Two‐tier healthcare service systems and cost of waiting for patients

Waiting has been a significant concern for healthcare services. We address this issue in the context of a two‐tier service system in this study. A two‐tier healthcare service system consists of two different service providers, typically one public service provider and one private service provider. In a baseline model, the two service providers are modeled by two queue servers, which charge each patient a common fixed fee for the service. Then, we study a queue model in which one service provider offers a subsidy or charges a premium while the other maintains the fixed service fee. This system provides a mechanism to segment patients along their waiting time cost through price discrimination. We analyze the problem from both the perspective of minimizing total waiting cost for all patients and the perspective of maximizing social gain for the public service provider or profit for the private service provider. We show that this model can significantly alleviate the burden of waiting for patients. The study addresses the design, the efficiency, and the implementation of two‐tier healthcare service systems. Copyright © 2017 John Wiley & Sons, Ltd.     

Differentiated waiting time management according to patient class in an emergency care center using an open Jackson network integrated with pooling and prioritizing

Unlike ordinary outpatient clinics, an emergency care center sees a variety of patients with diverse diseases and injuries of different levels of severity. Since patients who are in a critical condition face serious consequences, target waiting times must be determined based on patient acuity levels. To reflect the special situation in emergency care centers included in this study, patient flows are formulated using an open Jackson network with multiple patient classes. This paper is unique because of the integration of pooling and prioritizing patient classes with the open Jackson network. In particular, a hybrid priority model is presented in which a first-come-first-served discipline is applied in some processes and a priority discipline is applied in other processes in the open Jackson network, in order to minimize waiting times for patients with more urgent concerns. A case study based on actual data from an emergency care center demonstrates that the proposed model of pooling and prioritizing patient classes is effective in decreasing waiting times for higher-priority classes without substantially sacrificing those for lower-priority classes.     

Dynamic multi-priority,multi-class patient scheduling with stochastic service times

Efficient patient scheduling has significant operational, clinical and economical benefits on health care systems by not only increasing the timely access of patients to care but also reducing costs. However, patient scheduling is complex due to, among other aspects, the existence of multiple priority levels, the presence of multiple service requirements, and its stochastic nature. Patient appointment (allocation) scheduling refers to the assignment of specific appointment start times to a set of patients scheduled for a particular day while advance patient scheduling refers to the assignment of future appointment days to patients. These two problems have generally been addressed separately despite each being highly dependent on the form of the other. This paper develops a framework that incorporates stochastic service times into the advance scheduling problem as a first step towards bridging these two problems. In this way, we not only take into account the waiting time until the day of service but also the idle time/overtime of medical resources on the day of service. We first extend the current literature by providing theoretical and numerical results for the case with multi-class, multi-priority patients and deterministic service times. We then adapt the model to incorporate stochastic service times and perform a comprehensive numerical analysis on a number of scenarios, including a practical application. Results suggest that the advance scheduling policies based on deterministic service times cannot be easily improved upon by incorporating stochastic service times, a finding that has important implications for practice and future research on the combined problem.     

Waiting list behaviour and the consequences for NHS targets

The United Kingdom's National Health Service (NHS) is investing considerable resources in reducing patient waiting times for elective treatment. This paper describes the development of a waiting list model and its use in a simulation to assess management options. Simulation usually assumes that waiting is adequately described by simple queuing disciplines, typically first-in-first-out. However, waiting in the United Kingdom's NHS is a more complex phenomenon. The waiting list behaviour is explored through an analysis of the changes in waiting time distributions for elective orthopaedics in one Scottish Health Board, NHS Fife. The evolving distributions suggest that there have been substantial changes in priorities in response to the various NHS targets. However, in the short or medium term, the form of the distribution appears reasonably stable, providing a basis for estimating future waiting times in different scenarios. A model of the waiting behaviour and prioritization in the appointment allocations was embedded in a simulation of the complete elective orthopaedic patient journey from referral, through outpatients and diagnostics to surgery. The model has been used to explore the consequences of various management options in the context of the NHS target that no patient should wait more than 18 weeks between referral and treatment.     

Efficiency and welfare implications of managed public sector hospital waiting lists

A queuing model for public health service waiting lists is developed, and the implications for patient welfare of different systems for managing the waiting list are analysed. If patients are admitted to hospital on a first-come-first-served basis, a welfare gain is achieved by moving from a system of implicit to one of explicit rationing of access to the waiting list. If individual waiting times and hospital admissions are dependent on clinical priority, a further welfare gain is achievable without the use of explicit rationing, by reallocating the total waiting time from the more towards the less seriously ill. On efficiency and welfare criteria, a maximum waiting time guarantee does not appear to be a desirable development.     

Modelling toolkit to assist with introducing a stepped care system design in mental health care

We describe a modelling toolkit that was developed with the aim of assisting those responsible for introducing stepped care systems to local mental health services in the UK. The toolkit was pre-populated with real patient flow data collected from four sites that piloted the stepped care system design. Two analytical models were developed and coded as part of the toolkit to provide insights concerning workload, patient throughput, and changes in waiting times and waiting list size. An interface was built to allow users to specify their own stepped care system and input their own estimates or data of service demands and capacities at different steps. Despite the challenges and limitations, the use of modelling to inform the design of new service configurations is an important step in the right direction and we would recommend this as a reasonable way forward.     

Administrative days in acute care facilities: a queueing-analytic approach.

After acute care services are no longer required, a patient in an acute care hospital often must remain there while he or she awaits the provision of extended care services by a nursing home, through social support services, or by a home health care service. This waiting period is often referred to as "administrative days" because the time is spent in the acute facility not for medical reasons, but rather for administrative reasons. In this paper we use a queueing-analytic approach to describe the process by which patients await placement. We model the situation using a state-dependent placement rate for patients backed up in the acute care facility. We compare our model results with data collected from a convenience sample of 7 hospitals in New York State. We conclude with a discussion of the policy implications of our models.     

Introducing competition in healthcare services: The role of private care and increased patient mobility

We study the operational implications from competition in the provision of healthcare services, in the context of national public healthcare systems in Europe. Specifically, we study the potential impact of two alternative ways through which policy makers have introduced such competition: (i) via the introduction of private hospitals to operate alongside public hospitals and (ii) via the introduction of increased patient choice to grant European patients the freedom to choose the country they receive treatment at. We use a game-theoretic framework with a queueing component to capture the interactions among the patients, the hospitals and the healthcare funders. Specifically, we analyze two different sequential games and obtain closed form expressions for the patients’ waiting time and the funders’ reimbursement cost in equilibrium. We show that the presence of a private provider can be beneficial to the public system: the patients’ waiting time will decrease and the funders’ cost can decrease under certain conditions. Also, we show that the cross-border healthcare policy, which increases patient mobility, can also be beneficial to the public systems: when welfare requirements across countries are sufficiently close, all funders can reduce their costs without increasing the patients’ waiting time. Our analysis implies that in border regions, where the cost of crossing the border is low, “outsourcing” the high-cost country’s elective care services to the low-cost country is a viable strategy from which both countries’ systems can benefit.     

Simulation-based framework to improve patient experience in an emergency department

The global economic crisis has a significant impact on healthcare resource provision worldwide. The management of limited healthcare resources is further challenged by the high level of uncertainty in demand, which can lead to unbalanced utilization of the available resources and a potential deterioration of patient satisfaction in terms of longer waiting times and perceived reduced quality of services. Therefore, healthcare managers require timely and accurate tools to optimize resource utility in a complex and ever-changing patient care process. An interactive simulation-based decision support framework is presented in this paper for healthcare process improvement. Complexity and different levels of variability within the process are incorporated into the process modeling phase, followed by developing a simulation model to examine the impact of potential alternatives. As a performance management tool, balanced scorecard (BSC) is incorporated within the framework to support continual and sustainable improvement by using strategic-linked performance measures and actions. These actions are evaluated by the simulation model developed, whilst the trade-off between objectives, though somewhat conflicting, is analysed by a preference model. The preference model is designed in an interactive and iterative process considering decision makers preferences regarding the selected key performance indicators (KPIs). A detailed implementation of the framework is demonstrated on an emergency department (ED) of an adult teaching hospital in north Dublin, Ireland. The results show that the unblocking of ED outflows by in-patient bed management is more effective than increasing only the ED physical capacity or the ED workforce.     

A simulation study of scheduling clinic appointments in surgical care: individual surgeon <Emphasis Type="Italic">versus</Emphasis> pooled lists

The purpose of this paper is to compare two methods of scheduling outpatient clinic appointments in the setting where the availability of surgeons for appointments depends on other clinical activities. We used discrete-event simulation to evaluate the likely impact of the scheduling methods on the number of patients waiting for appointments, and the times to appointment and to surgery. The progression of individual patients in a surgical service was modelled as a series of updates in patient records in reaction to events generated by care delivery processes in an asynchronous fashion. We used the Statecharts visual formalism to define states and transitions within each care delivery process, based on detailed functional and behavioural specifications. Our results suggest that pooling referrals, so that clinic appointments are scheduled with the first available surgeon, has a differential impact on different segments of patient flow and across surgical priority groups.     

Optimal Sequencing of Servers in the Two-Station Series Queueing System

This paper deals with determining an optimal sequence of service stations in a series queueing system. Optimality is defined in terms of the total time spent waiting for service. Sequences are compared on the basis of the moments of their steady-state total waiting time. In addition, the rules of stochastic dominance are applied which allow comparison of sequences on the basis of their waiting time distributions. Analytical results in the sequencing of service stations in series queues have been limited to stations with constant or exponential service times. This study extends the investigation to service distributions with varying degrees of statistical regularity given by the family of Erlang distributions.Relationships are developed for predicting optimal sequences. Validation is accomplished by simulating a number of systems and comparing the waiting time distribution functions for each sequence. The relationships are shown to be good predictors and useful in the study and design of systems of servers in series.     

On a Queueing System with Various Input Sources and Phase Type Service

This paper develops the steady-state behaviour of a queueing model with K-parallel input sources, finite and infinite waiting space and feedback probabilities. The steady state of the system is derived through equations governing the model in terms of the traffic intensities. Probability distribution functions for the number of units waiting for service in each queue are obtained. The mean number of units in the system is also obtained. Finally, the model is generalized to increase the number of parallel servers in the final phase. Also the number of stages of service is increased in the first phase. The model is illustrated by suitable practical applications.     

Waiting times in a two-queue model with exhaustive and Bernoulli service

This paper deals with waiting times in a two-queue polling system in which one queue is served according to the Bernoulli service discipline and the other one attains exhaustive service. Exact results are derived for the LST's of the waiting time distributions via an iteration scheme. Based on those results the mean waiting times are expressed in the system parameters.     

Uniform pricing and subsidy coordination mechanism in a two-tier healthcare system under a co-payment policy

Recently, the lengthy waiting time in public hospitals (called the public system) under the free healthcare policy has become a serious problem. To address this issue, motivated by the Japanese healthcare system, this paper investigates a two-tier co-payment healthcare system under a uniform pricing and subsidy coordination mechanism. In such a setting, the public system and the private system (i.e., the private hospitals) compete for market share with different objectives, whereas the government uniformly sets the service price and the subsidy rate to maximize social welfare under a total budget constraint. Compared with two free healthcare policy cases implemented in the Canadian and Australian healthcare systems respectively in terms of social welfare, the results show that when the market demand (or the patient service quality sensitivity) is sufficiently high (sufficiently low), the uniform pricing and subsidy coordination mechanism is better and worse otherwise; and when the patient's waiting sensitivity (or the total government budget) is in an appropriate middle range (sufficiently low or high), the mechanism can outperform than the free policy cases.     

M/M/∞ Queues in series with non-homogeneous inputs

This paper studies the transient behaviour of tandem queueing system consisting of an arbitrary number r of queues in series with infinite server service facility at each queue. Poisson arrivals with time dependent parameter and exponential service times have been assumed. Infinite server queues realistically describe those queues in which sufficient service capacity exist to prevent virtually any waiting by the customer present. The model is suitable for both phase type service as well services in series. Very elegant solutions have been obtained and it has been shown that if the queue sizes are initially independent and Poisson then they remain independent and Poisson for all t.     

Stationary tail asymptotics of a tandem queue with feedback

Motivated by applications in manufacturing systems and computer networks, in this paper, we consider a tandem queue with feedback. In this model, the i.i.d. interarrival times and the i.i.d. service times are both exponential and independent. Upon completion of a service at the second station, the customer either leaves the system with probability p or goes back, together with all customers currently waiting in the second queue, to the first queue with probability 1−p. For any fixed number of customers in one queue (either queue 1 or queue 2), using newly developed methods we study properties of the exactly geometric tail asymptotics as the number of customers in the other queue increases to infinity. We hope that this work can serve as a demonstration of how to deal with a block generating function of GI/M/1 type, and an illustration of how the boundary behaviour can affect the tail decay rate.     

Developing a platform for comparison of hospital admission systems: An illustration

There is an increasing need to develop a platform for comparing hospital admission planning systems due to a shift in the service paradigm in the health sector. The current service concept of hospital admission planning aims at optimising the use of scarce hospital resources without paying much attention to the level of service offered to patients. As patients nowadays do not accept long waiting times for hospital admission, it becomes necessary to consider alternative admission service concepts. Waiting lists have also become a political issue, and alternative concepts have been advocated such as giving all patients an appointment for admission. A simulation model was built to examine the impacts of extreme admission service concepts in a simplified hospital setting. The alternative concepts considered are based on the ‘zero waiting time’ principle (immediate treatment), and the ‘booked admissions’ principle (using an appointment for admission). The results of these admission service concepts are compared with the results of the current concept, based on the ‘maximising resource use’ principle. The paper deals with the development of a framework and tool that allows evaluating different, somehow conflicting, hospital admission planning concepts and the usefulness of such framework and tool for more refined/real-life approaches to hospital admission planning.     

The costs and benefits of bowel cancer service developments using discrete event simulation

Colorectal cancer includes cancerous growths in the colon, rectum and appendix and affects around 30?000 people in England each year. Maximizing health benefits for patients with colorectal cancer requires consideration of costs and outcomes across the whole service. In an era of scarce healthcare resources, there is a need to consider not only whether technologies and services may be considered clinically effective, but also whether they are cost-effective, that is, whether they represent value for money for the health service. Through the development of a whole disease model, it is possible to evaluate the cost-effectiveness of a range of options for service development consistently within a common framework. Discrete event simulation has been used to model the complete colorectal cancer patient pathway from patient presentation through to referral and diagnosis, treatment, follow-up, potential recurrence, treatment of metastases and end-of-life care. This simulation model has been used to examine the potential cost-effectiveness of different options for change across the entire colorectal cancer pathway. This paper provides an empirical demonstration of the potential application of modelling entire disease areas to inform clinical policy and resource allocation decision-making.