Presenting a mathematical model of blood supply chain considering the efficiency of collection centers and development of metaheuristic algorithm in M/M/C/K queuing system.

In this study, a multiobjective model was devoted to the objectives of minimizing blood supply chain costs and minimizing the waiting time of blood donors for blood transfusion and minimizing blood transfusion schedule and increasing the efficiency of fixed and mobile centers in collecting blood. One of the most important constraints considered in the mathematical model is the capacity constraints of considering fixed and mobile blood facilities and management of the transfer of blood products to centers for collecting and distinguishing healthy and unhealthy blood. A multiobjective model was considered with the objectives of minimizing blood supply chain costs, the waiting time of blood donors for blood transfusion, and blood transfusion timing and increasing the efficiency of fixed and mobile centers in blood collection. The model findings were analyzed in order to validate the model on a larger scale, using the meta-innovative algorithm NSGAII and MOSPO. According to the research findings, we suggest that fuzzy uncertainty and fair distribution problem shouldn't be added to the dimensions of the main problem, and further analysis should be done in this area. It was shown that the NSGAII algorithm's performance was better than the MOPSO meta-heuristic algorithm.

Modeling an immune response to influenza A virus infection in alveolar epithelial cells.

Influenza A viruses (IAV) have been the cause of several influenza pandemics in history and are a significant threat for the next global pandemic. Hospitalized influenza patients often have excess interferon production and a dysregulated immune response to the IAV infection. Obtaining a better understanding of the mechanisms of IAV infection that induce these harmful effects would help drug developers and health professionals create more effective treatments for IAV infection and improve patient outcomes. IAV stimulates viral sensors and receptors expressed by alveolar epithelial cells, like RIG-I and toll-like receptor 3 (TLR3). These two pathways coordinate with one another to induce expression of type III interferons to combat the infection. Presented here is a queuing theory-based model of these pathways that was designed to analyze the timing and amount of interferons produced in response to IAV single stranded RNA and double-stranded RNA detection. The model accurately represents biological data showing the necessary coordination of the RIG-I and TLR3 pathways for effective interferon production. This model can serve as the framework for future studies of IAV infection and identify new targets for potential treatments.

Tracking Covid-19 cases and deaths in the United States: metrics of pandemic progression derived from a queueing framework.

We analyze the progression of COVID-19 in the United States over a nearly one-year period beginning March 1, 2020 with a novel metric motivated by queueing models, tracking partial-average day-of-event and cumulative probability distributions for events, where events are points in time when new cases and new deaths are reported. The partial average represents the average day of all events preceding a point of time, and is an indicator as to whether the pandemic is accelerating or decelerating in the context of the entire history of the pandemic. The measure supplements traditional metrics, and also enables direct comparisons of case and death histories on a common scale. We also compare methods for estimating actual infections and deaths to assess the timing and dynamics of the pandemic by location. Three example states are graphically compared as functions of date, as well as Hong Kong as an example that experienced a pronounced recent wave of the pandemic. In addition, statistics are compared for all 50 states. Over the period studied, average case day and average death day varied by two to five months among the 50 states, depending on data source, with the earliest averages in New York and surrounding states, as well as Louisiana.

A reinforcement learning-based optimal control approach for managing an elective surgery backlog after pandemic disruption.

Contagious disease pandemics, such as COVID-19, can cause hospitals around the world to delay nonemergent elective surgeries, which results in a large surgery backlog. To develop an operational solution for providing patients timely surgical care with limited health care resources, this study proposes a stochastic control process-based method that helps hospitals make operational recovery plans to clear their surgery backlog and restore surgical activity safely. The elective surgery backlog recovery process is modeled by a general discrete-time queueing network system, which is formulated by a Markov decision process. A scheduling optimization algorithm based on the piecewise decaying [Formula: see text]-greedy reinforcement learning algorithm is proposed to make dynamic daily surgery scheduling plans considering newly arrived patients, waiting time and clinical urgency. The proposed method is tested through a set of simulated dataset, and implemented on an elective surgery backlog that built up in one large general hospital in China after the outbreak of COVID-19. The results show that, compared with the current policy, the proposed method can effectively and rapidly clear the surgery backlog caused by a pandemic while ensuring that all patients receive timely surgical care. These results encourage the wider adoption of the proposed method to manage surgery scheduling during all phases of a public health crisis.

Obstetric operating room staffing and operating efficiency using queueing theory.

INTRODUCTION: Strategies to achieve efficiency in non-operating room locations have been described, but emergencies and competing priorities in a birth unit can make setting optimal staffing and operation benchmarks challenging. This study used Queuing Theory Analysis (QTA) to identify optimal birth center operating room (OR) and staffing resources using real-world data. METHODS: Data from a Level 4 Maternity Center (9,626 births/year, cesarean delivery (CD) rate 32%) were abstracted for all labor and delivery operating room activity from July 2019-June 2020. QTA has two variables: Mean Arrival Rate, λ and Mean Service Rate µ. QTA formulas computed probabilities: P0 = 1-(λ/ µ) and Pn = P0 (λ/µ)n where n = number of patients. P0…n is the probability there are zero patients in the queue at a given time. Multiphase multichannel analysis was used to gain insights on optimal staff and space utilization assuming a priori safety parameters (i.e., 30 min decision to incision in unscheduled CD; ≤ 5 min for emergent CD; no greater than 8 h for nil per os time). To achieve these safety targets, a < 0.5% probability that a patient would need to wait was assumed. RESULTS: There were 4,017 total activities in the operating room and 3,092 CD in the study period. Arrival rate λ was 0.45 (patients per hour) at peak hours 07:00-19:00 while λ was 0.34 over all 24 h. The service rate per OR team (µ) was 0.87 (patients per hour) regardless of peak or overall hours. The number of server teams (s) dedicated to OR activity was varied between two and five. Over 24 h, the probability of no patients in the system was P0 = 0.61, while the probability of 1 patient in the system was P1 = 0.23, and the probability of 2 or more patients in the system was P≥2 = 0.05 (P3 = 0.006). However, between peak hours 07:00-19:00, λ was 0.45, µ was 0.87, s was 3, P0 was 0.48; P1 was 0.25; and P≥2 was 0.07 (P3 = 0.01, P4 = 0.002, P5 = 0.0003). CONCLUSION: QTA is a useful tool to inform birth center OR efficiency while upholding assumed safety standards and factoring peaks and troughs of daily activity. Our findings suggest QTA is feasible to guide staffing for maternity centers of all volumes through varying model parameters. QTA can inform individual hospital-level decisions in setting staffing and space requirements to achieve safe and efficient maternity perioperative care.

The Age of Information in Wireless Cellular Systems: Gaps, Open Problems, and Research Challenges.

One of the critical use cases for prospective fifth generation (5G) cellular systems is the delivery of the state of the remote systems to the control center. Such services are relevant for both massive machine-type communications (mMTC) and ultra-reliable low-latency communications (URLLC) services that need to be supported by 5G systems. The recently introduced the age of information (AoI) metric representing the timeliness of the reception of the update at the receiver is nowadays commonly utilized to quantify the performance of such services. However, the metric itself is closely related to the queueing theory, which conventionally requires strict assumptions for analytical tractability. This review paper aims to: (i) identify the gaps between technical wireless systems and queueing models utilized for analysis of the AoI metric; (ii) provide a detailed review of studies that have addressed the AoI metric; and (iii) establish future research challenges in this area. Our major outcome is that the models proposed to date for the AoI performance evaluation and optimization deviate drastically from the technical specifics of modern and future wireless cellular systems, including those proposed for URLLC and mMTC services. Specifically, we identify that the majority of the models considered to date: (i) do not account for service processes of wireless channel that utilize orthogonal frequency division multiple access (OFDMA) technology and are able to serve more than a single packet in a time slot; (ii) neglect the specifics of the multiple access schemes utilized for mMTC communications, specifically, multi-channel random access followed by data transmission; (iii) do not consider special and temporal correlation properties in the set of end systems that may arise naturally in state monitoring applications; and finally, (iv) only few studies have assessed those practical use cases where queuing may happen at more than a single node along the route. Each of these areas requires further advances for performance optimization and integration of modern and future wireless provisioning technologies with mMTC and URLLC services.

Traffic Breakdown Probability Estimation for Mixed Flow of Autonomous Vehicles and Human Driven Vehicles.

Automated vehicles are expected to greatly boost traffic efficiency. However, how to estimate traffic breakdown probability for the mixed flow of autonomous vehicles and human driven vehicles around ramping areas remains to be answered. In this paper, we propose a stochastic temporal queueing model to reliably depict the queue dynamics of mixed traffic flow at ramping bottlenecks. The new model is a specified Newell's car-following model that allows two kinds of vehicle velocities and first-in-first-out (FIFO) queueing behaviors. The jam queue join time is supposed to be a random variable for human driven vehicles but a constant for automated vehicles. Different from many known models, we check the occurrence of significant velocity drop along the road instead of examining the duration of the simulated jam queue so as to avoid drawing the wrong conclusions of traffic breakdown. Monte Carlo simulation results show that the generated breakdown probability curves for pure human driven vehicles agree well with empirical observations. Having noticed that various driving strategy of automated vehicles exist, we carry out further analysis to show that the chosen car-following strategy of automated vehicles characterizes the breakdown probabilities. Further tests indicate that when the penetration rate of automated vehicles is larger than 20%, the traffic breakdown probability curve of the mixed traffic will be noticeably shifted rightward, if an appropriate car-following strategy is applied. This indicates the potential benefit of automated vehicles in improving traffic efficiency.

An Evaluation of e-Health Service Performance through the Integration of 5G IoT, Fog, and Cloud Computing.

In recent years, Internet of Things (IoT) advancements have led to the development of vastly improved remote healthcare services. Scalability, high bandwidth, low latency, and low power consumption are all essential features of the applications that make these services possible. An upcoming healthcare system and wireless sensor network that can fulfil these needs is based on fifth-generation network slicing. For better resource management, organizations can implement network slicing, which partitions the physical network into distinct logical slices according to quality of service (QoS) needs. Based on the findings of this research, an IoT-fog-cloud architecture is proposed for use in e-Health services. The framework is made up of three different but interconnected systems: a cloud radio access network, a fog computing system, and a cloud computing system. A queuing network serves as a model for the proposed system. The model's constituent parts are then subjected to analysis. To assess the system's performance, we run a numerical example simulation using Java modelling tools and then analyze the results to identify the key performance parameters. The analytical formulas that were derived ensure the precision of the results. Finally, the results show that the proposed model improves eHealth services' quality of service in an efficient way by selecting the right slice compared to the traditional systems.

A Channel Allocation Method Considering the Asymmetry of Available Channels for Centralized Underwater Cognitive Acoustic Networks.

Due to the unpredictable presence of Non-Cognitive Users (NCUs) in the time and frequency domains, the number of available channels (i.e., channels where no NCUs exist) and corresponding channel indices per Cognitive User (CU) may differ. In this paper, we propose a heuristic channel allocation method referred to as Enhanced Multi-Round Resource Allocation (EMRRA), which employs the asymmetry of available channels in existing MRRA to randomly allocate a CU to a channel in each round. EMRRA is designed to enhance the overall spectral efficiency and fairness of channel allocation. To do this, the available channel with the lowest redundancy is primarily selected upon allocating a channel to a CU. In addition, when there are multiple CUs with the same allocation priority, the CU with the smallest number of available channels is chosen. We execute extensive simulations in order to investigate the effect of the asymmetry of available channels on CUs and compare the performance of EMRRA to that of MRRA. As a result, in addition to the asymmetry of available channels, it is confirmed that most of the channels are simultaneously available to multiple CUs. Furthermore, EMRRA outperforms MRRA in terms of the channel allocation rate, fairness, and drop rate and has a slightly higher collision rate. In particular, EMRRA can remarkably reduce the drop rate compared to MRRA.

Dynamic fair balancing of COVID-19 patients over hospitals based on forecasts of bed occupancy.

This paper introduces mathematical models that support dynamic fair balancing of COVID-19 patients over hospitals in a region and across regions. Patient flow is captured in an infinite server queueing network. The dynamic fair balancing model within a region is a load balancing model incorporating a forecast of the bed occupancy, while across regions, it is a stochastic program taking into account scenarios of the future bed surpluses or shortages. Our dynamic fair balancing models yield decision rules for patient allocation to hospitals within the region and reallocation across regions based on safety levels and forecast bed surplus or bed shortage for each hospital or region. Input for the model is an accurate real-time forecast of the number of COVID-19 patients hospitalised in the ward and the Intensive Care Unit (ICU) of the hospitals based on the predicted inflow of patients, their Length of Stay and patient transfer probabilities among ward and ICU. The required data is obtained from the hospitals' data warehouses and regional infection data as recorded in the Netherlands. The algorithm is evaluated in Dutch regions for allocation of COVID-19 patients to hospitals within the region and reallocation across regions using data from the second COVID-19 peak.

Noise dissipation in gene regulatory networks via second order statistics of networks of infinite server queues.

RNA and protein concentrations within cells constantly fluctuate. Some molecular species typically have very low copy numbers, so stochastic changes in their abundances can dramatically alter cellular concentration levels. Such noise can be harmful through constrained functionality or reduced efficiency. Gene regulatory networks have evolved to be robust in the face of noise. We obtain exact analytical expressions for noise dissipation in an idealised stochastic model of a gene regulatory network. We show that noise decays exponentially fast. The decay rate for RNA molecular counts is given by the integral of the tail of the cumulative distribution function of the degradation time. For proteins, it is given by the slowest rate-limiting step of RNA degradation or proteolytic breakdown. This is intuitive because memory of the chemical composition of the system is manifested through molecular persistence. The results are obtained by analysing a non-standard tandem of infinite server queues, in which the number of customers present in one queue modulates the arrival rate into the next.

Incorporating medication therapy management into community pharmacy workflows.

Medication Therapy Management (MTM) is a group of pharmacist-provided services that optimize individual patients' drug therapy outcomes. Since community pharmacies' primary business platform is the dispensing of medications, and providing MTM services is a secondary source of revenue, pharmacies with limited resources are operationally challenged when trying to efficiently deliver both types of services. To address this problem, we follow a queueing network approach to develop an operational model of a community pharmacy workflow. Through our model, we derive structural results to determine conditions for a pharmacy to achieve economies of scope when providing both prescription and MTM services. We also develop a process simulation to compare different scenarios according to our economies of scope model, varying in provided services, personnel, service demand, and other operational variables. Outcomes examined include profitability, service rate, and sensitivity of some operation variables to profitability. Based on our results, we provide practical insights to help community pharmacy administrators and healthcare policy makers in their decision process.

Impact of the Dropping Function on Clustering of Packet Losses.

The dropping function mechanism is known to improve the performance of TCP/IP networks by reducing queueing delays and desynchronizing flows. In this paper, we study yet another positive effect caused by this mechanism, i.e., the reduction in the clustering of packet losses, measured by the burst ratio. The main contribution consists of two new formulas for the burst ratio in systems with and without the dropping function, respectively. These formulas enable the easy calculation of the burst ratio for a general, non-Poisson traffic, and for an arbitrary form of the dropping function. Having the formulas, we provide several numerical examples that demonstrate their usability. In particular, we test the effect of the dropping function's shape on the burst ratio. Several shapes of the dropping function proposed in the literature are compared in this context. We also demonstrate, how the optimal shape can be found in a parameter-depended class of functions. Finally, we investigate the impact of different system parameters on the burst ratio, including the load of the system and the variance of the service time. The most important conclusion drawn from these examples is that it is not only the dropping function that reduces the burst ratio by far; simultaneously, the more variable the traffic, the more beneficial the application of the dropping function.

Optimal Task Allocation Algorithm Based on Queueing Theory for Future Internet Application in Mobile Edge Computing Platform.

For 5G and future Internet, in this paper, we propose a task allocation method for future Internet application to reduce the total latency in a mobile edge computing (MEC) platform with three types of servers: a dedicated MEC server, a shared MEC server, and a cloud server. For this platform, we first calculate the delay between sending a task and receiving a response for the dedicated MEC server, shared MEC server, and cloud server by considering the processing time and transmission delay. Here, the transmission delay for the shared MEC server is derived using queueing theory. Then, we formulate an optimization problem for task allocation to minimize the total latency for all tasks. By solving this optimization problem, tasks can be allocated to the MEC servers and cloud server appropriately. In addition, we propose a heuristic algorithm to obtain the approximate optimal solution in a shorter time. This heuristic algorithm consists of four algorithms: a main algorithm and three additional algorithms. In this algorithm, tasks are divided into two groups, and task allocation is executed for each group. We compare the performance of our proposed heuristic algorithm with the solution obtained by three other methods and investigate the effectiveness of our algorithm. Numerical examples are used to demonstrate the effectiveness of our proposed heuristic algorithm. From some results, we observe that our proposed heuristic algorithm can perform task allocation in a short time and can effectively reduce the total latency in a short time. We conclude that our proposed heuristic algorithm is effective for task allocation in a MEC platform with multiple types of MEC servers.

Prioritizing and queueing the emergency departments' patients using a novel data-driven decision-making methodology, a real case study.

One of the principal problems in epidemic disruptions like the COVID-19 pandemic is that the number of patients needing hospitals' emergency departments' services significantly grows. Since COVID-19 is an infectious disease, any aggregation has to be prevented accordingly. However, few aggregations cannot be prevented, including hospitals. To the best of our knowledge, COVID-19 is a life-threatening disease, especially for people in poor health conditions. Therefore, it sounds reasonable to optimize the health care queuing systems to minimize the infection rate by prioritizing patients based on their health condition so patients with a higher risk of infection will leave the queue sooner. In this paper, relying on data mining models and expert's opinions, we propose a method for patient classification and prioritizing. The optimal number of servers (treatment systems) will be determined by benefiting from a mixed-integer model and the grasshopper optimization algorithm.

Prediction of personal protective equipment use in hospitals during COVID-19.

Demand for Personal Protective Equipment (PPE) such as surgical masks, gloves, and gowns has increased significantly since the onset of the COVID-19 pandemic. In hospital settings, both medical staff and patients are required to wear PPE. As these facilities resume regular operations, staff will be required to wear PPE at all times while additional PPE will be mandated during medical procedures. This will put increased pressure on hospitals which have had problems predicting PPE usage and sourcing its supply. To meet this challenge, we propose an approach to predict demand for PPE. Specifically, we model the admission of patients to a medical department using multiple independent [Formula: see text] queues. Each queue represents a class of patients with similar treatment plans and hospital length-of-stay. By estimating the total workload of each class, we derive closed-form estimates for the expected amount of PPE required over a specified time horizon using current PPE guidelines. We apply our approach to a data set of 22,039 patients admitted to the general internal medicine department at St. Michael's hospital in Toronto, Canada from April 2010 to November 2019. We find that gloves and surgical masks represent approximately 90% of predicted PPE usage. We also find that while demand for gloves is driven entirely by patient-practitioner interactions, 86% of the predicted demand for surgical masks can be attributed to the requirement that medical practitioners will need to wear them when not interacting with patients.

Markov chain analysis for the neonatal inpatient flow in a hospital.

Discrete-time Markov chain and queueing-theoretic models are used to quantitatively formulate the flow of neonatal inpatients over several wards in a hospital. Parameters of the models are determined from the operational analysis of the record of the numbers of admission/departure for each ward every day and the order log of patient movement from ward to ward for two years provided by the Medical Information Department of the University of Tsukuba Hospital in Japan. Our formulation is based on the analysis of the precise routes (the route of an inpatient is defined as a sequence of the wards in which he/she stays from admission to discharge) and their length-of-stay (LoS) in days in each ward on their routes for all neonatal inpatients. Our theoretical model calculates the probability distribution for the number of patients staying in each ward per day which agrees well with the corresponding histogram observed for each ward as well as for the whole hospital. The proposed method can be used for the long-term capacity planning of hospital wards with respect to the probabilistic bed utilization.

On the Time to Buffer Overflow in a Queueing Model with a General Independent Input Stream and Power-Saving Mechanism Based on Working Vacations.

A single server GI/M/1 queue with a limited buffer and an energy-saving mechanism based on a single working vacation policy is analyzed. The general independent input stream and exponential service times are considered. When the queue is empty after a service completion epoch, the server lowers the service speed for a random amount of time following an exponential distribution. Packets that arrive while the buffer is saturated are rejected. The analysis is focused on the duration of the time period with no packet losses. A system of equations for the transient time to the first buffer overflow cumulative distribution functions conditioned by the initial state and working mode of the service unit is stated using the idea of an embedded Markov chain and the continuous version of the law of total probability. The explicit representation for the Laplace transform of considered characteristics is found using a linear algebra-based approach. The results are illustrated using numerical examples, and the impact of the key parameters of the model is investigated.

Model for Risk Calculation and Reliability Comparison of Level Crossings.

There is not a single country in the world that is so rich that it can remove all level crossings or provide their denivelation in order to absolutely avoid the possibility of accidents at the intersections of railways and road traffic. In the Republic of Serbia alone, the largest number of accidents occur at passive crossings, which make up three-quarters of the total number of crossings. Therefore, it is necessary to constantly find solutions to the problem of priorities when choosing level crossings where it is necessary to raise the level of security, primarily by analyzing the risk and reliability at all level crossings. This paper presents a model that enables this. The calculation of the maximal risk of a level crossing is achieved under the conditions of generating the maximum entropy in the virtual operating mode. The basis of the model is a heterogeneous queuing system. Maximum entropy is based on the mandatory application of an exponential distribution. The system is Markovian and is solved by a standard analytical concept. The basic input parameters for the calculation of the maximal risk are the geometric characteristics of the level crossing and the intensities and structure of the flows of road and railway vehicles. The real risk is based on statistical records of accidents and flow intensities. The exact reliability of the level crossing is calculated from the ratio of real and maximal risk, which enables their further comparison in order to raise the level of safety, and that is the basic idea of this paper.

Analysis of a Queueing Model with Batch Markovian Arrival Process and General Distribution for Group Clearance.

In this paper we consider a single server queueing model with under general bulk service rule with infinite upper bound on the batch size which we call group clearance. The arrivals occur according to a batch Markovian point process and the services are generally distributed. The customers arriving after the service initiation cannot enter the ongoing service. The service time is independent on the batch size. First, we employ the classical embedded Markov renewal process approach to study the model. Secondly, under the assumption that the services are of phase type, we study the model as a continuous-time Markov chain whose generator has a very special structure. Using matrix-analytic methods we study the model in steady-state and discuss some special cases of the model as well as representative numerical examples covering a wide range of service time distributions such as constant, uniform, Weibull, and phase type.