalability is key. But there is a problem.  Most networks today currently don’t  scale well.

 

Scalability is the ability to add capacity in a linear fashion without adding incremental operational complexity. The typical Ethernet backbone in the data center fails to meet that definition, because as you add more devices (physical or virtual) to the network and need to have more switches, it actually gets exponentially more complex.

 

Why is that?

 

I’ve recently blogged about the legacy tree structures that are characteristic of most data center networks today (designed for north-south traffic, not east-west) and how they introduce significant complexity and latency into the network. Let’s look closely at the inherent complexity of such structures.

 


THE FACTORIAL OF COMPLEXITY

Networks are challenged to keep pace with the exponential growth of devices (virtual and physical) in the data center.  As the number of devices grow, so must the number of switches that interconnect those devices. Since each switch is an autonomous device, it deals with a packet on its own terms and then cooperates with other switches via shared protocols.

 

The complexity in managing the network is a function of the number of device interactions, not the number of devices.  In fact, there is a an exponential increase in the number of interactions that occur between switches. Essentially what you have to manage is not just the number of switches in the network. You also have to manage the number of interactions in the network. Networking protocols like spanning tree, link aggregation protocols (LAGs), routing, and security rely on effective interactions between two or more switches. 

These interactions increase exponentially with each added switch. In fact it can be expressed in the formula 108i8E05B8C12773306E, where i is the number of potential interactions, and n is the number of managed devices. 

 

For example, 10 switches can generate 45 interactions. But with 100 switches the number of potential interactions increases to just under 5,000, and with 1,000 switches the number expands to 5 million.

 

The best way to address complexity is to eliminate the number of interactions altogether, and get the data center network to behave as a single device.

 

The goal is to reduce n to 1, with one device and no interactions. Is it possible? By applying the concept of a fabric, not a legacy tree structure, it is. And at Juniper, we we’re creating a single network fabric for the data center that can achieve this very objective.    

Comments
by Aleksey Mints(anon) on ‎04-16-2010 10:50 AM

Andy, minor qualm:

 

the growth of interactions with each added device is polynomial, not exponential.  The former is a simple power of n (in this case, it's the 2nd power), while the latter would have something to the n-th power.  I believe in computer science terminology, i(n) is a function of order n-squared - O(n^2)

 

As you mention:

i(2)=1

i(10)=45

i(100)=4,950

i(1000)=499,500

by Juniper Employee on ‎04-22-2010 09:02 AM

 

Thank you, Aleksey.  Yes you are correct.  The equation is actually quadratic, not exponential.  I took a bit of marketing license.  :smileyhappy:

by WMiniscalco(anon) on ‎04-29-2010 01:04 PM

And, digging a little deeper, one sees that while the total traffic increases quadratically, the processing load on any given switch increases linearly.

--Bill

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