Android: How to determine how many customers are associated with the service?

There is no API to find out how many customers are associated with the Service.
If you are implementing your own service, then in your ServiceConnection you can increase / decrease the reference counter to track the number of connected clients.

Below is some psudo code to demonstrate the idea:

MyService extends Service {

   ...

   private static int sNumBoundClients = 0;

   public static void clientConnected() {
      sNumBoundClients++;
   }

   public static void clientDisconnected() {
      sNumBoundClients--;
   }

   public static int getNumberOfBoundClients() {
      return sNumBoundClients;
   }
}

MyServiceConnection extends ServiceConnection {

    // Called when the connection with the service is established
    public void onServiceConnected(ComponentName className, IBinder service) {
        ...
        MyService.clientConnected();
        Log.d("MyServiceConnection", "Client Connected!   clients = " + MyService.getNumberOfBoundClients());
    }

    // Called when the connection with the service disconnects
    public void onServiceDisconnected(ComponentName className) {
        ...
        MyService.clientDisconnected();
        Log.d("MyServiceConnection", "Client disconnected!   clients = " + MyService.getNumberOfBoundClients());
    }
}