Since you're running Ubuntu, your system crontab is located at /etc/crontab
.
As the root user (or using sudo), you can simply edit this file and specify the user that should run this command. Here is the format of entries in the system crontab and how you should enter your command:
# m h dom mon dow user command
*/1 * * * * www-data php5 /var/www/web/includes/crontab/queue_process.php >> /var/www/web/includes/crontab/queue.log 2>&1
Of course the permissions for your php script and your log file should be set so that the www-data
user has access to them.