I am building a web application that requires long time script execution, does anyone knows where to find a hosting service allowing this?
see in control panel of hosting in settings of PHP. or using in begin of script set_time_limit ( int $seconds )
How long are we talking? If it's more than several minutes, I don't know any host short of a dedicated server that even wants you on their box.
You could most likely get a semi-dedicated, or a VPS and set whatever time limit you want. As stated above, there's probably not many shared hosts that would allow longer than 30 seconds or so. Most hosts will hard code the limits so that you cannot overwrite them via set_time_limit or through htaccess.
Course even with my own dedicated server (I have two), I would find a way to make the code more robust rather than trying to just simply extend the time limit. Perhaps mainly because I write code that gets distributed to machines I may have no control over.
I have my own server in my computer, however I can not use it as internet server. I setup the time execution to 3600 seconds. The time of execution of the script varies.
Well technically you can use it as an internet server if you set up with dynip or another dynamic ip type of service (basically like a nameserver that points a domain or subdomain to your computer, and you use a client to update it if your IP changes). But the connection speed in live production would suck. My advice though, take it or leave it: worry less about trying to increase the execution time, and more about finding out why it's taking so long in the first place.