Hospitals can use queuing theory to better manage capacity in the ED.
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| Dave Eitel, M.D. |
It’s time to put to rest the health care myth that hospitals cannot survive financially unless they operate near capacity. Not only is connecting financial success with capacity a fallacy, but it can also ultimately harm a hospital’s operating performance. To understand why, you need only visit your local grocery store for a lesson in queuing theory.
Queuing, which simply means waiting in line, is a common issue for any service business, which does indeed include hospitals and health care systems. It’s also an issue that can cause extreme frustration for customers. Take the emergency department. The busier the ED is, the longer the average waiting time for patients. In fact, there’s a point at which a customer’s waiting time will skyrocket exponentially (see figure 1 below). When you also factor in random patient arrivals, which you always have in the ED, these unexpected patients will definitely experience longer waiting times than patients with scheduled services.
As long as the randomness of the ED and patient demand remain realities, operating at capacity will not be a good strategy for hospitals. Matching capacity with demand, a skill learned long ago in other service industries, therefore becomes a better alternative. Queuing theory, based on a mathematical formula that helps match random demand to fixed capacity, is behind many of the improvements made to customer wait times in telecommunications, banking, airlines and especially grocery stores.
Patterns in Customer Flow
In 1916 in Memphis, Tenn., Clarence Saunders created a paradigm shift by opening Piggly Wiggly, the first self-service grocery store, which he patented in 1917. The store incorporated shopping baskets, self-service branded products and checkouts at the front. Data captured from entry turnstiles and checkout counters generated reliable forecasts for customer arrival and departure, down to 15-minute blocks of time.
The ability to predict and understand patterns in customer flow meant that grocery stores could statistically manage their approach to queuing and reduce wait times for their customers. Since then, other stores have continued to create innovative ways of managing waiting lines. Some Whole Foods locations, for instance, use a model more commonly associated with banks than with grocery stores: A single line feeds into all available cash registers.
From the Checkout to the ED
Basic queuing theory is just gaining recognition as a critical tool for improving hospital efficiency. At first, predicting how busy an ED will be seems impossible, but just as patterns exist in grocery stores, they’re found in the ED. While there is a great deal of variation in patient flow overall, there is a great deal of predictability in arrival patterns by day of the week. Sundays look like Sundays, and Wednesdays look like Wednesdays (see figure 2 below).
Queuing thinking can help make use of discernable patterns in patient flow, and it contributes to hospital planning by prompting us to examine three core principles that we each experience every day: variability, dependency and interdependency. In terms of the ED, this simply means taking into account that a patient activity will never take exactly as long as we expect and that very often one activity needs to be completed before the next one can begin. These principles demonstrate that the use of total volume and averages—in other words, attempting to apply linear thinking in an environment of variability and interdependence—can end up greatly harming hospital operating performance.
Using queuing theory to anticipate this flow is even more essential when you consider that the capital investment to build one hospital bed exceeds $1 million, not to mention an operating cost that usually exceeds a quarter of a million annually. (See S. Butterfield, “A New Rx for Crowded Hospitals: Math,” ACP Hospitalist, December 2007.)
Case Studies
How do we translate the queuing success of the grocery industry to hospitals, and specifically the ED? Banner Health in Phoenix offers a prime example with its Door to Doc Split Patient Flow model, created in 2002.
In partnership with Jeff Cochran and his team at Arizona State University, Banner applied a queuing thinking approach to resolve a major problem: not enough ED capacity to handle an overflow of patients.
“In some of our facilities, we were treating twice as many patients as the ED was designed to accommodate,” says Twila Burdick, vice president of organizational performance for Banner Health Systems. “Our growing concern was having more patients get frustrated with the resulting long waits and self-triage, putting themselves at risk by leaving without treatment. One of our facilities recognized that getting patients to see a physician sooner was key to reducing the walk-outs and designed a process to reduce that time.”
Together with Cochran, Banner Health developed a queuing network model to analyze the variability, dependency and interdependencies of its ED system. As a result, hospital managers and executives at Banner can predict their ED performance in various situations, compare alternative system designs and determine the effects of alternative policies on the performance of a system—without disrupting the system. The result is a process that allows a patient to see a doctor sooner.
“In the ER, it is not uncommon to find that patients with an earache go through the same process as those with internal bleeding,” Burdick notes. Banner designed the Door to Doc Split Patient Flow process to start with a “quick look” method that rates patients based on their level of illness. This change reduces time spent in triage and allows patients to see a physician sooner. The method also directs the least sick patients into a care process in which they don’t occupy a bed and can stay dressed and ambulatory, much like in a clinic setting. This increases the capacity of EDs that have been limited because of bed occupancy.
“Applying queuing network analysis to this patient flow model has helped us better predict the number of doctors and beds we’ll need at each point in the process, which enables us to manage our patient flow much more effectively,” says Burdick. Queuing has also allowed Banner to replicate its improvements at its eight largest hospitals. Instead of relying on gut instincts, Banner can apply data from each location and generate specific and reliable predictions. Having tracked the results of Door to Doc with each of its hospitals, Banner has reduced the rate of patients who would have left without treatment by 50 percent or more.
According to Joseph Guarisco, M.D., chairman of emergency medicine for Ochsner Health Systems in New Orleans, Banner Health’s ED capacity planning efforts represent the most significant analytical work ever done using an engineering perspective. Ochsner is one of a growing number of health care organizations across the United States using similar capacity planning principles.
Heavily hit by Hurricane Katrina in 2005, Ochsner experienced major bottlenecks that elevated the normal 20-minute ED wait times to one to three hours post-Katrina. In response, Guarisco and a joint practice team developed q-Track, a system based on lean engineering principles and the overall credo that patients “don’t get a bed unless they need one.” Immediate results included a rise in patient satisfaction from 50 percent to 90 percent and a decrease in wait times to 30 minutes.
“Our biggest challenge has been changing the organization’s culture to take a more retail focus with patients,” says Guarisco. “But involving staff in every area of the ED from registration personnel to physicians has enabled us to create rules of engagement and build consensus.”
While it is refreshing to know that hospitals are increasingly adopting these queuing quality and systems engineering methodologies, which have long been espoused by other industries and organizations like the American Society for Quality, they still have a long way to go to make such practices part of the organizational culture. But one way to begin is by asking some basic questions.
Considerations When Applying Queuing Thinking
Hospital service managers who want to integrate queuing thinking must begin to think about service performance in a different way. Here are some questions to consider:
- What is the typical customer throughput time (length of stay)? How will this change based on varying customer demand, as well as variations in the many decisions that affect capacity to serve, such as differing system designs, staff schedules and skills mix?
- Where are the bottlenecks (delays) and how do they change over time?
- What do waiting lines look like? What are their lengths and locations?
- What are the resource constraints (number and type)? That is, how busy is each resource type? Do they have undoable workloads with this process design and this customer demand (rate of arrivals)?
Answering these questions will provide a strong basis on which to build a queuing system customized for your organization. Health care professionals who are struggling to balance cost, quality and capacity in any area of their hospital will find that using queuing theory provides a tested scientific way to move beyond intuition when making decisions. When the right model is applied to the right setting, results are often dramatic: saving time, increasing revenue, and increasing staff and patient satisfaction.
Dave Eitel, M.D., M.B.A., is a member of the quality management department at the Wellspan Health System in York, Pa., and is chair elect of the American Society for Quality’s health care division.
The Banner/ASU Emergency Room Door-to-Doc Capacity Planning Toolkit is available for download at www.bannerhealthinnovations.org. (Note: You will need to have implemented ESI triage at www.ahrq.gov/research/esi.)
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Figure 1: The Relationship between Capacity Utilization and Waiting Time in a Service (Queuing) System
Figure 2: Rate of Incoming Patients, by Hour of Day, for a Typical Wednesday
