Some excellent answers have been given already, but let me throw in my 2 cents. Radio stations use a variety of software applications to run their stations:
Automation: Big corporately owned stations use audio automation systems to reduce their payroll, since they don’t have to pay a computer a salary or benefits. Smaller stations, including community and educational stations, use the same software to allow their small staffs to multitask without having to worry what song, commercial, public service announcement or other broadcast element has to be played next.
The better known broadcast automation systems includes Simian and Op-X by Broadcast Software International (owned by Cumulus Media), DAD by Enco Systems, Zetta by RCS Software (owned by Clear Channel / iHeart Media), iMediaTouch by OMT Technologies and WideOrbit (formerly owned by Google). Lesser known entries include StationPlaylist (I use this for many small stations), Zararadio, DigitalJukebox, RadioDJ and Rivendell.
Music Format Software: While some broadcast automation software systems have a companion program scheduler module some stations prefer to use software to create a program flow that is distinctive from their competition. Programs such as Natural Music and RCS Selector allow a station’s program director to customize the station’s music presentation and prevent playing too many songs from a common artist, genre or tempo.
Audio Editing: Commercials, promo announcements, etc., need to be produced and editing by station staff. Programs such as Adobe Audition had been a mainstay in the broadcast production room but since Adobe moved the the subscription-based sales model more stations are moving to other alternatives. There are various paid offerings for both the Windows and Macintosh operating system which will perform the task and the freeware Audacity is available for both systems in addition to Linux systems.
Traffic Software: No, this has nothing to do with the parking lot! Traffic software keeps track of billing for aired commercial content so the station can bill their clients and earn revenue.
Engineering: Some station engineers use software to monitor the health of their transmitter(s) and are capable to switch to a backup transmitter should one fail while operating. Many broadcast audio processors include web-based interfaces which allow the station engineer or program director to customize the sound of the station while listening in a location less noisy than the station’s transmitter room.