There is no direct Mitel support on 3cx and Mitel uses a proprietary voip protocol, however it is possible to use SIP trunks on Mitel and route between them. You can also use gateway ISDN boxes to simply move over from ISDN to SIP on 3CX but setting up test numbers that will go over SIP while others go over ISDN.
Make sure you do careful testing of the 3cx contact centre part though to make sure it meets your needs properly (and your call centre manager signs off on it). There are a lot of weakness in 3cx that Mitel has (and a lot of strengths to).
Off the top of my head:
PRO: 3cx set up and configuration is really easy - setting up queues, inbound routing, setting up extensions etc is simple
PRO: 3cx licencing is great - no per user/per device/per ACD etc licencing on top of the proprietary phones. Just max lines in use and buy whatever device you want (as long as it's supported) or use the softphone for free.
CON: it is difficult to see historically how many lines you have used to see if you came close to the maximum, only the current lines in use are available
PRO: The CFD is very powerful for creating inbound (or outbound) scripting. Takes a little bit of getting used to - such as remembering to always quote strings - and compile time errors are confusing but you can do a lot with it, readin customer details from a database, changing prompts based upon date and time, dynamic routing, recording messages etc
CON: any CFD application you create will take down all your queues and lose all callers so they can only be uploaded out of hours. As it is only available on the PRO licence you will probably need to buy a test 4 licence pro version to test your CFD apps (as they often need to be tested and refined a lot). You can easily switch between live and test system on your softphone though for testing.
CON: The reporting is quite weak compared to Mitel and other third party solutions. The queue have no stats about agents logged in, etc. There are a number of options but often you can't get reports the way you might have been used to. You also can't create ad hoc reports and change them you have to recreate them or schedule them for a couple of minutes from now to test.
CON: Wrap up is really poor. You have to specify a standard amount of wrap for every agent and it only works per queue so if you have multiple queues with calls the wrap up will be ignored. If your agents do not all do the same wrap up task (some taking seconds, some minutes, some various)then there is no easy way to stop taking calls without logging right out of the queues (which then messes up you logged in stats). Mitel has a 'make busy' feature to pause you in the queue but still stake internal calls. What is really required is a wrap up button per agent (with wrap up codes) as well as a global wrap up across all queues.
PRO: the callback features, position in queue etc are simple to set up and work well.
CON: The 3cx system is single channel - Mitel can do multi channel - chats, e-mail, social etc and the agent can
CON: The 3cx Q-manager console is not very good. It is difficult to get a good visibility of exactly what your agents are doing especially with multiple queues. It should have a queue view showing the individual callers status in each queue in order, including call backs and an agent view showing the detailed status of each agent at the moment.
CON: The wallboard is fixed, you can't customise it at all - other than the message.
PRO: voice recording built in for free
CON: Voice recording cannot be set to force recording or force not recording - the agent can control it. Difficult if you have policies around that in your call centre.
