You are attempting to backup the database with multiple operations. These can either be Native or LiteSpeed for SQL Server jobs.
Please check the SQL Server agent for multiple Full/Log/Differential job operations for the same database.
There are two jobs attempting to process "database_name" at the same time.
SQL Server 2008 does not allow two backup processes to run against the same database simultaneously.
Run these two queries to determine which jobs are stepping on each other.
SELECT * FROM msdb.dbo.sysschedules
SELECT job_id, [name] FROM msdb.dbo.sysjobs
This link explains how to read the results of this query:
Reschedule or cancel one of the backup jobs for this database, the LiteSpeed process will be able to complete successfully.
The error and information is much easier to interpret in SQL Server 2008 (than SQL 2000 or SQL 2005)