If you are using K2 4.7 you can use the new management tool to schedule processes. I assume this is also true of K2 5 as the new management tool was created for it to replace workspace but in 4.7 you have both.
If you are still using Sharepoint 2010 there is a web part that allows scheduling.
However if you are running K2 on a version prior to 4.7 and Sharepoint 2013 you can call a process from the window AT scheduler using poweshell using a script like this.
Add-Type -AssemblyName (‘SourceCode.Workflow.Client, Version=4.0.0.0, Culture=neutral, PublicKeyToken=16a2c5aaaa1b130d’)
$conn = New-Object -TypeName SourceCode.Workflow.Client.Connection
$conn.Open(“K2SERVERNAME“)
$pi = $conn.CreateProcessInstance(“PROCESSNAME“)
$conn.StartProcessInstance($pi)
$conn.Close
The at shceduler call is
Start a program- Powershell
Add arguments (your PS1 file) - e:callworkflow.ps1
I hope on of the will help you
I think an API will be great.
However I post a while back a Post that explain how to use the Windows Scheduler and securely schedule Loops and Workflows in BlackPearl for reminders and notifications.
http://community.k2.com/t5/K2-blackpearl/Ability-to-schedule-Loops-and-Workflows-in-BlackPearl/m-p/86451#M26656
Hope this helps =)