One of the ways we encourage people to submit tickets, besides reminding them about it when they phone/e-mail/walk-over-and-interrupt us, is we more or less drop everything to deal with issues submitted via tickets. We accept/assign the issue as soon as someone reads it (which is usually within 5 minutes during business hours, rarely more than 15 mins.) If we're working on a project, or something that wasn't submitted via ticket, we'll stop that to address the ticket. If it's a relatively simple issue we will deal with it right away. If it it's more involved, we'll reply and indicate what we'll be doing to address it and when.
On the other hard, if someone e-mails us we generally take our sweet time replying (e.g. after lunch, end of the day, next morning.) Phone calls are usually responded to with "we'll call you back", unless it's some sort of a legitamit "system down/I can't do my work because this thing is broken" call. We also make hints like "Ok, I just have to finish fixing this ticket from Joe then I'll come look at it"
