Nowadays, we all seem to have too many demands on our time. It doesn't matter who you talk to, everyone says the same thing, "there isn't enough time to get everything done." The computer was supposed to make life easier, but now with all the different ways to communicate, everyone wants their answer right away.
I know that we have had to set our mobile devices to automatically turn off at night and on in the morning, otherwise we would be woken up in the middle of the night by the notification of new messages. Also, setting which accounts notify us of new messages has also made managing messages a little easier. The other practice we have is if we are in meetings we are only notified when specific accounts get messages and this is done by setting our notification to silent mode, so it only vibrates. Yes, we have more than one account that goes to our mobile device.
Being able to take some time away from constant contact can be so rewarding. I think people understand that sometimes answers aren't going to be immediate no matter how hard they try.
Have you ever got a phone call from someone right after they have sent you can email? Normally the call is a repeat of the email or a request for an answer immediately. These normally are the emails that require some research before an answer can be given.
It is important to remember that one means of communication can fail, so if it is URGENT to communicate with someone, ensure you try to communicate with them in more than one method. Emails sometimes don't get through due to technical issues same as texting or instant messages or the person is in an area with low or no reception. So remember, if it's urgent, try multiple methods of communication.
So before I have everyone yelling, remember how we communicate before email and cell phones. It did take a bit longer to get an answer, but we survived.
Make sure that you sometimes take a little bit of a break from being constantly reachable. Everyone needs a break every once in a while, so respect others when they take a bit longer to reply to a message. We don't know everyone's total schedule, so understand you aren't going to get immediate responses each time you send out some communication.
Modern communication has made things easier in a lot of ways because we can get the message anywhere, but remember we still need time to get other things done. So maybe one day we won't be saying, "there isn't enough time to get everything done." Until that time, understand the demands on everyone's time and remember you're not the only one asking for their attention.