Slack Is Needed to Solve the Shortage of Nurses.

Healthcare systems are facing a shortage of nurses. This article identifies some of the major causes of this and the issues that need to be solved. We take a perspective derived from queuing theory: the patient-nurse relationship is characterized by a scarcity of time and resources, requiring comprehensive coordination at all levels. For coordination, we take an information-theoretic perspective. Using both perspectives, we analyze the nature of healthcare services and show that ensuring slack, meaning a less than exhaustive use of human resources, is a sine qua non to having a good, functioning healthcare system. We analyze what coordination efforts are needed to manage relatively simple office hours, wards, and home care. Next, we address the level of care where providers cannot themselves prevent the complexity of organization that possibly damages care tasks and job quality. A lack of job quality may result in nurses leaving the profession. Job quality, in this context, depends on the ability of nurses to coordinate their activities. This requires slack resources. The availability of slack that is efficient depends on a stable inflow and retention rate of nurses. The healthcare system as a whole should ensure that the required nurse workforce will be able to coordinate and execute their tasks. Above that, workforce policies need more stability.

Determination of server location in emergency care systems: an index proposal using data envelopment analysis and the hypercube queuing model.

The objective of this article is to propose a new composite index (CI) that helps to determine the most effective location of servers in an Emergency Care System (ECS), using Benefit of the Doubt (BoD)/Data Envelopment Analysis (DEA) and the Hypercube queuing model. The CI proposed was developed in four stages: (1) definition of a number of possible ECS configurations through the application of mathematical partitions and permutations; (2) application of the hypercube queuing model to determine performance parameters for each ECS configuration; (3) application of DEA/BoD to build the CI and generate performance rankings, and (4) evaluation of the rankings obtained to define the best configuration for the ECS analyzed. Data from two real cases from Brazil were used to assess the CI proposal. The results obtained confirm that: (a) the hypercube model could, relatively quickly, determine the configuration parameters generated; (b) the application of an appropriate DEA/BoD model enabled the different configurations to be ranked with good discrimination; (c) a pattern in the relationship between ambulance concentration and configuration effectiveness could be identified; and (d) the CI proposed would benefit ECS managers who are making resource location decisions.

Addressing the Knowledge Deficit in Hospital Bed Planning and Defining an Optimum Region for the Number of Different Types of Hospital Beds in an Effective Health Care System.

Based upon 30-years of research by the author, a new approach to hospital bed planning and international benchmarking is proposed. The number of hospital beds per 1000 people is commonly used to compare international bed numbers. This method is flawed because it does not consider population age structure or the effect of nearness-to-death on hospital utilization. Deaths are also serving as a proxy for wider bed demand arising from undetected outbreaks of 3000 species of human pathogens. To remedy this problem, a new approach to bed modeling has been developed that plots beds per 1000 deaths against deaths per 1000 population. Lines of equivalence can be drawn on the plot to delineate countries with a higher or lower bed supply. This method is extended to attempt to define the optimum region for bed supply in an effective health care system. England is used as an example of a health system descending into operational chaos due to too few beds and manpower. The former Soviet bloc countries represent a health system overly dependent on hospital beds. Several countries also show evidence of overutilization of hospital beds. The new method is used to define a potential range for bed supply and manpower where the most effective health systems currently reside. The method is applied to total curative beds, medical beds, psychiatric beds, critical care, geriatric care, etc., and can also be used to compare different types of healthcare staff, i.e., nurses, physicians, and surgeons. Issues surrounding the optimum hospital size and the optimum average occupancy will also be discussed. The role of poor policy in the English NHS is used to show how the NHS has been led into a bed crisis. The method is also extended beyond international benchmarking to illustrate how it can be applied at a local or regional level in the process of long-term bed planning. Issues regarding the volatility in hospital admissions are also addressed to explain the need for surge capacity and why an adequate average bed occupancy margin is required for an optimally functioning hospital.

A novel queue-based stochastic epidemic model with adaptive stabilising control.

The main objective of this paper is to propose a novel SEIR stochastic epidemic model. A distinguishing feature of this new model is that it allows us to consider a setup under general latency and infectious period distributions. To some extent, queuing systems with infinitely many servers and a Markov chain with time-varying transition rate comprise the very technical underpinning of the paper. Although more general, the Markov chain is as tractable as previous models for exponentially distributed latency and infection periods. It is also significantly more straightforward and tractable than semi-Markov models with a similar level of generality. Based on stochastic stability, we derive a sufficient condition for a shrinking epidemic regarding the queuing system's occupation rate that drives the dynamics. Relying on this condition, we propose a class of ad-hoc stabilising mitigation strategies that seek to keep a balanced occupation rate after a prescribed mitigation-free period. We validate the approach in the light of the COVID-19 epidemic in England and in the state of Amazonas, Brazil, and assess the effect of different stabilising strategies in the latter setting. Results suggest that the proposed approach can curb the epidemic with various occupation rate levels if the mitigation is timely.

Impact of application of queuing theory on operational efficiency of patient registration.

Background: Hospital administrators are often challenged with overcrowding at hospitals. The study hospital receives referred patients; however, they have to wait in long queues even for getting registered. This was a cause of concern for hospital administrators. The study was undertaken to find an amicable solution to the queues at registration using Queuing Theory. Method: This observational and interventional study was carried out in a tertiary care ophthalmic hospital. In the first phase, data of service time and arrival rate was collected. The queuing model was built using the coefficient of variation (CoV) of the observed times. Server utilization for new patient registration was found to be 1.21 and was 0.63 for revisit patients. Scenario-based simulation carried out using free software for optimal utilization of both types of servers. Recommendations made to combine the registration process and to increase one server were implemented.In the second phase, after one year, patient registration data were collected and compared for the number of patients registered using SPSS 17. Results: Number of patients registered within the registration timings increased whereas the number of patients registered after the registration timings decreased significantly at 95% CI with a p-value of less than 0.001. Queues finished early and more number of patients were registered in the same time. Conclusion: Using queuing theory, the bottleneck of the systems can be identified. Scenario and software-based simulations provide solutions to the problem of queues. The study is an application of Queuing Theory with a focus on efficient resource utilization. It can be replicated in an organization with limited resources facing the challenge of queues.

Scientific planning of urban cordon sanitaire for desired queuing time.

The outbreak of the COVID-19 pandemic disrupted ofur normal life. Many cities enforced a cordon sanitaire as a countermeasure to protect densely inhabited areas. Travelers can only cross the cordon after being checked. To minimize the waiting time in the queue, this paper proposes a method to determine the scientific planning of urban cordon sanitaire for desired queuing time, which is a significant problem that has not been explored. A novel two-stage optimization model is proposed where the first stage is the transportation system equilibrium problem to predict traffic inflow, and the second stage is the queuing network design problem to determine the allocation of test stations. This method aims to minimize the total health infrastructure investment for the desired maximum queuing time. Note that queuing theory is used to represent the queuing phenomenon at each urban entrance. A heuristic algorithm is designed to solve the proposed model where the Method of Successive Averages (MSA) is adopted for the first stage, and the Genetic Algorithm (GA) with elite strategy is adopted for the second stage. An experimental study with sensitivity analysis is conducted to demonstrate the effectiveness of the proposed methods. The results show that the methods can find a good heuristic optimal solution. This research is helpful for policymakers to determine the optimal investment and planning of cordon sanitaire for disease prevention and control, as well as other criminal activities such as drunk driving, terrorists, and smuggling.

Data Freshness and End-to-End Delay in Cross-Layer Two-Tier Linear IoT Networks.

The operational and technological structures of radio access networks have undergone tremendous changes in recent years. A displacement of priority from capacity-coverage optimization (to ensure data freshness) has emerged. Multiple radio access technology (multi-RAT) is a solution that addresses the exponential growth of traffic demands, providing degrees of freedom in meeting various performance goals, including energy efficiencies in IoT networks. The purpose of the present study was to investigate the possibility of leveraging multi-RAT to reduce each user's transmission delay while preserving the requisite quality of service (QoS) and maintaining the freshness of the received information via the age of information (AoI) metric. First, we investigated the coordination between a multi-hop network and a cellular network. Each IoT device served as an information source that generated packets (transmitting them toward the base station) and a relay (for packets generated upstream). We created a queuing system that included the network and MAC layers. We propose a framework comprised of various models and tools for forecasting network performances in terms of the end-to-end delay of ongoing flows and AoI. Finally, to highlight the benefits of our framework, we performed comprehensive simulations. In discussing these numerical results, insights regarding various aspects and metrics (parameter tuning, expected QoS, and performance) are made apparent.

An intelligent spatial stream processing framework for digital forensics amid the COVID-19 outbreak.

In recent times, several strategies to minimize the spread of 2019 novel coronavirus disease (COVID-19) have been adopted. Some recent technological breakthroughs like the drone-based tracking systems have focused on devising specific dynamical approaches for administering public mobility and providing early detection of symptomatic patients. In this paper, a smart real-time image processing framework converged with a non-contact thermal temperature screening module was implemented. The proposed framework comprised of three modules v i z . , smart temperature screening system, tracking infection footprint, and monitoring social distancing policies. This was accomplished by employing Histogram of Oriented Gradients (HOG) transformation to identify infection hotspots. Further, Haar Cascade and local binary pattern histogram (LBPH) algorithms were used for real-time facial recognition and enforcing social distancing policies. In order to manage the redundant video frames generated at the local computing device, two holistic models, namely, event-triggered video framing (ETVF) and real-time video framing (RTVF) have been deduced, and their respective processing costs were studied for different arrival rates of the video frame. It was observed that the proposed ETVF approach outperforms the performance of RTVF by providing optimal processing costs resulting from the elimination of redundant data frames. Results corresponding to autocorrelation analysis have been presented for the case study of India pertaining to the number of confirmed COVID-19 cases, recovered cases, and deaths to obtain an understanding of epidemiological spread of the virus. Further, choropleth analysis was performed for indicating the magnitude of COVID-19 spread corresponding to different regions in India.

The injury severity score: an operations perspective.

BACKGROUND: The statistical evaluation of aggregation functions for trauma grades, such as the Injury Severity Score (ISS), is largely based on measurements of their Pearson product-moment correlation with mortality. However, correlation analysis makes assumptions about the nature of the involved random variables (cardinality) and their relationship (linearity) that may not be applicable to ordinal scores such as the ISS. Moreover, using correlation as a sole evaluation criterion neglects the dynamic properties of these aggregation functions scores. METHODS: We analyze the domain and ordinal properties of the ISS comparatively to arbitrary linear and cubic aggregation functions. Moreover, we investigate the axiomatic properties of the ISS as a multicriteria aggregation procedure. Finally, we use a queuing simulation with various empirical distributions of Abbreviated Injury Scale (AIS) grades reported in the literature, to evaluate the queuing performance of the three aggregation functions. RESULTS: We show that the assumptions required for the computation of Pearson's product-moment correlation coefficients are not applicable to the analysis of the association between the ISS and mortality. We suggest the use of Mutual Information, a information-theoretic statistic that is able to assess general dependence rather than a specialized, linear view based on curve-fitting. Using this metric on the same data set as the seminal study that introduced the ISS, we show that the sum of cubes conveys more information on mortality than the ISS. Moreover, we highlight some unintended, undesirable axiomatic properties of the ISS that can lead to bias in its use as a patient triage criterion. Lastly, our queuing simulation highlights the sensitivity of the queuing performance of different aggregation procedures to the underlying distribution of AIS grades among patients. CONCLUSIONS: Viewing the ISS, and other possible aggregation functions for multiple AIS scores, as mere operational indicators of the priority of care, rather than cardinal measures of the response of the human body to multiple injuries (as was conjectured in the seminal study introducing the ISS) offers a perspective for their construction and evaluation on more robust grounds than the correlation coefficient. In this regard, Mutual Information appears as a more appropriate measure for the study of the association between injury severity and mortality, and queuing simulations as an actionable way to adapt the choice of an aggregation function to the underlying distribution of AIS scores.

Throughput Analysis of an Amazon Go Retail under the COVID-19-related Capacity Constraints.

The throughput of a finite-capacity queueing system is the mean number of clients served during a time interval. The COVID-19 outbreak has posed a serious challenge for many commercial establishments, including the retails, which have struggled to adapt to new working dynamics. Retails have been forced to adjust their service guidelines to comply with biosecurity protocols, ensuring to observe governmental and public health policies. A significant change for the retail market has been the capacity restrictions to ensure social distancing, i.e., a limitation on the number of customers simultaneously shopping in the store. Such a constraint has an impact on the throughput that can be achieved by a retail. This article assesses the impact of the capacity restriction measures on an Amazon Go-like retail performance through a throughput analysis under COVID-19-related capacity restrictions. For the assessment, we first retrieved real data from a retail located in Cartagena, Colombia. Two scenarios were considered: i) low demand and ii) high demand. Further, we built an Amazon Go-like, two-queue, M/M/c/K retail model with a CONWIP (Constant Work-In-Process) approach, considering biosecurity-based capacity restrictions due to the COVID-19 pandemic. The R package 'queueing' was used to set up the model, and an algorithm was created to go over each sampling period and find the hourly optimum capacity and throughput under the dynamic conditions of both scenarios (low and high demand). Results from the performance analysis show that, for some operational conditions, the optimum maximum throughput is achieved with capacities below the biosecurity-based capacity, while for some other operational conditions the maximum throughput cannot be achieved with the restrictions, as the optimum capacity lies beyond the biosecurity-based capacity. These results suggest that the maximum capacity definition should not be static. Instead, it should be done considering the retail's dimensions, the biosecurity policies, and the dynamic retail's operational conditions such as the demand and service capacity.

ESCOVE: Energy-SLA-Aware Edge-Cloud Computation Offloading in Vehicular Networks.

The vehicular network is an emerging technology in the Intelligent Smart Transportation era. The network provides mechanisms for running different applications, such as accident prevention, publishing and consuming services, and traffic flow management. In such scenarios, edge and cloud computing come into the picture to offload computation from vehicles that have limited processing capabilities. Optimizing the energy consumption of the edge and cloud servers becomes crucial. However, existing research efforts focus on either vehicle or edge energy optimization, and do not account for vehicular applications' quality of services. In this paper, we address this void by proposing a novel offloading algorithm, ESCOVE, which optimizes the energy of the edge-cloud computing platform. The proposed algorithm respects the Service level agreement (SLA) in terms of latency, processing and total execution times. The experimental results show that ESCOVE is a promising approach in energy savings while preserving SLAs compared to the state-of-the-art approach.

Research on Self-Balancing System of Autonomous Vehicles Based on Queuing Theory.

In order to explore the changes that autonomous vehicles on the road would bring to the current traffic and make full use of the intelligent features of autonomous vehicles, the article defines a self-balancing system of autonomous vehicles. Based on queuing theory and stochastic process, the self-balancing system model with self-balancing characteristics is established to balance the utilization rate of autonomous vehicles under the conditions of ensuring demand and avoiding an uneven distribution of vehicle resources in the road network. The performance indicators of the system are calculated by the MVA (Mean Value Analysis) method. The analysis results show that the self-balancing process could reduce the average waiting time of customers significantly in the system, alleviate the service pressure while ensuring travel demand, fundamentally solve the phenomenon of concentrated idleness after the use of vehicles in the current traffic, maximize the use of the mobile vehicles in the system, and realize the self-balancing of the traffic network while reducing environmental pollution and saving energy.

Size-Based Routing Policies: Non-Asymptotic Analysis and Design of Decentralized Systems.

Size-based routing policies are known to perform well when the variance of the distribution of the job size is very high. We consider two size-based policies in this paper: Task Assignment with Guessing Size (TAGS) and Size Interval Task Assignment (SITA). The latter assumes that the size of jobs is known, whereas the former does not. Recently, it has been shown by our previous work that when the ratio of the largest to shortest job tends to infinity and the system load is fixed and low, the average waiting time of SITA is, at most, two times less than that of TAGS. In this article, we first analyze the ratio between the mean waiting time of TAGS and the mean waiting time of SITA in a non-asymptotic regime, and we show that for two servers, and when the job size distribution is Bounded Pareto with parameter α=1, this ratio is unbounded from above. We then consider a system with an arbitrary number of servers and we compare the mean waiting time of TAGS with that of Size Interval Task Assignment with Equal load (SITA-E), which is a SITA policy where the load of all the servers are equal. We show that in the light traffic regime, the performance ratio under consideration is unbounded from above when (i) the job size distribution is Bounded Pareto with parameter α=1 and an arbitrary number of servers as well as (ii) for Bounded Pareto distributed job sizes with α∈(0,2)\{1} and the number of servers tends to infinity. Finally, we use the result of our previous work to show how to design decentralized systems with quality of service constraints.

[Bed capacity analysis for an intensive care unit : Retrospective analysis and projection for need of intensive care beds in over 65 year olds with selected cardiovascular diseases]. / Bettenkapazitätsanalyse für eine internistische Intensivstation : Retrospektive Analyse und Projektion des Intensivbettenbedarfs bei über 65-Jährigen mit ausgewählten kardiovaskulären Erkrankungen.

BACKGROUND: The increasing number of elderly individuals in the population and the simultaneous increase of the intensive care demand emphasizes the relevance of an efficient bed capacity analysis. Particularly, cardiovascular diseases represent a frequently occurring disease in the population group over 65 years of age. The objective of the following paper is the analysis of the retrospective and prospective intensive care demand by patients over 65 years with 6 selected (cardiovascular) codes of the International Statistical Classification of Diseases and Related Health Problems (ICD-10). METHODS: For the retrospective analysis, data from 2015-2017 were analyzed applying descriptive and bivariate methods. The analysis of the intensive care bed demand was based on the queuing theory. RESULTS: The monthly capacity utilization rates were constantly higher than the target capacity utilization rate of a maximum of 80% and in some cases even higher than 100%. In particular, the demand of patients with I50.14 was very high throughout the entire hospital. The bed demand analysis shows an increase from 9 needed beds in 2017 to 11 beds by 2030 for the 6 diagnosis groups. Regarding the 5 diagnosis groups without I50.14, only approximately half of the required beds were needed, retrospectively and in future. CONCLUSION: The effect of demographic change on the intensive care demand already exists, and a continuing, prospective increase of the demand is expected. The results underline the need of effective and demand-oriented intensive care capacity planning. However, prior to expanding bed capacities, the analysis of admission criteria of intensive care unit patients is necessary to reserve capacities primarily for patients with real intensive care needs.

Modeling of an immune response: Queuing network analysis of the impact of zinc and cadmium on macrophage activation.

Chronic obstructive pulmonary disease is characterized by progressive, irreversible airflow obstruction resulting from an abnormal inflammatory response to noxious gases and particles. Alveolar macrophages rely on the transcription factors, nuclear factor κB and mitogen-activated protein kinase, among others, to facilitate the production of inflammatory mediators designed to help rid the lung of foreign pathogens and noxious stimuli. Building a kinetic model using queuing networks, provides a quantitative approach incorporating an initial number of individual molecules along with rates of the reactions in any given pathway. Accordingly, this model has been shown useful to model cell behavior including signal transduction, transcription, and metabolic pathways. The aim of this study was to determine whether a queuing theory model that involves lipopolysaccharide-mediated macrophage activation in tandem with changes in intracellular Cd and zinc (Zn) content or a lack thereof, would be useful to predict their impact on immune activation. We then validate our model with biologic cytokine output from human macrophages relative to the timing of innate immune activation. We believe that our results further prove the validity of the queuing theory approach to model intracellular molecular signaling and postulate that it can be useful to predict additional cell signaling pathways and the corresponding biological outcomes.

An optimized queue management system to improve patient flow in the absence of appointment system.

PURPOSE: The aim of this research study is to develop a queue assessment model to evaluate the inflow of walk-in outpatients in a busy public hospital of an emerging economy, in the absence of appointment systems, and construct a dynamic framework dedicated towards the practical implementation of the proposed model, for continuous monitoring of the queue system. DESIGN/METHODOLOGY/APPROACH: The current study utilizes data envelopment analysis (DEA) to develop a combined queuing-DEA model as applied to evaluate the wait times of patients, within different stages of the outpatients' department at the Combined Military Hospital (CMH) in Lahore, Pakistan, over a period of seven weeks (23rd April to 28th May 2014). The number of doctors/personnel and consultation time were considered as outputs, where consultation time was the non-discretionary output. The two inputs were wait time and length of queue. Additionally, VBA programming in Excel has been utilized to develop the dynamic framework for continuous queue monitoring. FINDINGS: The inadequate availability of personnel was observed as the critical issue for long wait times, along with overcrowding and variable arrival pattern of walk-in patients. The DEA model displayed the "required" number of personnel, corresponding to different wait times, indicating queue build-up. ORIGINALITY/VALUE: The current study develops a queue evaluation model for a busy outpatients' department in a public hospital, where "all" patients are walk-in and no appointment systems. This model provides vital information in the form of "required" number of personnel which allows the administrators to control the queue pre-emptively minimizing wait times, with optimal yet dynamic staff allocation. Additionally, the dynamic framework specifically targets practical implementation in resource-poor public hospitals of emerging economies for continuous queue monitoring.

The 85% bed occupancy fallacy: The use, misuse and insights of queuing theory.

Queuing theory can and has been used to inform bed pool capacity decision making, though rarely by managers themselves. The insights it brings are also not widely and properly understood by healthcare managers. These two shortcomings lead to the persistent fallacy of there being a globally applicable optimum average occupancy target, for example 85%, which can in turn lead to over- or under-provision of resources. Through this paper, we aim both to make queuing models more accessible and to provide visual demonstrations of the general insights managers should absorb from queuing theory. Occupancy is a consequence of the patient arrival rate and 'treatment' rate (the number of beds and length of stay). There is a trade-off between the average occupancy and access to beds (measured by, for example, the risk of access block due to all beds being full or the average waiting time for a bed). Managerially, the decision-making input should be the level of access to beds required, and so bed occupancy should be an output. Queuing models are useful to quickly draw the shape of these access-occupancy trade-off curves. Moreover, they can explicitly show the effect that variation (lack of regularity) in the times between arrivals and in the lengths of stay of individual patients has on the shape of the trade-off curves. In particular, with the same level of access, bed pools subject to lower variation can operate at higher average occupancy. Further, to improve access to a bed pool, reducing variation should be considered.

Application of Queuing Theory to Optimize the Triage Process in a Tertiary Emergency Care ("ER") Department.

CONTEXT: Time from triage to patient care is usually evaluated, but time elapsed between the arrival of patient to emergency room (ER) and triage (pretriage) is not usually measured. AIMS: The present study evaluates how the application of the queuing (or "waiting line") theory in the triage process can generate effective strategies to improve patient care in the ER. SETTINGS AND DESIGN: A "before-and-after" study was conducted in the ER of the Hospital Universitario San Ignacio, a tertiary emergency care in Bogotá, Colombia. SUBJECTS AND METHODS: The pretriage time was evaluated, and queuing theory was applied to the evaluation; according to the results, the number and distribution of the necessary nursing personnel were determined. STATISTICAL ANALYSIS USED: The change in waiting times was compared using a paired t-test. RESULTS: In a first 7 months evaluation period, 89,898 patient visits were considered, with an average pretriage time of 22.15 min. According to the arrival distribution by hours and days of the week and considering the results of the calculations made using queuing theory, the number of nurses needed in the service per hour was determined for each day of the week, and schedule changes were implemented without increasing staff. In a second similar evaluation period, 94,497 patient visits were considered demonstrating a reduction of the pretriage time to 7.5 min (mean difference 14.64 min, 95% confidence interval 14.42-14.85, P < 0.001). CONCLUSIONS: The use of queuing theory in the planning of the daily personnel requirements in the triage area of ER can reduce the pretriage time by 65% without incurring additional cost.

Decision Support for the Optimization of Provider Staffing for Hospital Emergency Departments with a Queue-Based Approach.

: Deployment or distribution of valuable medical resources has emerged as an increasing challenge to hospital administrators and health policy makers. The hospital emergency department (HED) census and workload can be highly variable. Improvement of emergency services is an important stage in the development of the healthcare system and research on the optimal deployment of medical resources appears to be an important issue for HED long-term management. HED performance, in terms of patient flow and available resources, can be studied using the queue-based approach. The kernel point of this research is to approach the optimal cost on logistics using queuing theory. To model the proposed approach for a qualitative profile, a generic HED system is mapped into the M/M/R/N queue-based model, which assumes an R-server queuing system with Poisson arrivals, exponentially distributed service times and a system capacity of N. A comprehensive quantitative mathematical analysis on the cost pattern was done, while relevant simulations were also conducted to validate the proposed optimization model. The design illustration is presented in this paper to demonstrate the application scenario in a HED platform. Hence, the proposed approach provides a feasibly cost-oriented decision support framework to adapt a HED management requirement.

Optimal Evacuation Strategy for Parking Lots Considering the Dynamic Background Traffic Flows.

An optimal evacuation strategy for parking lots can shorten evacuation times and reduce casualties and economic loss. However, the impact of dynamic background traffic flows in a road network on the evacuation plan is rarely taken into account in existing approaches. This research develops an optimal evacuation model with total evacuation time minimization by dividing the evacuation process in a parking lot into two periods. In the first period, a queuing theory is used to estimate the queuing time, and in the second period, a traffic flow equilibrium model and an intersection delay model are employed to simulate vehicles' route choice. To deal with these models, a modified ant colony algorithm is developed. The results of a numerical example prove that the proposed method has an advantage in improving evacuation efficiency. The results also show that background traffic flows affect not only vehicles' average queuing time in parking lots but also optimal evacuation route choice. Additionally, a sensitivity analysis indicates that the minimum threshold of headway time that allows vehicles out of a parking lot to merge into the background traffic flows on the roads connecting the exits has a great impact on average queuing time, average travel time, and total evacuation time.