Fluid approximations and control of queues in emergency departments

Niyirora, Jerome; Zhuang, Jun

doi:10.1016/j.ejor.2017.03.013

Cited by 13 publications

(4 citation statements)

References 74 publications

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“…In the queueing literature, overflow policies have been widely studied. The most simple overflow strategy is to reject or outsource (in the context of call centers) some customers at arrival from a single queue (Ku and Jordan 2003, Maglaras and Van Mieghem 2005, Ward and Kumar 2008, Xu 2015, Niyirora and Zhuang 2017. These papers study the relation between the wait and the rejection flow.…”

Section: Literature Reviewmentioning

confidence: 99%

Performance Evaluation of Stochastic Systems with Dedicated Delivery Bays and General On-Street Parking

Abhishek

Legros

Fransoo

2021

Transportation Science

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As freight deliveries in cities increase due to retail fragmentation and e-commerce, parking is becoming a more and more relevant part of transportation. In fact, many freight vehicles in cities spend more time parked than they are moving. Moreover, part of the public parking space is shared with passenger vehicles, especially cars. Both arrival processes and parking and delivery processes are stochastic in nature. In order to develop a framework for analysis, we propose a queueing model for an urban parking system consisting of delivery bays and general on-street parking spaces. Freight vehicles may park both in the dedicated bays and in general on-street parking, whereas passenger vehicles only make use of general on-street parking. Our model allows us to create parsimonious insights into the behavior of a delivery bay parking stretch as part of a limited length of curbside. We are able to find explicit expressions for the relevant performance measures, and formally prove a number of monotonicity results. We further conduct a series of numerical experiments to show more intricate properties that cannot be shown analytically. The model helps us shed light onto the effects of allocating scarce urban curb space to dedicated unloading bays at the expense of general on-street parking. In particular, we show that allocating more space to dedicated delivery bays can also make passenger cars better off.

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Section: Literature Reviewmentioning

confidence: 99%

Performance Evaluation of Stochastic Systems with Dedicated Delivery Bays and General On-Street Parking

Abhishek

Legros

Fransoo

2021

Transportation Science

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“…The existing rare works lack the attempts to recognize one essential common feature of enzyme and server: they both interact with the input being transformed to form a short-lived intermediate that subsequently releases the output. For example, Niyirora and Zhuang [28] do introduce the transient server-patient complex in their continuous model of queue in an emergency department, but do not compare time dynamics of the servers with that of the patients whatsoever. However, the coexistence of strongly varying timescales in the process of conversion may have important implications as is known from biochemistry.…”

Section: Customermentioning

confidence: 99%

“…where overdots mean differentiation with respect to time t. All parameters in the model are nonnegative. (Notice that the model suggested in [28] is a special case of the system (2.1) with k −1 = k 3 = k 5 = 0.) Adding equations (2.1c) and (2.1d) reveals a conserved quantity u 0 , the total number of servers, free and busy:…”

Section: The Modelmentioning

confidence: 99%

“…The rapid development of the service sector in many economies has stimulated a renewed interest in multi-server queueing models. These models are particularly important in large-scale service systems, such as customer contact centers and health-care centers [4,28,35,36]. Operations research, of which queueing theory is a branch, treats act of service and production (manufacturing) uniformly, from cybernetics perspective, as a kind of an input-output transformation process going on in an imaginary converter box [8]:…”

Section: Introductionmentioning

confidence: 99%

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A Biologically Inspired Fluid Model of the Cyclic Service System

Kantarbayeva

Mustafin

2020

Mathematical Modelling and Analysis

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A deterministic ﬂuid model in the form of nonlinear ordinary diﬀerential equations is developed to provide the description for a multichannel service system with service-in-random-order queue discipline, abandonment and re-entry, where servers are treated like enzyme molecules. The parametric analysis of the model’s ﬁxed point is given, particularly, how the arrival rate of new customers aﬀects the steady-state demand. It is also shown that the model implies a saturating clearing function (yield vs. demand) of the Karmarkar type providing the mean service time is much shorter than the characteristic waiting time.

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A proactive transfer policy for critical patient flow management

González

Ferrer

Cataldo

et al. 2018

Health Care Manag Sci

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Hospital emergency departments are often overcrowded, resulting in long wait times and a public perception of poor attention. Delays in transferring patients needing further treatment increases emergency department congestion, has negative impacts on their health and may increase their mortality rates. A model built around a Markov decision process is proposed to improve the efficiency of patient flows between the emergency department and other hospital units. With each day divided into time periods, the formulation estimates bed demand for the next period as the basis for determining a proactive rather than reactive transfer decision policy. Due to the high dimensionality of the optimization problem involved, an approximate dynamic programming approach is used to derive an approximation of the optimal decision policy, which indicates that a certain number of beds should be kept free in the different units as a function of the next period demand estimate. Testing the model on two instances of different sizes demonstrates that the optimal number of patient transfers between units changes when the emergency patient arrival rate for transfer to other units changes at a single unit, but remains stable if the change is proportionally the same for all units. In a simulation using real data for a hospital in Chile, significant improvements are achieved by the model in key emergency department performance indicators such as patient wait times (reduction higher than 50%), patient capacity (21% increase) and queue abandonment (from 7% down to less than 1%).

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Fluid approximations and control of queues in emergency departments

Cited by 13 publications

References 74 publications

Performance Evaluation of Stochastic Systems with Dedicated Delivery Bays and General On-Street Parking

Performance Evaluation of Stochastic Systems with Dedicated Delivery Bays and General On-Street Parking

A Biologically Inspired Fluid Model of the Cyclic Service System

A proactive transfer policy for critical patient flow management

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