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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]

This study presents a simple approach for analyzing the BMAP/G/1 queueing system under N policy. In this policy, the server goes idle at the end of a busy period and the queue length is checked at every arrival moment. The idle server starts serving customers when the queue length reaches or above a predetermined number, namely N, and keeps doing so until the system is completely empty. We first use a simple sequential substitution approach to derive the system length distribution at departure epoch. A comparative study is also conducted to highlight the benefits and strength of our straightforward approach to that of the RG-factorization technique and the roots finding method. We extract the distribution of system length at a random time point by utilizing the remaining service time of a customer who is currently being served as the supplementary variable. The probability density function of the sojourn time distribution for an arbitrary customer of an incoming batch is also computed. We propose an expected linear cost function to estimate the optimal value of N at minimum cost. The validity of our analytic technique has been shown through a variety of numerical examples involving different service time distributions. [ABSTRACT FROM AUTHOR]

A single-server queue with renewal arrivals and generally distributed independent and identically distributed service times is considered. Customers are served using the longest remaining time first scheduling algorithm. In case of a tie, processor sharing is utilized. We introduce a fluid model for the evolution of a measure-valued state descriptor of this queue, and we investigate its properties. We also prove a fluid limit theorem justifying our fluid model as the first-order approximation of the queueing system under consideration. [ABSTRACT FROM AUTHOR]

In queueing systems where queues are invisible, it is critical for companies to make decisions about the timing of announcing the anticipated delay to customers. In this paper, a simulation model is built to simulate an invisible queueing system, and several queueing scenarios are considered, including different system congestion and different company goals, to explore the impact of different announcement timings. In the modeling of customer behavior, we argue that it is difficult for companies to announce perfectly accurate delay and rarely have customers fully trust the announcement, so the quantal-response model is included to model customers' probabilistic choice behavior due to the bounded rationality. Meanwhile, we consider customer heterogeneity, assign customers different initial patience and, as an extension, also assume that patience will be updated. We perform simulation experiments and analyze the experimental data to dissect the underlying reasons, and then give sound management suggestions. The experiments show that the optimal announcement timing is different for different scenarios, which shows that in practical decisions, companies should adopt different announcement strategies for different scenarios. What's more, in some scenarios, delayed announcement at specific time is better than on-arrival announcement, which suggests that when we judge the value of announcement, we should add the definite word of specific timing to the announcement. The breakthrough point of this paper is to consider customers' bounded rationality and the dynamic patience; meanwhile, it fills the gap of announcement timing research and explores the value of additional announcements after the initial announcement. [ABSTRACT FROM AUTHOR]

One dominant approach for reducing response times in large-scale systems is Join-the-Shortest-Queue-d: whenever a job arrives, the dispatcher queries d servers at random and then assigns the job to the queried server with the shortest queue. While JSQ -d is known to perform quite well in systems where all servers run at the same speed, this is not the case in systems that exhibit heterogeneity with respect to server speeds. Unfortunately, there is no straightforward way to extend JSQ -d (or other so-called power-of-d policies) to heterogeneous systems. Should a job be assigned to the queried server with the shortest queue even if much faster servers were among those queried? Should a job be assigned to the queried server where it is expected to complete the soonest even if there is an idle, albeit slower, server available among those queried? And for that matter, should we query faster servers more often than their slower counterparts? Recent work has introduced a framework for developing strong dispatching policies by pairing suitably chosen querying and assignment rules. Within this framework, prior work has focused on finding strong-performing dispatching policies that use only the idle/busy statuses of the queried servers, rather than detailed queue length information. In this paper, we overcome the challenge of evaluating the performance of—and finding strong-performing—general scalable dispatching policies that make use of both server speed and detailed queue length information, through a combination of mean field analysis and a sequence of modified optimization problems. We find that well-designed length-aware dispatching policies can significantly outperform their idleness-based counterparts in large-scale heterogeneous systems. While the best policies of this kind are often complicated to describe, we find that in the vast majority of cases the relatively simple Shortest Expected Wait policy performs nearly as well, without the need for an especially sophisticated and time-consuming optimization procedure. [ABSTRACT FROM AUTHOR]

Over a period of just few days in March 2023, the Silicon Valley Bank of California went from solvent to broke and eventually closed on March 10th. This event marked the second largest bank failure in U.S. history, after Washington Mutual's in 2008. A few days later on March 12th, the Signature Bank of New York was shut down. Then on May 1st, the First Republic Bank was closed by the California Department of Financial Protection and Innovation. At that point a large number of financial institutions, on war footing, had to swiftly plan and execute multiple projects of critical and strategic importance. The author was tasked with leading a few such projects that were to be completed within 12-16 weeks. After a couple of failed deployment attempts, finally, in the 16th week, major product features were deployed to production environment and rolled out to the entire company across the globe, thus marking the success of this critical initiative. The suddenness of these few projects created the need to build a foundation of how to plan and execute unforeseen yet strategically critical projects in a compressed timeframe. One of the important learnings was the recognition and understanding that environment induced stress narrows focus of the human mind. Based on this experience, for future projects of a similar nature, we had to develop appropriate processes and tools. We realized that the project team must develop adaptive thinking habits so that our cognitive behavior would become automatic. Habits develop only through repetitive performance to cause our behavior to become automatic. We conceptualized this within our group and built relevant important processes and tools to execute similar critical projects in the future. [ABSTRACT FROM AUTHOR]

Blockchain has emerged as a disruptive technology with potential applications in various industries. Although the proof-of-work (PoW) blockchain systems have worked so successfully, the mining pools in PoW-based blockchain systems have certain drawbacks: high-power expenditure, mining competition and fault. It is essential to implement the power-saving and evaluate the performance of the mining pool with these characteristics in PoW-based blockchain systems. In this paper, we consider a queueing system with sleep–wakeup, working breakdown and impatient strategies that are suitable to express well power-saving, fault and mining competition in the mining process. By using a z-transform approach, the closed-form expressions about various performance measures such as the mean number of blocks and the mean confirmation time of block are obtained. Furthermore, we analyze the power consumption by constructing the linear function based on the performance measures and analyze the improvement of power-saving by comparing the power consumption of a queueing model without various strategies. In order to mitigate the negative effect stemming from the mining competition, we formulate the Nash bargaining game to induce the cooperation and obtain the Nash solution and the corresponding mining pool's optimal computation power. [ABSTRACT FROM AUTHOR]

Ensuring customer satisfaction is one of the main objectives of a call center. We focus on the question of how many agents are necessary and how they should be allocated to maintain a service level threshold and reduce the expected waiting time of the customers. In this paper, we consider a multistage call center that consists of a front and a back office, impatient customers, and an overflow mechanism. Based on the performance evaluation of such a system using a continuous-time Markov chain, a configuration of agents is determined using a binary search algorithm. We focus on structural insights, e.g., convexity conditions, to obtain a quick solution for the staffing problem. Since monotonicity does not always hold, the approach is heuristic. The numerical results show the performance of the algorithm. The influence of the fraction requiring second-level service in the back office and the impatience rate for the minimum number of agents is shown. [ABSTRACT FROM AUTHOR]

In various real-life queueing systems, part of the service can be rendered without involvement or presence of the customers themselves. In those queues, customers whose service order is still in process may leave the service station, go to ‘orbit’ for a random length of time, and then return to find out if their order has been completed. Common examples are car’s annual maintenance works, food ordering, etc. In this paper, a thorough analysis of a single-server ‘orbit while in service’ queueing model with general service time is presented. Assuming an Exponentially distributed orbit time, we derive general formulae for the distributions of (i) a customer’s total residence time in the system; (ii) a customer’s net actual residence time in the system during service (not including orbit time); (iii) the time an orbiting customer is late to return, i.e., remains in orbit after his/her service has been completed; and (iv) the total number of customers in the system. Considering the family of Gamma-distributed service times (spanning the range of distributions between the Exponential and the Deterministic), as well as the Uniform distribution, we further derive explicit formulae for the distributions of the above variables. Under linear cost assumptions, the optimal mean orbit time is numerically calculated for each of the above service-time distributions. Figures depicting the behavior of the measures as functions of the parameters are presented. [ABSTRACT FROM AUTHOR]

The rise of online marketplaces has raised customer expectations regarding customization and lead time. It poses significant challenges to manufacturing firms and prompts a move from make-to-stock to a more flexible make-to-order system. Compared to make-to-stock settings, make-to-order systems cannot smooth fluctuations in demand using available stock. While viewing dynamic pricing as a useful strategy to balance supply with demand, many manufacturing firms can also create capacity flexibility. In that scenario, system costs could be cut by managing capacity and demand simultaneously. In this paper, we consider a make-to-order production environment with base and surge capacity as well as the ability to adjust product pricing. Our main focus is on operational decision-making, assuming that the base capacity and surge capacity are fixed, but activating the surge capacity incurs a setup cost. Initially, we propose a stochastic control model to reflect this complex decision problem. However, our initial model leads to an intractable dynamic programming problem. To overcome this, we convert the problem to a more tractable diffusion control problem. This approach helps to reveal the conditions under which utilizing flexible capacity is more advantageous than relying solely on fixed capacity. When flexible capacity is advantageous, we provide a solution to the diffusion control problem that can guide optimal capacity and price adjustments. We discover an interesting interplay between capacity adjustment and dynamic pricing. In particular, we find that the price, which aims at reducing congestion, may not monotonically increase with the congestion level when capacity adjustments incur a fixed cost. [ABSTRACT FROM AUTHOR]

The present study considers a single-server Markovian queueing system by observing the number of customer arrivals during the service time of a customer. We estimate the traffic intensity in this queueing system along with the average queue length and the expected number of customers in the system. We propose classical and Bayesian frameworks to estimate the parameters of interest. In the Bayesian setup, three forms of prior distributions for ρ and two loss functions are considered. Furthermore, the predictive distribution of the number of customer arrivals during the service time of a customer and the equal-tailed credible region of ρ are obtained. The aforementioned approaches are illustrated with numerical examples based on simulation studies. [ABSTRACT FROM AUTHOR]

We consider a queueing system which opens at a given point in time and serves a finite number of users according to the last-come first-served discipline with preemptive-resume (LCFS-PR). Each user must decide individually when to join the queue. We allow for general classes of user preferences and service time distributions and show existence and uniqueness of a symmetric Nash equilibrium. Furthermore, we show that no continuous asymmetric equilibrium exists, if the population consists of only two users, or if arrival strategies satisfy a mild regularity condition. For an illustrative example, we implement a numerical procedure for computing the symmetric equilibrium strategy based on our constructive existence proof for the symmetric equilibrium. We then compare its social efficiency to that obtained if users are instead served on a first-come first-served (FCFS) basis. [ABSTRACT FROM AUTHOR]

We study how to optimally match agents in a dynamic matching market with heterogeneous match cardinalities and values. A network topology determines the feasible matches in the market. In general, a fundamental tradeoff exists between short-term value—which calls for performing matches frequently—and long-term value—which calls, sometimes, for delaying match decisions in order to perform better matches. We find that in networks that satisfy a general position condition, the tension between short- and long-term value is limited, and a simple periodic clearing policy (nearly) maximizes the total match value simultaneously at all times. Central to our results is the general position gap ϵ; a proxy for capacity slack in the market. With the exception of trivial cases, no policy can achieve an all-time regret that is smaller, in terms of order, than ϵ−1. We achieve this lower bound with a policy, which periodically resolves a natural matching integer linear program, provided that the delay between resolving periods is of the order of ϵ−1. Examples illustrate the necessity of some delay to alleviate the tension between short- and long-term value. This paper was accepted by David Simchi-Levi, revenue management and market analytics. Funding: This work was supported by the National Science Foundation [Grant CMM-2010940] and the U.S. Department of Defense [Grant STTR A18B-T007]. [ABSTRACT FROM AUTHOR]

We consider a Markovian queueing model with abandonment where customer arrival, service and abandonment processes are all modulated by an external environmental process. The environmental process depicts all factors that affect the exponential arrival, service, and abandonment rates. Moreover, the environmental process is a hidden Markov process whose true state is not observable. Instead, our observations consist only of customer arrival, service, and departure times during some period of time. The main objective is to conduct Bayesian analysis in order to infer the parameters of the stochastic system, as well as some important queueing performance measures. This also includes the unknown dimension of the environmental process. We illustrate the implementation of our model and the Bayesian approach by using simulated and actual data on call centers. [ABSTRACT FROM AUTHOR]

• A chat service with actively involved customers and repeating interactions is studied. • The capacity of parallel chats and the server's response effort are derived. • A queueing game for a dual-channel system of chat service and call center is analyzed. • Customer bounded rationality is considered. Many service systems in various type of industry provide services via chat technologies. This type of service system is characterized by an interesting combination of properties. First, the customer is actively involved in service execution, since the service is comprised of responses of the server and the customer to each other, until the customer's request is satisfied. In addition, in such a system, the service can be provided by a single server in a parallel manner to a number of customers. Motivated by these and others interesting properties of the chat service, we formulate and analyze the stochastic queueing system as a two-dimensional quasi-birth-and-death process and derive its steady-state probabilities using matrix geometric methods. By means of economic analysis, we provide a scheme for deriving the optimal capacity of parallel chats and the optimal response effort that should be made by the server, considering that higher effort lengthens the response time but increases the probability of successful service completion. We next investigate a queueing game that considers a multi-channel service system consisting of a chat service and a traditional multi-server call center, and we consider strategic customers under both a centralized and a decentralized scenario. We show that competition between service channels may lead to lower service utilization even though customers enjoy higher expected utility. Finally, customer bounded rationality is considered and it is shown that customers who are less rational may enjoy higher utility. Sensitivity analyses are conducted for all scenarios. [ABSTRACT FROM AUTHOR]

A queue‐jumping argument concludes that some course of action is impermissible by likening it to the presumptively impermissible act of jumping a queue. Arguments of this sort may be found in a disparate range of contexts and in support of policies favoured by both left and right. Examples include arguments against private education and private health care but also arguments against accommodations for learning disabilities, refugee resettlement, and birthright citizenship. We infer that, although queue‐jumping arguments are strictly analogies, they constitute a sufficiently distinct class of arguments to justify their separate treatment. The paper proposes an argumentation scheme for queue‐jumping arguments and demonstrates its applicability to some existing arguments of this type. [ABSTRACT FROM AUTHOR]

A 2-queue system with a single-server operating according to the combined 'Join the Shortest Queue–Serve the Longest Queue' regime is analyzed. Both cases, with or without server's switch-over times, are investigated under the non-preemptive discipline. Instead of dealing with a state space comprised of two un-bounded dimensions, a non-conventional formulation is constructed, leading to an alternative two-dimensional state space, where only one dimension is infinite. As a result, the system is defined as a quasi birth and death process and is analyzed via both the probability generating functions method and the matrix geometric formulation. Consequently, the system's two-dimensional probability mass function is derived, from which the system's performance measures, such as mean queue sizes, mean sojourn times, fraction of time the server resides in each queue, correlation coefficient between the queue sizes, and the probability mass function of the difference between the queue sizes, are obtained. Extensive numerical results for various values of the system's parameters are presented, as well as a comparison between the current non-preemptive model and its twin system of preemptive service regime. One of the conclusions is that, depending on the variability of the various parameters, the preemptive regime is not necessarily more efficient than the non-preemptive one. Finally, economic issues are discussed and numerical comparisons are presented, showing the advantages and disadvantages of each regime. [ABSTRACT FROM AUTHOR]

Self-interested customers' form of reasoning and its consequences for system performance affect the planning decisions of service providers. We study procedurally rational customers—customers who make decisions based on a sample containing anecdotes of the system times experienced by other customers. Specifically, we consider procedurally rational customers in two-station service networks with open routing, that is, customers can choose the order in which to visit the stations. Because some actions may be less represented in the population, a given customer may not succeed in obtaining anecdotes about all possible actions. We introduce a novel sampling framework that extends the procedurally rational framework to incorporate the possibility that a customer may not receive any anecdotes for one of the actions; in this case, the customer uses a prior point estimate in lieu of the missing anecdotes. Under this framework, we study the procedurally rational equilibrium in open routing. We show first that as the sample size grows large, customers' estimates become more accurate, and the procedurally rational equilibrium converges to the fully rational equilibrium (which is also socially optimal). We then uncover two main findings. First, we obtain bounds on the distance between the procedurally rational and fully rational equilibrium, aiding operational planning and showing the rate of convergence to the fully rational outcome as the sample size of anecdotes of each individual customer grows. Second, if customers obtain anecdotes of both actions with high probability, then the equilibrium will approximate the fully rational outcome, despite the sampling error inherent to procedural rationality. [ABSTRACT FROM AUTHOR]

Abstract 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. P 0…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

Productivity in open pit operations in the mining industry is conditioned by the manual assignment of trucks by the dispatcher, who does not have the ability to find the optimal policy by himself, having many variables that consider. To this end, an MIP optimization model is proposed that considers the scheduling of a discretized operating shift in smaller stages that consider positions and capacities of available trucks, and congestion based on a differential speed based on the number of trucks in different sections of the transport route. The model seeks to prioritize the transfer of material to crushers and meet material goals during the planning horizon. Preliminary results indicate that it is possible to reduce the violation of the production plan by destination by 12% and increase productivity by 46% with respect to the state of the art of similar solutions. [ABSTRACT FROM AUTHOR]

Managing on-time delivery systems is challenging because of the underlying uncertainties and combinatorial nature of the routing decision. In practice, the efficiency of such systems also hinges on the driver's familiarity with the local neighborhood. In "Provably Good Region Partitioning for On-Time Last-Mile Delivery," Carlsson et al. study a region partitioning policy to minimize the expected delivery time of customer orders in a stochastic and dynamic setting. This policy assigns every driver to a subregion, ensuring that drivers are only dispatched to their territories. The authors characterize the structure of the optimal partitioning policy and show its expected on-time performance converges to that of the flexible dispatching policy in heavy traffic. The optimal characterization features two insightful conditions that are critical to the on-time performance of last-mile delivery systems. Furthermore, the paper develops partitioning algorithms with performance guarantees, leveraging ham sandwich cuts and three-partitions from discrete geometry. On-time last-mile delivery is expanding rapidly as people expect faster delivery of goods ranging from grocery to medicines. Managing on-time delivery systems is challenging because of the underlying uncertainties and combinatorial nature of the routing decision. In practice, the efficiency of such systems also hinges on the driver's familiarity with the local neighborhood. This paper studies the optimal region partitioning policy to minimize the expected delivery time of customer orders in a stochastic and dynamic setting. We allow both the order locations and on-site service times to be random and generally distributed. This policy assigns every driver to a subregion, hence making sure drivers will only be dispatched to their own territories. We characterize the structure of the optimal partitioning policy and show its expected on-time performance converges to that of the flexible dispatching policy in heavy traffic. The optimal characterization features two insightful conditions that are critical to the on-time performance of last-mile delivery systems. We then develop partitioning algorithms with performance guarantees, leveraging ham sandwich cuts and three-partitions from discrete geometry. This algorithmic development can be of independent interest for other logistics problems. We demonstrate the efficiency of the proposed region partitioning policy via numerical experiments using synthetic and real-world data sets. Funding: The first author gratefully acknowledges the support of the Office of Naval Research [Grant N00014-21-1-2208] and METRANS [Grant PSR-21-22]. The second author gratefully acknowledges the support of the Natural Sciences and Engineering Research Council of Canada [Grant RGPIN-2022-04950] and the National Natural Science Foundation of China [Grant 72242106]. The third author gratefully acknowledges the support of the Natural Sciences and Engineering Research Council of Canada [Grant RGPIN-2023-04453]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2021.0588. [ABSTRACT FROM AUTHOR]

Consumers tend to perceive a service of higher value when more consumers, under the influence of others, make the same choice. In this article, we investigate the impact of social interactions in service operations under various price, waiting time target, and capacity decisions. The service is delivered through an M/M/1 queue system which attempts to achieve a waiting time target through a volume-based capacity allocation policy. Consumers perceive a positive (negative) value of the service if the queue length is longer (shorter) than the base queue length – an anchor point in their value perception. We examine the relationship of the intrinsic value of the service and the consumer's value perception (in terms of the queue length anchor point) with the price, the waiting time target, and the capacity decisions. We also quantify the potential gain or loss in profit when the influence of social interactions is ignored. Theoretical results are derived to guide the price, waiting time target, and capacity decisions to exploit the influence of social interactions. It is found that there exist delicate dynamics among key parameters and variables, when ignored, that could lead to undesirable outcomes. The study offers new insights to balance the demand-inducing effect and the congestion-aggravating effect in a service system under the influence of social interactions. [ABSTRACT FROM AUTHOR]

In this work, we consider a novel single-server retrial queue with event-dependent arrival rates. Contrary to other related works, the primary customers' arrival rates depend on the last realized event, which refers either to a departure, or to an arrival of either type, or to when a customer arrives during a busy period, compared with others. Our motivation stems from the modeling of service systems, in which the customers express their willingness to join the system based on the last realized event. We investigate the stability conditions, and derive the stationary distribution both at service completion epochs, and at an arbitrary epoch. We also study the asymptotic behaviour under high rate of retrials. Performance measures are explicitly derived, and extensive numerical examples are performed to investigate the impact of event-dependency. Moreover, constrained optimisation problems are formulated and solved with ultimate goal to derive optimal joining probabilities. [ABSTRACT FROM AUTHOR]

Pelican Crossing is a crossing with a signaling device that is operated by pedestrians and will stop the flow of vehicle traffic. Pedestrians must press a button to request green time from vehicle drivers so that vehicle drivers stop and pedestrians can cross the road. As a metropolitan city, Central Jakarta is full of activity. The increase in the number of vehicles is not the main factor causing congestion. There are other factors such as the movement of pedestrians crossing the road using Pelican Crossing, causing queues and delays. This study aims to analyze the effect of pedestrians crossing at pelican crossing on the queue length of vehicles, to analyze the characteristics of traffic flow and pedestrians due to pelican crossing and to apply a model that connects the characteristics of traffic flow and pedestrians at pelican crossing. The research was conducted by surveying the existing traffic conditions. The results of the research show that after calculating the PV2 value, we can see the discrepancy in the existing pelican crossing facilities on Jalan MH Thamrin and Jalan Sudirman based on the calculation of pedestrian crossings and traffic volume, which in calculating the PV2 value recommends a non-level crossing type. [ABSTRACT FROM AUTHOR]

We consider a system of two parallel discrete-time single-server queues, queue 1 and queue 2. The service time of any customer in either queue is equal to 1 time slot. Arrivals during consecutive slots occur independently from slot to slot. However, the arrival streams into both queues are possibly mutually interdependent, i.e., during any slot, the numbers of arrivals in queue 1 and queue 2 need not be statistically independent. Their joint probability generating function (pgf) A(x, y) fully characterizes the queueing model. As a consequence of the possible intra-slot correlation in the arrival process, the numbers of customers present ("system contents") in queues 1 and 2, at any given slot boundary, are not necessarily independent either. In a previous paper, we have already discussed the mathematical difficulty of computing their steady-state joint pgf U (z 1 , z 2) ; explicit closed-form results can only be obtained for specific choices of A(x, y). In this paper, we therefore look at the problem from an other angle. Specifically, we study the (asymptotic) conditional steady-state behavior of the system under the condition that the content of queue 1 is (temporarily) very high (goes to infinity). For ease of terminology, we refer to the system as the "asymptotic system" in these circumstances. We prove that the asymptotic system is nearly identical to the original (unconditional) system, but with a modified joint arrival pgf A ∗ (x , y) that can be computed explicitly from A(x, y). This fundamental result allows us to determine the stability condition of queue 2 in the asymptotic system, and explicitly compute the classical queueing performance metrics of queue 2, such as the pgf, the moments and the approximate tail distribution of its system content, when this condition is fulfilled. It also leads to accurate approximative closed-form expressions for the joint tail distribution of the system contents in both queues, in the original (unconditional) system. We extensively illustrate our methodology by means of various specific (popular) choices of A(x, y). In some examples, where an explicit solution for U (z 1 , z 2) or for the (approximative) joint tail distribution is known, we retrieve the known results easily. In other cases, new results are found for arrival pgfs A(x, y) for which no explicit results were known until now. [ABSTRACT FROM AUTHOR]

Homotopy perturbation method (HPM) is applied in this paper for the transient study of some queueing/inventory/healthcare models. Semi-analytic approximate transient probabilities are obtained as power series in the time variable. The numerical implementation of the method using a programming language like MATLAB, is easy. However, the number of terms that is required in the above power series, to get an accurate approximation, grows with time. This obstacle is overcame by adopting a step-by-step HPM method. Implementation of the method is discussed in the case of the classic M/M/1 queue, the (s, S) inventory model with random replenishment time but without backlogs, the (s, S) inventory model with positive service and replenishment times, allowing infinite backlogs, and the Markov chain model for the patient handoff process in emergency departments. Numerical experimentation has been carried out to evaluate the efficiency of the method and to understand the challenges involved in its implementation. [ABSTRACT FROM AUTHOR]

This work aims to study customer strategic behavior and operational optimization of an M/M/1 queue with N-policy and dynamic service-rate control in general, and of a make-to-order production system with a strategic manufacturer as a practical example in particular. With the N-policy and hysteretic control, the service rate is dynamically adjusted according to the queue length. An empty system is required to initiate service only when the number of waiting customers reaches a given threshold N. If the queue length exceeds M (> N) , the server serves customers with a higher service rate until the number of customers is lower than another threshold m. Based on a linear reward-cost structure, arriving customers are allowed to decide whether to join the system or not. The focus is on comparing the self equilibrium performance and socially-optimal arrival under the interaction between the server’s states and customers’ joining decisions. The influence of N-policy and hysteretic control on customer’s equilibrium joining probability under unobservable scenario is analysed. The optimal value of threshold N and m are discussed by taking server’s operational cost into consideration. These findings have important managerial implications on the overall social welfare with dynamic service rate. [ABSTRACT FROM AUTHOR]

This paper presents a physical space design method for mixed reality-based immersive environments by improving the color rendering of optically visible head-mounted displays. In OST-HMD, the phenomenon that the light of the external environment is combined with the enhanced image occurs, which reduces the visibility of the content. Moreover, previous studies to solve this problem required additional optical components or performed only simple verification. Proposed physical space was designed using black curtains, blinds, low-reflection structures, and adjustable lighting. The physical space can be adapted to the intended use of the physical space through physical transitions for multiple users without additional optics. To verify the usefulness of this environment, we measured the color gamut and intensity spectrum in three experimental environments. Also, we analyzed the factors that change the color gamut according to the components and the surrounding environment. As a result, the color gamut improved by up to 4.7 times from 19.92% to 93.53% based on the environment and improved by up to 4.1 times from 21% to 86.29% depending on the location. The experimental results revealed that the presented method could reduce the factors that degrade the color gamut within all measurement locations and significantly improve the color gamut. [ABSTRACT FROM AUTHOR]

Many hospitals struggle with insufficient capacity for their inpatients. As a result, hospitals may benefit from an approach that evaluates the occupancy of inpatient wards. In this study, we approximate the occupancy distributions of inpatient wards, accounting for the cases where patients relocate due to a shortage of beds. The approximation employs a homogeneous continuous-time Markov chain to evaluate each ward as a queue containing multiple classes of patients. We avoid computational intractability by evaluating each ward separately and accommodating patients arriving from the remaining wards by interrupting the arrival processes, where the interruption times follow hyper-exponential distributions. Numerical experimentation shows that our approach is robust concerning the type of length-of-stay distribution and generally results in a minor loss of accuracy. Further validation indicates that our model reflects the occupancy distributions of inpatient wards in a Danish hospital.

In emergency departments (EDs), one of the major reasons behind long waiting times and crowding overall is the time it takes to move admitted patients from the ED to an appropriate bed in the main hospital. In "Using Hospital Admission Predictions at Triage for Improving Patient Length of Stay in Emergency Departments," Chen et al. develop a methodology that can be used to shorten these times by predicting the likelihood of admission for each patient at the time of triage and starting the process of identifying a suitable hospital bed and making preparations for the patient's eventual transfer to the bed right away if the predicted probability of admission is deemed high enough. A simulation study suggests that the proposed methodology, particularly when it takes into account ED census levels, has the potential to shorten average waiting times in the ED without leading to too many false early bed requests. Long boarding times have long been recognized as one of the main reasons behind emergency department (ED) crowding. One of the suggestions made in the literature to reduce boarding times was to predict, at the time of triage, whether a patient will eventually be admitted to the hospital and if the prediction turns out to be "admit," start preparations for the patient's transfer to the main hospital early in the ED visit. However, there has been no systematic effort in developing a method to help determine whether an estimate for the probability of admit would be considered high enough to request a bed early, whether this determination should depend on ED census, and what the potential benefits of adopting such a policy would be. This paper aims to help fill this gap. The methodology we propose estimates hospital admission probabilities using standard logistic regression techniques. To determine whether a given probability of admission is high enough to qualify a bed request early, we develop and analyze two mathematical decision models. Both models are simplified representations and thus, do not lead to directly implementable policies. However, building on the solutions to these simple models, we propose two policies that can be used in practice. Then, using data from an academic hospital ED in the southeastern United States, we develop a simulation model, investigate the potential benefits of adopting the two policies, and compare their performances with that under a simple benchmark policy. We find that both policies can bring modest to substantial benefits, with the state-dependent policy outperforming the state-independent one particularly under conditions when the ED experiences more than usual levels of patient demand. Funding: This work was supported by the National Science Foundation [Grants CMMI-1234212 and CMMI-1635574]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2022.2405. [ABSTRACT FROM AUTHOR]

This paper investigates a single server batch arrival and batch service queueing model with infinite waiting space. The inter-occurrence time of arrival batches with random size is distributed arbitrarily. Customers are served using the discrete-time Markovian service process in accordance with the general bulk-service rule. We compute the prearrival epoch probability vectors using the UL-type RG-factorization method based on censoring technique. The random epoch probability vectors are then obtained using the Markov renewal theory based on the prearrival epoch probability vectors. We derive analytically simple expressions for the outside observer's, intermediate, and post-departure epochs probability vectors by evolving the relationships among them. Determining the probability mass functions of the waiting time distribution and the service batch size distribution for an arbitrary customer in an arriving batch is the most challenging aspect of this work. Finally, we discuss computational experience for the purpose of validating the analytical results presented in this paper. [ABSTRACT FROM AUTHOR]

The interaction between projects and servers has grown significantly in complexity; thus, applying parallel calculations increases dramatically. However, it should not be ignored that parallel processing gives rise to synchronization constraints and delays, generating penalty costs that may overshadow the savings obtained from parallel processing. Motivated by this trade-off, this study investigates two special and symmetric systems of split–join structures: (i) parallel structure and (ii) serial structure. In a parallel structure, the project arrives, splits into m parallel groups (subprojects), each comprising n subsequent stages, and ends after all groups are completed. In the serial structure, the project requires synchronization after each stage. Employing a numerical study, we investigates the time profile of the project by focusing on two types of delays: delay due to synchronization overhead (occurring due to the parallel structure), and delay due to overloaded servers (occurring due to the serial structure). In particular, the author studies the effect of the number of stages, the number of groups, and the utilization of the servers on the time profile and performance of the system. Further, this study shows the efficiency of lower and upper bounds for the mean sojourn time. The results show that the added time grows logarithmically with m (parallelism) and linearly with n (seriality) in both structures. However, comparing the two types of split–join structures shows that the synchronization overhead grows logarithmically undr both parallelism and seriality; this yields an unexpected duality property of the added time to the serial system. [ABSTRACT FROM AUTHOR]

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

Problem definition: Delay announcements have become an essential tool in service system operations: They influence customer behavior and network efficiency. Most current delay announcement methods are designed for relatively simple environments with a single service station or stations in tandem. However, complex service systems, such as healthcare systems, often have fork-join (FJ) structures. Such systems usually suffer from long delays as a result of both resource scarcity and process synchronization, even when queues are fairly short. These systems may thus require more accurate delay estimation techniques than currently available. Methodology/results: We analyze a network comprising a single-server queue followed by a two-station FJ structure using a recursive construction of the Laplace–Stieltjes transform of the joint delay distribution, conditioning on customers' movements in the network. Delay estimations are made at the time of arrival to the first station. Using data from an emergency department, we examine the accuracy and the robustness of the proposed approach, explore different model structures, and draw insights regarding the conditions under which the FJ structure should be explicitly modeled. We provide evidence that the proposed methodology is better than other commonly used queueing theory estimators such as last-to-enter-service (which is based on snapshot-principle arguments) and queue length, and we replicate previous results showing that the most accurate estimations are obtained when using our model result as a feature in state-of-the-art machine learning estimation methods. Managerial implications: Our results allow management to implement individual, real-time, state-dependent delay announcements in complex FJ networks. We also provide rules of thumb with which one could decide whether to use a model with an explicit FJ structure or to reduce it to a simpler model requiring less computational effort. Funding: This work was supported by the Dutch Research Council (NWO) Gravitation Programme NETWORKS [Grant 024.002.003], the Israel Ministry of Science and Technology [Grant 880011], and the Israel Science Foundation [Grant 1955/15]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.1167. [ABSTRACT FROM AUTHOR]

A threshold-type queue-length control strategy is proposed in the paper to investigate the influence of external shocks to a queueing system where customers are strategic and the server is vulnerable. An empty system is required to initiate service only when the number of waiting customers reaches a given threshold. External shocks occur according to a Poisson process, and once occur, the server breaks down and the customer being served is forced to leave the system. Arriving customers have to decide whether to join the system or not based on a reward-cost structure under different levels of information. The focus is on examining the equilibrium performance of the system under the interaction between the server's states and customers' joining decisions for different information levels. The equilibrium threshold in the observable queue and mixed joining probability in the unobservable queue are obtained. The optimal value of threshold $ N $ is discussed by taking strategic customer behavior and vulnerability of the server into consideration. These findings have important managerial implications on the evaluation of the shield threshold for the system with external attacks and unreliability factor, and also on optimal operation management of the system. [ABSTRACT FROM AUTHOR]

This paper studies a pricing problem for a single-server queue where customers arrive according to a Poisson process. For each arriving customer, the service provider announces a price rate and system wait time. In response, the customer decides whether to join the queue, and, if so, the duration of the service time. The objective is to maximize either the long-run average revenue or social welfare. We formulate this problem as a continuous-time control model whose optimality conditions involve solving a set of delay differential equations. We develop an innovative method to obtain the optimal control policy, whose structure reveals interesting insights. The optimal dynamic price rate policy is not monotone in the wait time. That is, in addition to the congestion effect (the optimal price rate increases in the wait time), we find a compensation effect, meaning that the service provider should lower the price rate when the wait time is longer than a threshold. Compared with the prevalent static pricing policy, our optimal dynamic pricing policy improves the objective value through admission control, which, in turn, increases the utilization of the server. In a numerical study, we find that our revenue-maximizing pricing policy outperforms the best static pricing policy, especially when the arrival rate is low, and customers are impatient. Interestingly, the revenue-maximizing policy also improves social welfare over the static pricing policy in most of the tested cases. We extend our model to consider nonlinear pricing and heterogeneous customers. Nonlinear pricing may improve the revenue significantly, although linear pricing is easier to implement. For the hetergeneous customer case, we obtain similar policy insights as our base model. This paper was accepted by Baris Ata, stochastic models and simulation. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2022.4474. [ABSTRACT FROM AUTHOR]

This paper studies a discrete-time single server batch arrival and batch service queueing model with unlimited waiting space. The discrete-time batch Markovian arrival process and discrete-time batch Markovian service process, respectively, manage the arrival and service processes. We adopt the UL-type RG-factorization approach based on censoring methodology for variable size batch service queue to calculate the stationary probability vectors of the transition probability matrix with general structure Markov chain at outside observer’s epoch. We reblock the transition probability matrix to its desired M/G/1 structure to find the stationary probability vectors at outside observer’s epoch for fixed size batch service queue using the matrix analytic method. We also develop relationships to determine probability vector expressions for other important time epochs such as pre-arrival, intermediate, post-departure, and random epochs. The most challenging aspect of our study is to obtain the probability mass functions of sojourn time in the system for both the variable and fixed size batch service queues. We use our suggested queueing model to derive the results of several specific well-known queueing models. We also discuss about possible managerial implication of our model to produce fruit juices in manufacturing industry. We present computational experience based on the execution of parametrized experiments with various categories in order to validate the analytical results reported in this study. [ABSTRACT FROM AUTHOR]

Bounded rationality includes potential cognitive deficits that limit human rational behaviour. In this paper, we allow for estimation errors of their utility and consider bounded rationality in queueing models with retrials. Upon arrival, customers decide whether to join the system based on their perceived utility, and their choice behaviour is characterised by a logit choice model. For a revenue-seeking server and a social planner, we investigate corresponding optimal pricing strategies. We find that the revenue-optimal price is no longer socially efficient in general but depends on the retrial rate. There exists a threshold such that the socially optimal price is greater than the revenue-optimal one when the retrial rate is below this threshold; otherwise, the revenue-optimal price is greater. A larger bounded rationality widens the gap between social welfare under the revenue- and socially optimal prices. Furthermore, the server's revenue may increase or first decrease and then increase with respect to customers' rationality levels, and the server may find it beneficial to reveal waiting time information when customers' rationality is high. Finally, failing to account for customers' bounded rationality can lead a significant revenue loss for the server and the proportion of such a revenue loss is close to 1 as customers become fully boundedly rational. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Streaming dataflow applications are an attractive target to parallelize on wide-SIMD processors such as GPUs. These applications can be expressed as a pipeline of compute nodes connected by edges, which feed outputs from one node to the next. Streaming applications often exhibit irregular dataflow, where the amount of output produced for one input is unknown a priori. Inserting finite queues between pipeline nodes can ameliorate the impact of irregularity and improve SIMD lane occupancy. The sizing of these queues is driven by both performance and safety considerations- relative queue sizes should be chosen to reduce runtime overhead and maximize throughput, but each node's output queue must be large enough to accommodate the maximum number of outputs produced by one SIMD vector of inputs to the node. When safety and performance considerations conflict, the application may incur excessive memory usage and runtime overhead. In this work, we identify properties of applications that lead to such undesirable behaviors, with examples from applications implemented in our MERCATOR framework for irregular streaming on GPUs. To address these issues, we propose extensions to support interruptible nodes that can be suspended mid-execution if their output queues fill. We illustrate the impacts of adding interruptible nodes to the MERCATOR framework on representative irregular streaming applications from the domains of branching search and bioinformatics. [ABSTRACT FROM AUTHOR]