×

zbMATH — the first resource for mathematics

On patient flow in hospitals: a data-based queueing-science perspective. (English) Zbl 1359.60116
Summary: Hospitals are complex systems with essential societal benefits and huge mounting costs. These costs are exacerbated by inefficiencies in hospital processes, which are often manifested by congestion and long delays in patient care. Thus, a queueing-network view of patient flow in hospitals is natural for studying and improving its performance. The goal of our research is to explore patient flow data through the lens of a queueing scientist. The means is exploratory data analysis (EDA) in a large Israeli hospital, which reveals important features that are not readily explainable by existing models. {
} Questions raised by our EDA include: Can a simple (parsimonious) queueing model usefully capture the complex operational reality of the Emergency Department (ED)? What time scales and operational regimes are relevant for modeling patient length of stay in the Internal Wards (IWs)? How do protocols of patient transfer between the ED and the IWs influence patient delay, workload division and fairness? EDA also underscores the importance of an integrative view of hospital units by, for example, relating ED bottlenecks to IW physician protocols. The significance of such questions and our related findings raise the need for novel queueing models and theory, which we present here as research opportunities. {
} Hospital data, and specifically patient flow data at the level of the individual patient, is increasingly collected but is typically confidential and/or proprietary. We have been fortunate to partner with a hospital that allowed us to open up its data for everyone to access. This enables reproducibility of our findings, through a user-friendly platform that is accessible via the Technion SEELab.

MSC:
60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
92C50 Medical applications (general)
PDF BibTeX XML Cite
Full Text: DOI Euclid
References:
[1] Aksin, O. Z., Karaesmen, F. and Ormeci, E. L. (2007). A Review of Workforce Cross-Training in Call Centers from an Operations Management Perspective. In Workforce Cross Training Handbook (D. Nembhard, ed.), CRC Press.
[2] Allon, G., Bassamboo, A. and Gurvich, I. (2011). “We Will Be Right with You”: Managing Customer Expectations with Vague Promises and Cheap Talk. Operations Research 59 1382-1394. · Zbl 1241.91032
[3] Armony, M. (2005). Dynamic Routing in Large-Scale Service Systems with Heterogeneous Servers. Queueing Systems 51 287-329. · Zbl 1094.60058
[4] Armony, M., Chan, C. W. and Zhu, B. (2013). Critical Care in Hospitals: When to Introduce a Step Down Unit? Working paper, Columbia University.
[5] Armony, M. and Ward, A. (2010). Fair Dynamic Routing in Large-Scale Heterogeneous-Server Systems. Operations Research 58 624-637. · Zbl 1231.90133
[6] Armony, M., Israelit, S., Mandelbaum, A., Marmor, Y. N., Tseytlin, Y. and Yom-Tov, G. B. (2015). On Patient Flow in Hospitals: A Data-Based Queueing-Science Perspective. An Extended Version (EV). Working paper, . · Zbl 1359.60116
[7] Atar, R., Mandelbaum, A. and Zviran, A. (2012). Control of Fork-Join Networks in Heavy Traffic. Allerton Conference.
[8] Atar, R. and Shwartz, A. (2008). Efficient Routing in Heavy Traffic under Partial Sampling of Service Times. Mathematics of Operations Research 33 899-909. · Zbl 1213.60066
[9] Balasubramanian, H., Muriel, A. and Wang, L. (2012). The Impact of Flexibility and Capacity Allocation on the Performance of Primary Care Practices. Flexible Services and Manufacturing Journal 24 422-447.
[10] Balasubramanian, H., Banerjee, R., Denton, B., Naessens, J., Wood, D. and Stahl, J. (2010). Improving Clinical Access and Continuity Using Physician Panel RSSedesign. Journal of General Internal Medicine 25 1109-1115.
[11] Barak-Corren, Y., Israelit, S. and Reis, B. Y. (2013). Progressive Prediction of Hospitalization in The Emergency Department: Uncovering Hidden Patterns to Improve Patient Flow. Working paper.
[12] Baron, O., Berman, O., Krass, D. and Wang, J. (2014). Using Strategic Idleness to Improve Customer Service Experience in Service Networks. Operations Research 62 123-140. · Zbl 1291.90062
[13] Batt, R. J. and Terwiesch, C. (2014). Doctors Under Load: An Empirical Study of State Dependent Service Times in Emergency Care. Working paper.
[14] Bekker, R. andde Bruin, A. M. (2010). Time-Dependent Analysis for Refused Admissions in Clinical Wards. Annals of Operations Research 178 45-65. · Zbl 1197.90089
[15] Bernstein, S. L., Verghese, V., Leung, W., Lunney, A. T. and Perez, I. (2003). Development and Validation of a New Index to Measure Emergency Department Crowding. Academic Emergency Medicine 10 938-942.
[16] Bertsimas, D. and Mourtzinou, G. (1997). Transient Laws of Non-stationary Queueing Systems and Their Applications. Queueing Systems 25 115-155. · Zbl 0894.60087
[17] Brandeau, M. L., Sainfort, F. and Pierskalla, W. P., eds. (2004). Operations Research and Health Care: A Handbook of Methods and Applications . Kluwer Academic Publishers, London. · Zbl 1050.90001
[18] Brown, L., Gans, N., Mandelbaum, A., Sakov, A., Shen, H., Zeltyn, S. and Zhao, L. (2005). Statistical Analysis of a Telephone Call Center: A Queueing-Science Perspective. Journal of the American Statistical Association 100 36-50. · Zbl 1117.62303
[19] Burnham, K. P. and Anderson, D. R. (2002). Model Selection and Multimodal Inference: A Practical Information-Theoretic Approach, 2nd Edition . Springer. · Zbl 1005.62007
[20] Canadadian-Triage Admission of Paitents to Over-Capacity Inpatient Beds. Appendix A, .
[21] Chalfin, D. B., Trzeciak, S., Likourezos, A., Baumann, B. M. and Dellinger, R. P. (2007). Impact of Delayed Transfer of Critically Ill Patients from the Emergency Department to the Intensive Care Unit. Critical Care Medicine 35 1477-1483.
[22] Chan, C., Farias, V. and Escobar, G. (2014). The Impact of Delays on Service Times in the Intensive Care Unit. Working paper.
[23] Chan, C., Yom-Tov, G. B. and Escobar, G. (2014). When to Use Speedup: An Examination of Service Systems with Returns. Operations Research 62 462-482. · Zbl 1304.90064
[24] Chao, X., Miyazawa, M. and Pinedo, M. (1999). Queueing Networks: Customers, Signals and Product Form Solutions . Wiley. · Zbl 0936.90010
[25] Chen, C., Jia, Z. and Varaiya, P. (2001). Causes and Cures of Highway Congestion. Control Systems, IEEE 21 26-33. · Zbl 1220.93026
[26] Chen, H. and Yao, D. D. (2001). Fundamentals of Queuing Networks: Performance, Asymptotics, and Optimization . Springer. · Zbl 0992.60003
[27] Cooper, A. B., Litvak, E., Long, M. C. and McManus, M. L. (2001). Emergency Department Diversion: Causes and Solutions. Academic Emergency Medicine 8 1108-1110.
[28] de Bruin, A. M., van Rossum, A. C., Visser, M. C. and Koole, G. M. (2007). Modeling the Emergency Cardiac In-Patient Flow: An Application of Queuing Theory. Health Care Management Science 10 125-137.
[29] de Bruin, A. M., Bekker, R., van Zanten, L. and Koole, G. M. (2009). Dimensioning Hospital Wards Using the Erlang Loss Model. Annals of Operations Research 178 23-43. · Zbl 1197.90092
[30] Denton, B. T., ed. (2013). Handbook of Healthcare Operations Management: Methods and Applications . Springer.
[31] Dong, J. and Whitt, W. (2014). On Fitted Birth-and-Death Queue Models. Working paper, Columbia University.
[32] Dong, J., Yom-Tov, E. and Yom-Tov, G. B. (2014). Hospital Network Synchronization Through Waiting Time Announcements. Working paper.
[33] Earnest, A., Chen, M. and Seow, E. (2006). Exploring if Day and Time of Admission is Associated with Average Length of Stay Among Inpatients from a Tertiary Hospital in Singapore: An Analytic Study Based on Routine Admission Data. BMC Health Services Research 6 6.
[34] Elkin, K. and Rozenberg, N. (2007). Patients Flow from the Emergency Department to the Internal Wards. IE&M project, Technion (In Hebrew).
[35] Feldman, Z., Mandelbaum, A., Massey, W. A. and Whitt, W. (2008). Staffing of Time-Varying Queues to Achieve Time-Stable Performance. Management Science 54 324-338. · Zbl 1232.90275
[36] Froehle, C. M. and Magazine, M. J. (2013). Improving Scheduling and Flow in Complex Outpatient Clinics. In Handbook of Healthcare Operations Management: Methods and Applications (B. T. Denton, ed.) 9, 229-307. Springer.
[37] Gans, N., Koole, G. and Mandelbaum, A. (2003). Telephone Call Centers: Tutorial, Review and Research Prospects. Manufactoring, Services and Operations Management 5 79-141.
[38] Gerla, M. and Kleinrock, L. (1980). Flow Control: A Comparative Survey. IEEE Transactions on Communcations 28 553-574.
[39] Gorman, A. and Colliver, V. (2014). The Latest In Medical Convenience: ER Appointments. Chronicle for Kaiser Health News . .
[40] Green, L. (2004). Capacity Planning and Management in Hospitals. In Operations Research and Health Care: A Handbook of Methods and Applications (M. L. Brandeau, F. Sainfort and W. P. Pierskalla, eds.) 14-41. Kluwer Academic Publishers, London.
[41] Green, L. V. (2008). Using Operations Research to Reduce Delays for Healthcare. In Tutorials in Operations Research (Z.-L. Chen and S. Raghavan, eds.) 1-16. INFORMS.
[42] Green, L. V., Kolesar, P. J. and Whitt, W. (2007). Coping with Time-Varying Demand When Setting Staffing Requirements for a Service System. Production and Operations Management 16 13-39.
[43] Green, L. and Yankovic, N. (2011). Identifying Good Nursing Levels: A Queuing Approach. Operations Research 59 942-955. · Zbl 1342.90085
[44] Green, L., Soares, J., Giglio, J. F. and Green, R. A. (2006). Using Queuing Theory to Increase the Effectiveness of Emergency Department Provider Staffing. Academic Emergency Medicine 13 61-68.
[45] Gurvich, I. and Perry, O. (2012). Overflow Networks: Approximations and Implications to Call-Center Outsourcing. Operations Research 60 996-1009. · Zbl 1260.90047
[46] Gurvich, I. and Whitt, W. (2010). Service-Level Differentiation in Many-Server Service Systems via Queue-Ratio Routing. Operations Research 58 316-328. · Zbl 1233.90116
[47] Hagtvedt, R., Ferguson, M., Griffin, P., Jones, G. T. and Keskinocak, P. (2009). Cooperative Strategies To Reduce Ambulance Diversion. Proceedings of the 2009 Winter Simulation Conference 266 1085-1090.
[48] Hall, R. W., ed. (2012). Handbook of Healthcare System Scheduling . Springer.
[49] Hall, R. W., ed. (2013). Patient Flow: Reducing Delay in Healthcare Delivery . Springer. 2nd edition.
[50] Hall, R., Belson, D., Murali, P. and Dessouky, M. (2006). Modeling Patient Flows Through the Healthcare System. In Patient Flow: Reducing Delay in Healthcare Delivery (R. W. Hall, ed.) 1, 1-45. Springer.
[51] Hoot, N. R., Zhou, C., Jones, I. and Aronsky, D. (2007). Measuring and Forecasting Emergency Department Crowding in Real Time. Annals of Emergency Medicine 49 747-755.
[52] Huang, J. (2013). Patient Flow Management in Emergency Departments. PhD thesis, National University of Singapore (NUS).
[53] Huang, J., Carmeli, B. and Mandelbaum, A. (2015). Control of Patient Flow in Emergency Departments: Multiclass Queues with Feedback and Deadlines. Forthcoming in Operations Research. · Zbl 1329.90038
[54] Hwang, U., McCarthy, M. L., Aronsky, D., Asplin, B., Crane, P. W., Craven, C. K., Epstein, S. K., Fee, C., Handel, D. A., Pines, J. M., Rathlev, N. K., Schafermeyer, R. W., Zwemer, F. L. and Bernstein, S. L. (2011). Measures of Crowding in the Emergency Department: A Systematic Review. Academic Emergency Medicine 18 527-538.
[55] Ibrahim, R. and Whitt, W. (2011). Wait-Time Predictors for Customer Service Systems with Time-Varying Demand and Capacity. Operations Research 59 1106-1118. · Zbl 1233.90117
[56] IHI (2011). Patient First: Efficient Patient Flow Management Impact on the ED. Institute for Healthcare Improvement . .
[57] Janssen, A. J. E. M., van Leeuwaarden, J. S. H. and Zwart, B. (2011). Refining Square-Root Safety Staffing by Expanding Erlang C. Operations Research 56 1512-1522. · Zbl 1242.90064
[58] JCAHO (2004). JCAHO Requirement: New Leadership Standard on Managing Patient Flow for Hospitals. Joint Commission Perspectives 24 13-14.
[59] Jennings, O. B. and de Véricourt, F. (2008). Dimensioning Large-Scale Membership Services. Operations Research 56 173-187. · Zbl 1167.90447
[60] Jennings, O. B. and de Véricourt, F. (2011). Nurse Staffing in Medical Units: A Queueing Perspective. Operations Research 59 1320-1331. · Zbl 1241.90032
[61] Jouini, O., Dallery, Y. and Aksin, O. Z. (2009). Queueing Models for Full-Flexible Multi-class Call Centers with Real-Time Anticipated Delays. International Journal of Production Economics 120 389-399.
[62] Kaplan, R. S. and Porter, M. E. (2011). How to Solve the Cost Crisis in Health Care. Harvard Business Review 89 46-64.
[63] Kc, D. and Terwiesch, C. (2009). Impact of Workload on Service Time and Patient Safety: An Econometric Analysis of Hospital Operations. Management Science 55 1486-1498.
[64] Kelly, F. P. (1979). Markov Processes and Reversibility . Wiley.
[65] Kim, S. H. and Whitt, W. (2014). Are Call Center and Hospital Arrivals Well Modeled by Nonhomogeneous Poisson Processes? M&SOM 16 464-480.
[66] Koçağa, Y. L., Armony, M. and Ward, A. R. (2015). Staffing Call Centers with Uncertain Arrival Rates and Co-sourcing. Production and Operations Management n/a-n/a.
[67] Leite, S. C. and Fragoso, M. D. (2013). Diffusion Approximation for Signaling Stochastic Networks. Stochastic Processes and their Applications 123 2957-2982. · Zbl 1298.60091
[68] Long, E. F. and Mathews, K. M. (2012). “Patients Without Patience”: A Priority Queuing Simulation Model of the Intensive Care Unit. Working paper.
[69] Maa, J. (2011). The Waits that Matter. The New England Journal of Medicine 364 2279-2281.
[70] Maman, S. (2009). Uncertainty in the Demand for Service: The Case of Call Centers and Emergency Departments. Master’s thesis, Technion-Israel Institute of Technolo- gy.
[71] Maman, S., Zeltyn, S. and Mandelbaum, A. (2011). Uncertainty in the Demand for Service: The Case of Call Centers and Emergency Departments. Working paper.
[72] Mandelbaum, A., Momcilovic, P. and Tseytlin, Y. (2012). On Fair Routing from Emergency Departments to Hospital Wards: QED Queues with Heterogeneous Servers. Management Science 58 1273-1291.
[73] Mandelbaum, A. and Stolyar, S. (2004). Scheduling Flexible Servers with Convex Delay Costs: Heavy-Traffic Optimality of the Generalized \(c\mu\)-Rule. Operations Research 52 836-855. · Zbl 1165.90402
[74] Mandelbaum, A., Trofimov, V., Gavako, I. and Nadjhahrov, E. (2013). HomeHospital (Rambam): Readmission Analysis. .
[75] Marmor, Y. N. (2003). Developing a Simulation Tool for Analyzing Emergency Department Performance. Master’s thesis, Technion-Israel Institute of Technology.
[76] Marmor, Y. N. (2010). Emergency-Departments Simulation in Support of Service-Engineering: Staffing, Design, and Real-Time Tracking. PhD thesis, Technion-Israel Institute of Technology.
[77] Marmor, Y. N., Golany, B., Israelit, S. and Mandelbaum, A. (2012). Designing Patient Flow in Emergency Departments. IIE Transactions on Healthcare Systems Engineering 2 233-247.
[78] Marmor, Y. N., Rohleder, T., Cook, D., Huschka, T. and Thompson, J. (2013). Recovery Bed Planning in Cardiovascular Surgery: A Simulation Case Study. Health Care Management Science 16 314-327.
[79] McHugh, M., Van Dyke, K., McClelland, M. and Moss, D. (2011). Improving Patient Flow and Reducing Emergency Department Crowding. Agency for Healthcare Research and Quality . .
[80] Nadjhahrov, E., Trofimov, V., Gavako, I. and Mandelbaum, A. (2013). HomeHospital (Rambam): EDA via SEEStat 3.0 to Reproduce “On Patients Flow in Hospitals”. .
[81] Nestler, S. (2011). Reproducible (Operations) Research: A Primer on Reproducible Research and Why the O.R. Community Should Care About it. ORMS Today 38 .
[82] Nguyen, V. (1994). The Trouble with Diversity: Fork-Join Networks with Heterogeneous Customer Population. The Annals of Applied Probability 1-25. · Zbl 0797.60078
[83] Plambeck, E., Bayati, M., Ang, E., Kwasnick, S. and Aratow, M. (2015). Accurate ED Wait Time Prediction. Working paper, Stanford.
[84] Plonski, O., Efrat, D., Dorban, A., David, N., Gologorsky, M., Zaied, I., Mandelbaum, A. and Rafaeli, A. (2013). Fairness in Patient Routing: Maternity Ward in Rambam Hospital. Technical report.
[85] Ramakrishnan, M., Sier, D. and Taylor, P. G. (2005). A Two-Time-Scale Model for Hospital Patient Flow. IMA Journal of Management Mathematics 16 197-215. · Zbl 1125.90318
[86] Rambam Rambam Health Care Campus, Haifa, Israel. .
[87] RambamData Rambam Hospital Data Repositories. Technion SEELab, .
[88] Saghafian, S., Austin, G. and Traub, S. J. (2014). Operations Research Contributions to Emergency Department Patient Flow Optimization: Review and Research Prospects. Working paper.
[89] SEELab SEE Lab, Technion-Israel Institute of Technology. .
[90] SEEServer Server of the Center for Service Enterprise Engineering. .
[91] SEEStat SEEStat Documentation, Technion-Israel Institute of Technology. .
[92] Senderovich, A., Weidlich, M., Gal, A. and Mandelbaum, A. (2015). Queue Mining for Delay Prediction in Multi-class Service Processes. Information Systems n/a-n/a.
[93] Shi, P., Dai, J. G., Ding, D., Ang, J., Chou, M., Jin, X. and Sim, J. (2013). Patient Flow from Emergency Department to Inpatient Wards: Empirical Observations from a Singaporean Hospital. Working paper.
[94] Shi, P., Chou, M. C., Dai, J. G., Ding, D. and Sim, J. (2014). Models and Insights for Hospital Inpatient Operations: Time-Dependent ED Boarding Time. Management Science 24 13-14.
[95] Song, H., Tucker, A. L. and Murrell, K. L. (2015). The Diseconomies of Queue Pooling: An Empirical Investigation of Emergency Department Length of Stay. Forthcoming in Management Science n/a-n/a.
[96] Stolyar, S. (2005). Optimal Routing in Output-Queued Flexible Server Systems. Probability in the Engineering and Informational Sciences 19 141-189. · Zbl 1071.60090
[97] Sullivan, S. E. and Baghat, R. S. (1992). Organizational Stress, Job Satisfaction, and Job Performance: Where Do We Go from Here? Journal of Management 18 353-375.
[98] Sun, J. (2006). The Statistical Analysis of Interval-Censored Failure Time Data . Springer. · Zbl 1127.62090
[99] HCA North Texas Hospitals are Moving at the Speed of Life-Real Time Delays Announcement Web-page of Emergency Departments in North Texas, USA. FASTERTX.COM, .
[100] Tezcan, T. (2008). Optimal Control of Distributed Parallel Server Systems Under the Halfin and Whitt Regime. Math of Operations Research 33 51-90. · Zbl 1160.90001
[101] Thompson, S., Nunez, M., Garfinkel, R. and Dean, M. D. (2009). Efficient Short-Term Allocation and Reallocation of Patients to Floors of a Hospital During Demand Surges. Operations Research 57 261-273. · Zbl 0273.90002
[102] Thorin, O. (1977). On the Infinite Divisibility of the Lognormal Distribution. Scandinavian Actuarial Journal 1977 121-148. · Zbl 0372.60020
[103] Tseytlin, Y. (2009). Queueing Systems with Heterogeneous Servers: On Fair Routing of Patients in Emergency Departments. Master’s thesis, Technion-Israel Institute of Technology.
[104] Tseytlin, Y. and Zviran, A. (2008). Simulation of Patients Routing from an Emergency Department to Internal Wards in Rambam Hospital. OR Graduate project, IE&M, Technion.
[105] Tukey, J. W. (1977). Exploratory Data Analysis . Addison Wesley. · Zbl 0409.62003
[106] Medicare USA (2013). Hospital Compare: 30-Day Death and Readmission Measures Data. .
[107] Ward, A. and Armony, M. (2013). Blind Fair Routing in Large-Scale Service Systems with Heterogeneous Customers and Servers. Operations Research 61 228-243. · Zbl 1267.90042
[108] Whitt, W. (2012). Fitting Birth-and-Death Queueing Models to Data. Statistics and Probability Letters 82 998-1004. · Zbl 1241.62134
[109] Yom-Tov, G. B. (2010). Queues in Hospitals: Queueing Networks with ReEntering Customers in the QED Regime. PhD thesis, Technion-Israel Institute of Technology.
[110] Yom-Tov, G. B. and Mandelbaum, A. (2014). Erlang-R: A Time-Varying Queue with Reentrant Customers, in Support of Healthcare Staffing. M&SOM 16 283-299.
[111] Zacharias, C. and Armony, M. (2013). Joint Panel Sizing and Appointment Scheduling in Outpatient Care. Working paper, NYU.
[112] Zaied, I. (2011). The Offered Load in Fork-Join Networks: Calculations and Applications to Service Engineering of Emergency Department. Master’s thesis, Technion-Israel Institute of Technology.
[113] Zeltyn, S., Marmor, Y. N., Mandelbaum, A., Carmeli, B., Greenshpan, O., Mesika, Y., Wasserkrug, S., Vortman, P., Schwartz, D., Moskovitch, K., Tzafrir, S., Basis, F., Shtub, A. and Lauterman, T. (2011). Simulation-Based Models of Emergency Departments: Real-Time Control, Operations Planning and Scenario Analysis. Transactions on Modeling and Computer Simulation (TOMACS) 21 .
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.