There are several benefits of private cloud that make it more appealing than building a hybrid cloud or relying solely on the public cloud.
Hybrid clouds enable organizations to operate in a public cloud environment and reap the benefits of private cloud, such as using the hardware resources that live in their data centers. Some companies, such as startups, operate entirely in the public cloud. Still, others want control over their private cloud.
Private clouds are probably the least popular of the three, but they have their place.
Benefits of private cloud over public, hybrid options
One reason an organization might build a private cloud is that it's sometimes the most cost-effective option. The public cloud has a reputation for being affordable, but monthly usage fees can be substantial.
Public cloud providers such as Amazon and Microsoft bill customers based on the resources they consume, including network bandwidth, storage IOPS and virtual machine use; customers never truly own these resources. If an organization already has network, compute and storage resources in its data center, it's probably more cost-effective to use them than it would be to pay monthly service fees to a public cloud provider.
Some organizations choose to take advantage of the security and privacy benefits of private cloud. When a company puts data in the public cloud, it no longer has total control over it. The only way to truly guarantee the security and privacy of sensitive data is to keep it in house, under the organization's direct supervision.
Finally, private cloud environments can be a starting point rather than a final answer. When properly constructed, it is relatively easy for a company to start out with a private cloud, and then transition to a hybrid cloud when the organization outgrows its private cloud resources.
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How to get started building your private cloud
Comparing and contrasting public and private clouds