Since the birth of wired phones in the fifties, busy signals have disrupted our attempts to communicate. This hasn't changed with the arrival of cellular networks but the reasons for busy signals have. The wireless signal of your cell phone is affected by many variables including your distance to the nearest cell tower, your local terrain, the weather conditions and electrical interference. A fast busy signal lets you know there's a problem but the solution depends on your circumstances.
Just as wired phone networks are sometimes overloaded during holidays and emergencies, wireless networks get congested when too many users place calls at the same time to the same area. A fast busy signal could mean that your network is unable to handle the caller demand. Try waiting a few minutes and making the call again. If you still can't get through, turn your phone off and on again before attempting another call.
Out of Range
Some cellular providers have better coverage than others and coverage varies in different parts of the country. A fast busy signal might mean that your phone can't connect to the network because you're too far from the nearest cell tower. Check the links in "Resources" to learn more about the coverage in your area. Your service provider will also have this information.
Anonymous call blocking or caller ID blocking can cause a fast busy signal. If someone is getting this signal when they try to call you, check your phone settings to make sure they aren't blocked. If you're getting this signal when you call someone else, ask them to check their settings and unblock your number. Because every phone is different, read the instructions that came with your phone if you need help doing this.
Hardware or Software Problem
Although it's unlikely, there's always the possibility that cycling your phone's power by removing the battery for three seconds while it's on will allow you to connect when you power back up. A fast busy signal could also indicate that the PRL (Preferred Roaming List) of your phone's software needs to be updated. If you use Verizon you can do this by dialling *228, pressing "Send" and choosing option 2 to install the update when you're prompted by the operator. If you have another carrier, call them for instructions.
A past due payment or other account issue can suspend your service and give you a fast busy signal. If you're unable to place any calls, check your account status at the carrier's web site or call customer care from another phone to sort things out.