Use of Queuing Models in Health Care - PPT

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1 University of Wisconsin-Madison From the SelectedWorks of Vikas Singh December, 2006 Use of Queuing Models in Health Care - PPT Vikas Singh, University of Arkansas for Medical Sciences Available at:

2 Queuing Theory Vikas Singh 12/6/06

3 Queuing Theory.. Is the mathematical approach to the analysis of waiting lines in healthcare settings Most of healthcare systems have excess capacity to accommodate random variations, so queuing analysis can be used as: Short term measure, or For facilities and resource planning

4 Uses of Queuing analysis and simulation in healthcare Walk in patients in clinics Emergency room arrivals Phone calls from physician offices to HMO Outpatient clinics and outpatient surgeries Physician offices Pharmacy Inventory Control Healthcare resource and infrastructure planning for disaster management Public health, etc..

5 Rationale for use of Queuing Theory in Healthcare Variability in arrival pattern of patients Variability in type and level of service needed Variability in service rate To minimize total costs

6 Costs of waiting lines or queue Cost associated with patients having to wait for service Loss of business to HCO Costs incurred by society Decreased patient satisfaction

7 Costs of waiting lines or queue Capacity costs: costs of maintaining the ability to provide service Salaries paid to employees/servers while they wait for service from other server Fixed costs - Cost of waiting space, facility, equipment and supplies

8 Health Care Service Capacity and Costs Cost Total expected cost Minimum total cost Cost of providing service Low level of service Optimal service level Negative Cost of waiting time to company High level of service

9 Queuing System Characteristics Population Source: Infinite Source Finite Source Number of Servers: Capacity of each server (channel) Number of servers

10 Queuing System Characteristics Arrival Pattern: Poisson distribution or negative exponential distribution Service Patterns: service time and rate Queue Discipline: first come first serve, urgency, appointment, etc..

11 Types of queuing systems It can be single line-single phase single line-multiple phase multiple line-single phase or multiple line-multiple phase service

12 Arrivals Single line, single phase system Queue NP Served units Ships at sea Ship unloading system Waiting ship line Dock Empty ships

13 Arrivals Single-line, multi-phase system Queue Registrati on Physician office Served units Cars in area McDonald s drive-through Waiting cars Pay Pick-up

14 Arrivals Multi-line, single phase system Queue Pharmac y Served units Pharmac y Example: Patients waiting in queue at pharmacy store or hospital pharmacy

15 Arrivals Multi-line, multi-phase system Queue FO Staff FO Staff Specialist Or Unit Specialist Or Unit Served units Example: multi-specialty, outpatient clinic of a hospital

16 Measures of Queuing System Performance Average number of patients waiting (in queue or in system) Average waiting time Capacity utilization Cost of given level of capacity Probability that an arriving patient will have to wait and for how long

17 Diabetes Kiosk Example Single server: arrival rate 4 pts/hr Service rate 5pts/hr Multiple server: arrival rate 9 pts/hr service rate 5pts/hr operational cost-$40/hr waiting cost -$75/hr

18 Diabetes Kiosk Example

19 Diabetes Kiosk Example Diabetes Kiosk s Solution Number of servers Total cost based on waiting Total cost based on system 1 (insufficient capacity) n.a. n.a

20 Diabetes Kiosk Example Performance measure 2 stations 3 stations 4 stations Pt. arrival rate Service rate Overall system utilization 90% 60% 45% L (system) Lq W (system) - in hours Wq - in hours Po (idle) 5.30% 14.60% 16.20% Pw (busy) 85.30% 35.50% 12.80% Total system cost in $ per hour

21 Limitations: Takes average of all variables Based on assumption that service time is known Service times are independent from one another Service rate is known Service rate is greater than arrival rate Arrivals are served on first come first serve basis Service times are described by the negative exponential probability distribution Used for short term phenomenon and is deterministic

22 Questions?

Textbook: pp Chapter 12: Waiting Lines and Queuing Theory Models

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