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The Israeli Queue is a batch service polling system where a single server attends to multiple queues based on seniority. Each arriving customer belongs to one of several classes. Upon arrival, a customer either joins an existing queue for their class or initiates a new queue if they are the first of their class to arrive. Customers from the class with the most senior member are served together as a batch, with the service time remaining constant regardless of the batch size. This service model is found in applications like advanced elevator systems and on-demand shared mobility, where passengers heading to the same destination can share a ride. However, in many real-world scenarios, the vehicle capacities are small and constraining, which calls for a deeper exploration of the Israeli queue with a capacitated server (IQCS). In this paper, we formally define the IQCS and address the challenges of creating a mathematically tractable model to represent it. To approximate the IQCS, we develop a quasi-birth-death process and derive approximations for key performance measures. To validate our approach, we implement a simulation model and use it to compare the IQCS, the approximate model, and the original Israeli Queue. Our results across various scenarios demonstrate the accuracy of the approximate model. Nonetheless, the presence of a remaining gap underscores the ongoing challenge of precisely and efficiently modeling the IQCS, posing an open question for the research community. [ABSTRACT FROM AUTHOR]

Accurate modeling of viral outbreaks in living populations and computer networks is a prominent research field. Many researchers are in search for simple and realistic models to manage preventive resources and implement effective measures against hazardous circumstances. The ongoing Covid-19 pandemic has revealed the fact about deficiencies in health resource planning of some countries having relatively high case count and death toll. A unique epidemic model incorporating stochastic processes and queuing theory is presented, which was evaluated by computer simulation using pre-processed data obtained from an urban clinic providing family health services. Covid-19 data from a local corona-center was used as the initial model parameters (e.g. R 0 , infection rate, local population size, number of contacts with infected individuals, and recovery rate). A long–run trend analysis for 1 year was simulated. The results fit well to the current case data of the sample corona center. Effective preventive and reactive resource planning basically depends on accurately designed models, tools, and techniques needed for the prediction of feature threats, risks, and mitigation costs. In order to sufficiently analyze the transmission and recovery dynamics of epidemics it is important to choose concise mathematical models. Hence, a unique stochastic modeling approach tied to queueing theory and computer simulation has been chosen. The methods used here can also serve as a guidance for accurate modeling and classification of stages (or compartments) of epidemics in general. [ABSTRACT FROM AUTHOR]

Congestion at terminal gates is a significant issue that many ports are dealing with. The port of Songkhla, which serves as the main seaport in southern Thailand, has been confronted with this issue, together with an increase in the number of trucks over the last five years. This study aims to investigate alternatives for improving service operations at the terminal gate, including gate lane expansion, queueing policy in exit-gate sharing, and work process reorganization. A simulation model was developed to analyze the queueing performance: truck queue length and gate waiting time. Scenarios analysis was performed and compared to the baseline model to investigate the impact of proposed approaches on gate performance. The simulation results confirm that a gate-sharing policy can alleviate congestion at a certain truck arrival rate. The method of reorganizing work processes by separating customs work from gate operations and placing it in a new work station appears most appealing. It produces a significant improvement in congestion, comparable to the performance of the gate lane expansion approach while requiring less investment.

Cloud computing is continuing to prove its flexibility and versatility in helping industries and businesses as well as academia as a way of providing needed computing capacity. As an important alternative to cloud computing, desktop grids allow to utilize the idle computer resources of an enterprise/community by means of distributed computing system, providing a more secure and controllable environment with lower operational expenses. Further, both cloud computing and desktop grids are meant to optimize limited resources and at the same time to decrease the expected latency for users. The crucial parameter for optimization both in cloud computing and in desktop grids is the level of redundancy (replication) for service requests/workunits. In this paper we study the optimal replication policies by considering three variations of Fork-Join systems in the context of a multi-server queueing system with a versatile point process for the arrivals. For services we consider phase type distributions as well as shifted exponential and Weibull. We use both analytical and simulation approach in our analysis and report some interesting qualitative results.

Volunteer convergence refers to the influx of volunteers to affected areas after large‐scale disasters. There are not only many benefits to volunteer convergence, but it also creates significant logistical challenges that can impede relief efforts. This study examines polices for admitting volunteers into organized relief operations, and for assigning admitted volunteers to relief tasks. We represent this problem as a queueing system where, in addition to customer arrivals and departures, random server arrivals and abandonments are also present. Then, using a Markov decision process framework, we analyze server admission and assignment policies that seek to minimize relief tasks holding costs as well as volunteer holding and rejection costs. We show that the classic cμ rule, a server allocation policy that determines where to put servers based on relief tasks holding costs and processing requirements, is optimal under both collaborative and non‐collaborative service regimes and when batch server arrivals are allowed. Additionally, we find that the optimal server admission policy is a complex state‐dependent policy. As a result, we propose a class of admission heuristics that depend on the number of workers in the system and the remaining system workload. In a numerical study, we show that our heuristic policies perform well with respect to long‐run average costs, waiting times, number of volunteers in the system, and number of volunteers idling in the system over a range of parameter values and distributions that are based on real data from a case study. As such, they promise volunteer coordinators an effective and simple way to manage disaster volunteers. [ABSTRACT FROM AUTHOR]

The lot-sizing problem in batch manufacturing systems with capacity constraints is studied using queueing relationships and optimisation techniques. In this research, the effect of lot sizes when there are parallel machines and multiple part types is considered. Furthermore, the issue of whether or not to use pooled queues, based on part types, to feed the machines is examined. Different scenarios are evaluated using GI/G/n queueing approximations to predict performance and optimise lot sizes. Optimisation is based on minimising the mean flowtimes, which include queue and lot service times. The results show that if part types are very different, there are situations in which pooling is not advantageous. [ABSTRACT FROM AUTHOR]

Stochastic kriging is a popular metamodeling technique to approximate computationally expensive simulation models. However, it typically treats the simulation model as a black box in practice and often fails to capture the highly nonlinear response surfaces that arise from queueing simulations.We propose a simple, effective approach to improve the performance of stochastic kriging by incorporating stylized queueing models that contain useful information about the shape of the response surface. We provide several statistical tools to measure the usefulness of the incorporated stylized models. We show that even a relatively crude stylized model can substantially improve the prediction accuracy of stochastic kriging. [ABSTRACT FROM AUTHOR]

This paper considers a single-server queueing model in which the customers are served in batches of varying size depending on predetermined thresholds as well as available inventory. There is a finite buffer for the inventory and the service of every customer requires an inventory item. An ( s, S) -type inventory system is used for the models considered in this paper. Initially, the model is studied in detail using the matrix-analytic method by assuming all the underlying random variables to be exponentially distributed. Thereafter, an outline of the model in a more general set up is also presented. Due to complexity of the model when more general assumptions are made on the underlying random variables, simulation is opted after a satisfactory validation with the analytic counterpart of the exponential model. Finally, some illustrative numerical examples are also presented to accomplish our analysis. [ABSTRACT FROM AUTHOR]

We are considering the problem of obtaining the response time distribution of fault-tolerant multi-tier services. In the provision of software-as-a-service applications, the service provider is obliged to ensure a certain quality of service. Herein, we regard upper bounds on the response time. The services consist of multiple components with different functionality, which are prone to failures, and fail according to a certain failure time distribution. However, due to redundancy, a failure will not necessarily bring the service down, but rather increase the response time. A fundamental difficulty with estimating the response time distribution while considering failures is related to the disparity in the time scales of the time between failures and service times. To overcome this issue, we propose an approach based on a decomposition, which combines an analytic model of the failure process and a discrete event simulation model to sample the response time distribution. In an experimental study, we compare this simulation-based approach with an analytic approach, and illustrate how this approach can be utilised by service providers as decision support. We also show that in certain cases, the analytic approach might provide a safe bound on the response time. [ABSTRACT FROM AUTHOR]

Capitalizing on the operational concept of division-of-labor, clinics often reduce physician service time by off-loading some of his/her clinical activities to lower-cost personnel. These personnel, such as nurse practitioners and physician assistants, are often collectively referred to as 'mid-level providers' (MLPs) and can perform many patient-consultation tasks. The common rationale is that using an MLP allows the physician to serve more patients, increase patients' access to care, and, due to MLPs' lower salaries, improve the clinic's financial performance. An MLP is typically integrated into the outpatient clinic process in one of two modes: as an 'ice-breaker,' seeing each patient before the physician, or as a 'standalone' provider, a substitute for the physician for the entirety of some patients' visits. Despite both of these modes being widely used in practice, we find no research that identifies the circumstances under which either one is preferable. This study examines these two modes' effects on operational performance, such as patient flow and throughput, as well as on financial measures. Using queueing and bottleneck analysis, discrete-event simulation, and profit modeling, we compare these two deployment modes and identify the optimal policies for deploying MLPs as either ice-breakers or as standalone providers. Interestingly, we also find there exists a range of scenarios where not hiring an MLP at all (i.e., the physician works alone) is likely to be most profitable for the clinic. Implications for practice are discussed. [ABSTRACT FROM AUTHOR]

Electric vehicles (EVs), one of the biggest innovations in the automobile industry, are considered as a demand source as well as a supply source for power grids. Studies have been conducted on the effect of EV charging and utilization of EVs to control grid peak or to solve the intermittency problem of renewable generators. However, most of these studies focus on only one aspect of EVs. In this work, we demonstrate that the increased demand resulting from EV charging can be alleviated by utilizing idle EV charging stations as a vehicle-to-grid (V2G) service. The work is performed based on data from Jeju Island, Korea. The EV demand pattern in 2030 is modeled and forecasted using EV charging patterns from historical data and the EV and charging station deployment plan of Jeju Island’s local government. Then, using a Monte Carlo simulation, charging and V2G scenarios are generated, and the effect of V2G on peak time is analyzed. In addition, a sensitivity analysis is performed for EV and charging station deployment. The results show that the EV charging demand increase can be resolved within the EV ecosystem.

In a stochastic environment pooling naturally leads to economies of scale, but heterogeneity can also create variability. In the article, we investigate this trade-off in the case of a manufacturing environment. Pooling for queueing systems has been widely investigated in the literature on the design of service systems; however, much less attention has been given to manufacturing systems where jobs are given a due date upon arrival. In such systems it is not the elapsed time until the actual completion of the job that counts, but rather the due date lead time that can be promised to the customer in order to guarantee a high service level. The purpose of the article is to get a deeper understanding about how pooling strategies and lead-time decisions can be implemented to attain a high due-date performance. To this end, we develop a simulation and analytical study to determine the benefits of pooling manufacturing systems with heterogeneous demand streams. Our work allows managers to identify the characteristics of production systems such that a pooling strategy would be beneficial. Our results demonstrate that when a due-date setting and scheduling mechanism is implemented, heterogeneity does generally not lead to deterioration of performance, as previously observed in service environments. Our studies also reveal that the benefits of pooling in terms of the expected sojourn time obtained by a simple analytical treatment can serve as a good prediction of the benefits of pooling on the average due date lead time in a wide range of situations. [ABSTRACT FROM AUTHOR]

We apply service-operations-management concepts to improve the efficiency and equity of voting systems. Recent elections in the United States and elsewhere have been plagued by long lines, excessive waiting times, and perceptions of unfairness. We build models for the waiting lines at voting precincts using both traditional steady-state queueing methods and simulation models. We develop solution methods to allocate voting machines optimally to precincts. Our objective functions consider both the efficiency and the equity of the voting system. We compare our allocation algorithm to several competing methods, including those used in practice. We examine several different strategies for improving voting operations on both the demand and the capacity side of voting systems, and we present a complete case study of applying our method to data from the 2008 election for Franklin County, Ohio. We conclude that our method is superior to existing polices in terms of efficiency and equity and that it is robust in terms of uncertainties regarding turnout rates on Election Day. We also suggest several operational improvements to the voting process drawn from the service-operations literature. [ABSTRACT FROM AUTHOR]

This article considers the optimal design of unpaced assembly lines. Two key decisions in designing an unpaced assembly line are the allocation of work to the stations and the allocation of buffer storage space between the stations. To the best of the author's knowledge, this is the first article to jointly optimize both the allocation of workload and the allocation of buffer spaces simultaneously when the objective is to maximize the revenue from throughput minus the cost of work-in-process inventory. Exact solutions are provided for small lines (three or four stations) with a fixed kind of processing time distribution (exponential or Erlang). Ten observations are made about the characteristics of the allocation of workload and buffer spaces. Heuristics are suggested for designing lines with more stations or different processing time distributions. A simulation study is done to test the observations and heuristics for longer lines and different processing time distributions (lognormal). Significant savings can be achieved by jointly optimizing both the workload and the buffer space allocations. [ABSTRACT FROM PUBLISHER]

Abstract: We consider a multi-server queueing system in which two types of customers arrive according to a Markovian arrival process. Type 1 customers have preemptive priority over Type 2 customers. A Type 2 arrival finding all servers busy will be lost. However, a Type 1 customer finding all servers busy with at least one Type 2 in service will get into service by pre-empting one of the Type 2 customers in service. Pre-empted Type 2 customers enter into a buffer of finite capacity. These (preempted) customers eventually leave the system after completing a service. In the case of exponential services, this model is studied analytically in steady-state by exploiting the special nature of the queueing model. A number of useful performance measures along with some illustrative examples are reported. In the case of non-exponential services, we simulate the model and discuss the effect of the variatio the services on some selected performance measures. [Copyright &y& Elsevier]

This paper considers a fork-join system (or: parallel queue), which is a two-queue network in which any arrival generates jobs at both queues and the jobs synchronize before they leave the system. The focus is on methods to quantify the mean value of the 'system's sojourn time' S: with S denoting a job's sojourn time in queue i, S is defined as max{ S, S}. Earlier work has revealed that this class of models is notoriously hard to analyze. In this paper, we focus on the homogeneous case, in which the jobs generated at both queues stem from the same distribution. We first evaluate various bounds developed in the literature, and observe that under fairly broad circumstances these can be rather inaccurate. We then present a number of approximations, that are extensively tested by simulation and turn out to perform remarkably well. [ABSTRACT FROM AUTHOR]

Queueing networks have been used to model material handling in flexible manufacturing systems. We explore the use of a closed queueing network model to approximate an intrabay automated material handling system (AMHS) in semiconductor manufacturing. A simulation-based approach is proposed to obtain estimates of system performance measures. Current simulation models in the industry are very complex, require significant development time, and take a long time to run. The proposed simulation-based queueing network approximation can be used as an easy and fast alternative or as a precursor to a full-fledged modeling exercise depending on the type of decision being made and the level of granularity required in the output. Using a simple intrabay configuration, we compare estimates from the approximation approach and a more detailed modeling approach to characterize the performance of the approximation. In addition, a simulation information model is used to compare AMHS models based on the amount and types of information needed to model the system, and to obtain desired output. This classification aids modelers in determining the level of detail to incorporate in a model based on the objectives of the simulation study. [ABSTRACT FROM AUTHOR]

Litho cells are the most expensive equipment in a wafer fab. To support decision-making on this equipment, accurate simulation models for throughput and cycle time are helpful. The simulation models that are typically developed incorporate various shop floor details. To properly model these details, they should be quantified, which is difficult and time-consuming. In this article, a lumped parameter model is proposed for the litho cell. The model consists of two parts: a detailed representation of the processing inside the track and scanner, and an aggregate representation of the factory floor feeding the loadport. The track-scanner is modelled as a tandem flow line with blocking. The shop floor is represented by a delay distribution that incorporates all contributions outside the machine. Simulation results show that the suggested method provides a simple, yet accurate approximation of the litho cell. [ABSTRACT FROM AUTHOR]

Abstract: The blocking probability is commonly used to evaluate the quality-of-service (QoS) offered by dialup Internet Service Providers (ISPs). Unfortunately, dialup ISPs employ no blocking standards or thresholds. This raises questions as to exactly how providers measure and evaluate QoS with respect to network access and how they make capacity planning decisions. Many ISPs use the User-to-Modem Ratio (UMR) as a surrogate measure for service quality, but there are no well defined direct relationships between the UMR and the blocking probability. In this paper, relationships between the UMR and other well known traffic variables and the blocking probability are quantified, and the usefulness of the UMR as a standalone QoS metric is explored. Blocking probabilities are estimated for a range of UMRs via simulation from a range of demand scenarios developed from observed data. A predictive regression model is introduced to quantify the affects of independent predictor variables on blocking. Results show that the UMR is not a useful standalone QoS metric and traditionally favored UMRs such as 10:1 cannot be associated with “high quality service” in a de facto manner. [Copyright &y& Elsevier]

This paper is concerned with the study of the constant due-date assignment policy in a multistage assembly system. The multistage assembly system is modeled as an open queueing network. It is assumed that the product order arrives according to a Poisson process. In each service station, there is either one or infinite machine with exponentially distributed processing time. The transport times between every pair of service stations are independent random variables with generalized Erlang distributions. It is assumed that each product has a penalty cost that is some linear function of its due-date and its actual completion time. The due date is found by adding a constant to the time that the order arrives. This constant value is the constant lead time that a product might expect between time of placing the order and time of delivery. By applying the longest path analysis in queueing networks, we obtain the distribution function of manufacturing lead time. Then, the optimal constant lead time is computed by minimizing the expected aggregate cost per product. Finally, the results are verified by Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

Abstract: An i.i.d. process is considered on a compact metric space . Its marginal distribution is unknown, but is assumed to lie in a moment class of the form, where are real-valued, continuous functions on , and are constants. The following conclusions are obtained: [(i)] For any probability distribution on , Sanov’s rate-function for the empirical distributions of is equal to the Kullback–Leibler divergence . The worst-case rate-function is identified as where , and is a compact, convex set. [(ii)] A stochastic approximation algorithm for computing is introduced based on samples of the process . [(iii)] A solution to the worst-case one-dimensional large-deviation problem is obtained through properties of extremal distributions, generalizing Markov’s canonical distributions. [(iv)] Applications to robust hypothesis testing and to the theory of buffer overflows in queues are also developed. [Copyright &y& Elsevier]

Reducing congestion is a primary concern in the design and analysis of queueing networks, especially in systems where sources of randomness are characterized by high variability. This paper considers a multiserver first-come, first-served (FCFS) queueing model where we arrange servers in two stations in series. All arrivals join the first service center, where they receive a maximum of T units of service. Arrivals with service requirements that exceed the threshold T join the second queue, where they receive their remaining service. For a variety of heavy tail service time distributions, characterized by large coefficient of variations, analytical and numerical comparisons show that our scheme provides better system performance than the standard parallel multiserver model in the sense of reducing the mean delay per customer in heavy traffic systems. Our model is likely to be useful in systems where high variability is a cause for degradation and where numerous service interruptions are not desired. [ABSTRACT FROM AUTHOR]

The Multi Priority Dual Queue (MPDQ) is a new scheduling regime shown to reduce congestion for multi-class traffic over conventional scheduling disciplines in isolation. As the MPDQ improves traffic congestion, most notably in communication systems, it is not necessary to include it at every node, or service centre, within a network. To gain insight into the advantages of a mixed MPDQ / First In First Out network with prioritised traffic, simulations are performed with and without a dual queue and various Quality of Service (QoS) criteria are obtained. Queueing networks containing differentiated traffic, also known as multi-class networks, are complicated to solve analytically using existing queueing theory techniques. We discuss the complications of exact solutions and describe how we used simulation to obtain performance statistics. We also look at high-class traffic under different offered loads, and provide a comparison of the delay characteristics. These findings provide communication service providers valuable information in determining the improvement in QoS to differentiated networks with the MPDQ. They also highlight the importance of simulation as a tool of evaluation of networks, and the best MPDQ network scenario. [ABSTRACT FROM AUTHOR]

Both simulation and analytic models of computer systems can be very useful for predicting the performance of proposed new systems or proposed changes to existing systems. Unfortunately, many potential users of models are reluctant to use them because of the complexity of many such models and the difficulty of relating the model to the real system. This tutorial paper leads the reader through the development and use of an easily understood analytic model. This is then placed in context with a class of similar analytic models. In spite of the simplicity of these models they have proved useful and quite accurate in predicting performance (utilization, throughput, and response) using only the most basic system data as input. These parameters can either be estimates or measurements from a running system. The model equations and assumptions are defined, and a detailed case study is presented as an example of their use. [ABSTRACT FROM AUTHOR]

Cities with under 100,000 in population expend a significant portion of their budgets on emergency services. One option that a number of these cities have considered for improving service and cutting costs is training personnel to handle both police and fire roles. In this paper we describe a hierarchy of models that we have used to assess the performance viability of a merger as well as to design specific deployment plans. The modeling environment is more complex than a traditional police or fire system. We need to model the response pattern of four or more patrol units along with the simultaneous dispatch of fire equipment from one or more fire stations. The major contribution of the paper is the manner in which a series of models is linked together to forecast a wide range of performance measures under differing dispatch assumptions. We use a queueing model of police patrol to calculate steady state probabilities and expected delays without preemption. We then model two types of preemptive dispatch strategies utilized in responding initially to a major fire by superimposing a binomial distribution on the basic queueing model. There is also a travel time simulation model to calculate conditional expected response time statistics. The queueing models and the travel time simulation are then combined to estimate unconditional expected values. Lastly, we describe a simulation model used to address transient performance issues that are of concern during a major fire. [ABSTRACT FROM AUTHOR]

The three node Jackson queueing network is the simplest acyclic network in which in equilibrium the sojourn times of a customer at each of the nodes are dependent. We show that assuming the individual sojourn times are independent provides a good approximation to the total sojourn time. This is done by simulating the network and showing that the sojourn times generally pass a Kolmogorov-Smirnov test as having come from the approximating distribution. Since the sum of dependent random variables may have the same distribution as the sum of independent random variables with the same marginal distributions, it is conceivable that our approximation is exact. However, we numerically compute upper and lower bounds for the distribution of the total sojourn time; these bounds are so close that the approximating distribution lies outside of the bounds. Thus, the bounds are accurate enough to distinguish between the two distributions even though the Kolmogorov-Smirnov test generally cannot. [ABSTRACT FROM AUTHOR]

Electric vehicles (EVs), one of the biggest innovations in the automobile industry, are considered as a demand source as well as a supply source for power grids. Studies have been conducted on the effect of EV charging and utilization of EVs to control grid peak or to solve the intermittency problem of renewable generators. However, most of these studies focus on only one aspect of EVs. In this work, we demonstrate that the increased demand resulting from EV charging can be alleviated by utilizing idle EV charging stations as a vehicle-to-grid (V2G) service. The work is performed based on data from Jeju Island, Korea. The EV demand pattern in 2030 is modeled and forecasted using EV charging patterns from historical data and the EV and charging station deployment plan of Jeju Island’s local government. Then, using a Monte Carlo simulation, charging and V2G scenarios are generated, and the effect of V2G on peak time is analyzed. In addition, a sensitivity analysis is performed for EV and charging station deployment. The results show that the EV charging demand increase can be resolved within the EV ecosystem. [ABSTRACT FROM AUTHOR]