One of the factors which hosted PBX solutions are so popular is that they can satisfy the needs of a range of companies, from home-based start-ups to large companies with operations on several continents. Although hosted PBX services providers offer packages that work for most organizations, they may not be everyone's best solution. Some companies require particular aspects or better security than can be offered by cloud-hosted PBX products.
There are plenty of open-source PBX software solutions to select from for companies that need a more customized solution. These software packages are fully customizable and can be customized to meet any company's unique needs.

What is PBX (Private Branch Exchange)

PBX(Private Branch Exchange) is a small telephony system. PBX provides ease for enterprises to build an internal telephone connection for enterprise users. It also allows the user to share a specific number for external phone lines. The basic purpose of PBX is to save the communication cost in the enterprise. Instead of using separate telephone lines for each employee by using you can share one line with a number of employees. IP PBX is also a PBX but it used PBX with an Internet Protocol(IP) connection. By using IP PBX you can increase your communication features. With IP PBX you can communicate video, audio, and instant messaging.

Top Free and Open Source PBX Software Solutions

Here we have listed the wise ranking of the best open-source PBX systems and our criteria for ranking the best applications are based on popularity + update frequency + latest development + maturity + application relevance, but we are open to accepting any feedback from the personal user experience.

Asterisk

When it comes to open source VoIP systems, Asterisk is essentially the gold standard. It's an open-source PBX platform that a vast number of companies of all sizes use around the world. Actually, many cloud-based PBX solution providers use Asterisk to power their services.
The main benefit of using Asterisk is that it has an enormous list of characteristics that keep growing year by year. You can turn any computer into a comprehensive communications server with this open-source system. There are all common PBX features, such as voicemail, IVR, rule-based routing of calls, automatic distribution of calls, and conference calls.
The Asterisk PBX system is totally free and open-source, so without paying any licensing fees, you can deploy it and modify it as you need.

FreeSwitch

FreeSWITCH was also based on the Asterisk platform and was created and developed by three of the original programmers of the Asterisk platform. Anthony Minessale II, Brian West, and Michael Jerris. The platform is customizable, so only the components you need to run your system can be added. This results in improved stability and makes it simpler to use the whole system.
The FreeSWITCH team believes in utilizing the latest technological advances, so you'll find that all of the top communication technologies, like SIP, H.323, and WebRTC, are supported by the system. When you create a unified communications system using this platform, it is quite simple to integrate it with third-party apps, systems, and software compared to other open-source PBX systems.
As well as some rather unique ones, FreeSWITCH provides you with all the standard calling features you would assume from an enterprise-grade PBX. Examples that include voice recognition and synthesized components, if you build a custom IVR, can be very useful.

FreePBX

The FreePBX is Asterisk GUI and Freepbx EcoSystem has developed over the past decade to be the most widely deployed open source PBX platform in use across the world. The openness of the project allows users, resellers, enthusiasts, and Partners to utilize the FreePBX EcoSystem to build robust communications solutions that are powerful but at the same time easy to implement and support. Sangoma is proud to be the sponsor of the FreePBX project. If you are new to FreePBX you can get started quickly by downloading and installing the FreePBX Distro. The FreePBX Distro is an all-in-one platform that installs everything you need to build a phone system. Once You have a basic PBX in place you can add commercial modules to add advanced features to an already feature-rich base install of FreePBX.

FusionPBX

FusionPBX is an open-source FreeSWITCH GUI and multi-tenant PBX solution. FusionPBX included many features. It is a very powerful software tool based on FreeSWITCH. A number of ways for the utilization of this powerful software such as used for the carrier-grade switch, fax server, voice mail, VoIP server, conference server, voice application server, etc. It has been released under license MPL 1.1.

FusionPBX can be used as a single or domain-based multi-tenant PBX, carrier-grade switch, call center server, fax server, VoIP server, voicemail server, conference server, voice application server, multi-tenant appliance framework, and more. In addition to providing all of the usual PBX functionality, the Following FusionPBX features list allows you to configure:

• Multi-Tenant
• Unlimited Extensions
• Voicemail-to-Email
• Device Provisioning
• Music on Hold
• Call Parking
• Automatic Call Distribution
• Interactive Voice Response
• Ring Groups
• Find Me / Follow Me
• Hot desking
• High Availability and Redundancy
• Dialplan Programming allows nearly endless possibilities

Issabel

Issabel is a free and open source software developed over asterisk communications engine that allows you to build communication tools for businesses.

Issabel is open-source Unified Communications PBX software, providing user-friendly web-based configuration, management, and reporting for telephony. Modules providing predictive dialing can be added. It is a fork of the open-source versions of Elastix, developed by the user/developer community when 3CX acquired Elastix, closed the community, halted distribution and development of the open-source versions, and released a proprietary version.[1][2][3][4]

Issabel is based upon open-source versions of Elastix, Asterisk, FreePBX, HylaFAX, Openfire and Postfix and provides PBX, fax, instant messaging and e-mail server functionality.
source: https://en.wikipedia.org/wiki/Issabel