Rule No. 1: People don’t like to wait. Rule No. 2: People don’t like to overpay for things. Imagine what Rule No. 3 is.

If you guessed, “People don’t like to wait an agonizingly long time for something they’re almost sure to pay through the nose for,” then you win my Tuesday prize: Go buy yourself a Starbucks. (Hey, wait a minute. Isn’t that something that violates Rule No. 3…?)

Yes, but the Grande Cappa-Line-o aside, there is something worse—a gang of Rule No. 3 scofflaws that has made even the most pleasant and patient of us fume: I speak of hospitals, of course. Waiting times for ERs, elective surgeries, and hospital care across the board—and around the world—have been a cause of consternation for years. In the U.S., according to one report offered in Congressional testimony, 2 million patients admitted to hospitals each year wait 4.3 million days for a bed.

Enter the tools of the digital age: Sophisticated bed management, real-time locating devices for patients and staff, improvements in electronic health records, smartphone messaging services, virtual visits, and advanced information systems are all converging today in a way that offers real hope for efficient hospitals.

At Humber River Hospital in Toronto, tracking devices let administrators know where doctors, nurses, and patients are at any moment, and “back-of-the-hospital functions” from laundry to pharmacy are 75% automated, according to Modern Healthcare writer Beth Kutscher. Massachusetts General has been exploring virtual patient visits—which, in a pilot program, allowed doctors to make a determination on the next steps in care in just 3.6 minutes, versus 18 minutes for an office visit.

One of the more remarkable turnarounds, to believe the numbers, has been occurring at New Cross Hospital, part of the Royal Wolverhampton Hospitals NHS Trust in the UK—where, British innovators working with a Pittsburgh–based company, TeleTracking, have reportedly made remarkable progress reducing patient waiting times. Most discharged patients, for example, drop off their real-time location system (RTLS) wrist badges when leaving the hospital, which automatically signals the housekeeping team to clean the empty rooms—an improvement that has helped new beds be available to patients in under 40 minutes, hospital officials say.

And then there’s the inimitable Cleveland Clinic, which was able to grant same-day appointments last year to 98% of those who requested them—an extraordinary achievement for a hospital system that had 6.2 million outpatient visits last year. For part of the reason why, see No. 14 on Fortune’s Businessperson of the Year list.