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Analytics Magazine

Patient Flow

Spring 2008



The new queueing theory for healthcare.

by Randolph W. Hall

From birth to death, we are all part of the healthcare system. We rely on both public and private organizations to provide preventive care (such as inoculations) and to treat our illnesses, diseases and injuries. Healthcare is perhaps the strongest determinant of both our quality of life and our longevity.

Worldwide, and in the United States in particular, healthcare consumes an increasing percentage of our economic product. This rising cost can be attributed in part to aging populations and the expense of new, advanced treatments. Just as importantly, it can be attributed to inefficiencies in healthcare delivery. Simply put, the science of healthcare has progressed much more rapidly than our ability to manage healthcare as a truly integrated system.

Patient Flow

Patient flow represents the ability of the healthcare system to serve patients quickly and efficiently as they move through stages of care. When the system works well, patients flow like a river, meaning that each stage is completed with minimal delay. When the system is broken, patients accumulate like a reservoir, as in the chronic delays experienced in many big city emergency departments. Put another way, good patient flow means that patient queueing is minimized; poor patient flow means that patients suffer considerable queueing delays.

Healthcare systems resemble any complex queueing network in that delays can be reduced through: (1) synchronization of work among service stages (e.g., coordination of tests, treatments, discharge processes), (2) scheduling of resources (e.g., doctors and nurses) to match patterns of arrival, and (3) constant system monitoring (e.g., tracking number of patients waiting by location, diagnostic grouping and acuity) linked to immediate actions. But healthcare has unique features that make queueing problems particularly difficult to solve:

• Waiting creates additional work for clinicians. Patients must be monitored and served while waiting, and their conditions even deteriorate, necessitating additional work once they are seen. Thus, as queues become large, the workload increases and the capacity to serve patients deteriorates.

It can be difficult to distinguish productive waiting (e.g., recovery) from unproductive waiting (e.g., waiting for tests). In a traditional queueing system the most desirable outcome is a zero time in system with instantaneous service; in a hospital, it is undesirable to push length of stay all the way to zero, as patients need to be monitored and cared for during recovery periods. The result can be conflicting objectives in managing hospital beds as a limited resource.

Healthcare organizations operate within a unique regulatory and business environment that falls partly in the private sector and partly in the public sector. Hospitals may find it impossible to manage queues through pricing, and reimbursement schemes may be misaligned with costs. For example, under the Emergency Medical Treatment and Active Labor Act (EMTALA), hospitals are mandated to see all patients presenting to emergency rooms independent of their ability to pay. Thus, the economic environment precludes queueing solutions often found in the private sector, such as peak-period pricing. At the same time, physicians frequently act like independent entrepreneurs, making it difficult for healthcare organizations to fully integrate their systems under sound managerial practices.

Characterizing Patient Flow

My first exposure to the field of patient flow came through the Institute for Healthcare Improvement (IHI), an outstanding organization devoted to improving the quality and value of healthcare. IHI’s approach centers on the open sharing of best practices within “collaboratives,” groupings of hospitals and clinics, clinicians and managers, organized around common objectives, such as reliability, safety or patient flow.

The new queueing theory for healthcare

Important to the operations research community, IHI has emphasized evidence-based decision-making, meaning that performance measures and patient outcomes should be tracked and integrated into a system of continual improvement. Though not directly linked to industrial engineering, management science or operations research, IHI has adopted these field’s methods, focused on making radical improvements in health, not through creating new technology or treatments, but through using what we have now to maximum benefit.

At the University of Southern California, my colleagues David Belson, Maged Dessouky and I have used this philosophy as the launching point for a comprehensive evaluation of the Los Angeles County/University of Southern California (LAC/USC) General Hospital, one of the largest hospitals in the country. Like many urban public hospitals, healthcare at LAC/USC is dominated by the flow of patients through its emergency department. Patients by and large come to LAC/USC for one of two reasons: They believe that they have no other option due to lack of health insurance or they have suffered trauma or another emergency condition somewhere in the hospital’s vicinity and were taken there by ambulance or helicopter.

As at all hospitals, care is provided through many specialized departments, such as radiology, surgery and various types of patient wards, as well as by ancillary departments, such as admissions, medical records, laboratory, pharmacy, housekeeping and transportation. A patient arriving through the emergency department encounters repeated waits as he or she progresses from stage to stage, waiting for rooms, equipment, physicians, nurses, technicians, beds, medications, records, gurneys, orderlies and continuing care facilities once the patient is ready for discharge. As in other hospitals, when the system becomes overloaded, the patient may wait hours or even days from being seen in the emergency department until placement in a ward. A patient may have to wait days or even weeks for a surgery. These conditions are in some respect extreme, but certainly not unusual throughout the United States.

Our work has revealed that healthcare professionals are unusually committed to their jobs, even when working under extremely challenging conditions. They show a passion for their work and a camaraderie that is unlike what we have seen in other economic sectors. Yet clinicians, in particular, are frustrated because they cannot control activities that occur outside their own departments. We have also observed three major causes of queues in hospitals:

  • Idle capacity due to a failure to synchronize complementary resources (e.g., ensuring that needed technicians, nurses, physicians, supplies, patients, etc. are present at the same time to provide a needed service).
  • Inadequate communication to ensure downstream departments are prepared to receive patients from upstream departments and to ensure that all parties are prepared for foreseeable demand.
  • Inefficient processes that require more work than necessary or un-needed repetition of work.

For example, patients may wait for placement in a hospital bed because:

  • Other patients are waiting too long to complete the discharge process.
  • Beds remain idle too long from when a patient departs until a bed is prepared for the next patient, until “bed control” is notified of its availability, and until the next patient is transported to the bed.
  • Communication is poor between the emergency department and the ward as to the exact time patients will arrive and the care needed immediately upon arrival.
  • The suitability of individual beds for individual patients cannot be ascertained due to inadequate processes for tracking patients and their medical records and inadequate processes for tracking the state of hospital beds.

Similar observations can be made in surgical and radiological departments. A patient with a serious fracture cannot be operated on until the CAT scan is completed, which is delayed because there is a shortage of technicians, because cycle times are too long (the result of not sufficiently prepping patients before the test), or perhaps even because there is an inadequate number of gurneys to transport patients. Surgical capacity is wasted due to cancellations, because surgical times are mis-estimated or because insufficient hours are scheduled.


Healthcare systems can be changed for the better through a strategy that combines participation and creativity. But change cannot be sustained without vigilance and without analysis based on data. Herein lies the opportunity for the O.R. community. For instance, the O.R. community can work with hospital clinicians and administrators in these areas:

  • Process modeling to ascertain how patients are currently served, to determine where inefficiencies exist and to prioritize future changes. Process modeling can reveal unnecessary repetition, miscommunication, and inconsistency in methods.
  • Simulation modeling both to evaluate new processes and to understand and demonstrate the current causes of delay. For instance: simulating delays before and after, implementing a new appointment system, changing the methodology for assigning patients to beds, or implementing an electronic patient record system.
  • Optimization can be used in many aspects of system design, such as scheduling nurses, scheduling operating rooms or facility layout.
  • Queue analysis is invaluable when executed on a real-time basis to highlight the delays currently experienced throughout a hospital, and to make this information available to all key decision-makers, so that they can better understand delays both upstream and downstream, and act on these delays through reallocation of resources and appropriate prioritization of patients.

Future Challenges

The research challenge in patient flow goes back to the uniqueness of healthcare queues, namely understanding the human elements of the queueing system.

  • In some hospitals, the demand for patient care is perpetually larger than the capacity to serve patients. Unlike what theory may predict, queues do not grow without bound — instead, the system is brought to equilibrium by patients who leave without being seen.
  • The capacity and motivation to serve patients are greatly impeded when queues grow long, in the form of crowded waiting rooms, queues of patients waiting for placement to beds, and patients occupying beds while waiting for surgeries or tests. The performance of healthcare systems and its many actors (patients, nurses, doctors, administrators) under these stressed conditions is largely unknown and, for this reason, it can be extremely difficult to predict the effects of change.

Beyond these two examples, it is critical to create an environment whereby change is embraced throughout the organization and, in particular, to change the perspective from “how others are causing problems for my area”to “how I can make the entire system operate better.” The collaborative approach advocated by IHI is therefore essential.

The O.R. community can make a difference in the field of patient flow. This is not just a matter of improving efficiency. It is a case where our methods and talents can reduce suffering and save lives.

Randolph Hall is vice provost for research advancement at the University of Southern California and editor for “Patient Flow, Reducing Delay in Healthcare Delivery” (Springer, 2006).

The new queueing theory for healthcare

Reducing Delays Through Improved Surgical Scheduling

By Maged Dessouky, David Belson and Randolph Hall

Managing length of stay (LOS) is one of the most vexing challenges for any hospital. Though patients do need minimum stays for recovery and monitoring, LOS is sometimes too long because patients are forced to wait for surgeries. As a result, patients suffer and hospitals incur “denied days” – an insurer’s rejection of reimbursement because the stay is not medically necessary.

A research team at the University of Southern California, consisting of the authors and graduate students Pavankumar Murali and Bo Zhang, is addressing the LOS problem at the Los Angeles County General Hospital by targeting surgical scheduling and operations through process modeling, process improvement, optimization and simulation. We focus here on the last two steps: optimization and simulation. Operating rooms are a scarce resource that must be properly allocated among a set of specialties. Each surgical specialty (cardiac, ortho, neuro, etc.) wants its share of the available time. A common hospital surgery scheduling method is “block scheduling” where operating rooms are assigned weekly among each specialty and then the specialty selects among its patients to fill up its allotted block time. The planned weekly block times are a result of compromises among the competing demands.

A reduction of patient waiting times could be accomplished by accurately balancing the room allocation blocks with amount of demand for surgeries from each specialty. In the past, allocation decisions were the result of many factors. For example, since this is a teaching hospital, each specialty requested sufficient time to provide learning experiences for its medical students.

Surgery demand could be forecast based on the past frequency of surgeries by specialty. The average length of surgeries follows a consistent distribution. The surgeries within each specialty include inpatients who occupy a hospital bed until served, outpatients who are scheduled in advance and “red blanket” emergency patients who must be served immediately by preempting the existing schedule. All three of these subcategories follow a consistent pattern that we could use for allocating blocks.

Based on the demand pattern, we formulated a finite-horizon integer programming (IP) model that determines a weekly operating room allocation template that maximizes patient service. A number of patient type priorities (e.g., emergency over inpatient) and clinical constraints (e.g., minimum number of hours allocated to each specialty) are included in the formulation. The solution from the optimization model is entered into a computer simulation that captures the randomness of the processes (e.g., surgery time, demand, arrival time) and no-show rate of the outpatients) and non-linearties. Our models were created in conjunction with nurses, anesthesiologists and surgeons to assure the relevance of the system to their practice.

Results have been significant. The answers from our approach provide daily plans that reduce patient waiting and assure that the correct surgical team and surgery suite is available when needed.

Maged Dessouky is a professor and David Belson is a senior research associate and lecturer in the Daniel J. Epstein Department of Industrial and Systems Engineering in the Viterbi School of Engineering at the University of Southern California. Randolph Hall is vice provost for research advancement at USC.


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