Explore the vast range of titles available.

We present a broad literature survey of parameter and state estimation for queueing systems. Our approach is based on various inference activities, queueing models, observations schemes, and statistical methods. We categorize these into branches of research that we call estimation paradigms. These include: the classical sampling approach, inverse problems, inference for non-interacting systems, inference with discrete sampling, inference with queueing fundamentals, queue inference engine problems, Bayesian approaches, online prediction, implicit models, and control, design, and uncertainty quantification. For each of these estimation paradigms, we outline the principles and ideas, while surveying key references. We also present various simple numerical experiments. In addition to some key references mentioned here, a periodically updated comprehensive list of references dealing with parameter and state estimation of queues will be kept in an accompanying annotated bibliography.

PurposeNowadays, in many organizations, products are not delivered instantly. So, the customers should wait to receive their needed products, which will form a queueing-inventory model. Waiting a long time in the queue to receive products may cause dissatisfaction and churn of loyal customers, which can be a significant loss for organizations. Although many studies have been done on queueing-inventory models, more practical models in this area are needed, such as considering customer prioritization. Moreover, in many models, minimizing the total cost for the organization has been overlooked.Design/methodology/approachThis paper will compare several machine learning (ML) algorithms to prioritize customers. Moreover, benefiting from the best ML algorithm, customers will be categorized into different classes based on their value and importance. Finally, a mathematical model will be developed to determine the allocation policy of on-hand products to each group of customers through multi-channel service retailing to minimize the organization’s total costs and increase the loyal customers' satisfaction level.FindingsTo investigate the application of the proposed method, a real-life case study on vaccine distribution at Imam Khomeini Hospital in Tehran has been addressed to ensure model validation. The proposed model’s accuracy was assessed as excellent based on the results generated by the ML algorithms, problem modeling and case study.Originality/valuePrioritizing customers based on their value with the help of ML algorithms and optimizing the waiting queues to reduce customers' waiting time based on a mathematical model could lead to an increase in satisfaction levels among loyal customers and prevent their churn. This study’s uniqueness lies in its focus on determining the policy in which customers receive products based on their value in the queue, which is a relatively rare topic of research in queueing management systems. Additionally, the results obtained from the study provide strong validation for the model’s functionality.

Queueing applications are often complicated by dependence among interarrival times and service times. Such dependence is common in networks of queues, where arrivals are departures from other queues or superpositions of such complicated processes, especially when there are multiple customer classes with class-dependent service-time distributions. We show that the robust queueing approach for single-server queues proposed in the literature can be extended to yield improved steady-state performance approximations in the standard stochastic setting that includes dependence among interarrival times and service times. We propose a new functional robust queueing formulation for the steady-state workload that is exact for the steady-state mean in the M / GI /1 model and is asymptotically correct in both heavy traffic and light traffic. Simulation experiments show that it is effective more generally. The online appendix is available at https://doi.org/10.1287/opre.2017.1649 .

Mainstream queueing models are frequently employed in modeling healthcare delivery in a number of settings, and they further are used in making operational decisions for the same. The vast majority of these queueing models ignore the effects of delay experienced by a patient awaiting care. However, long delays may have adverse effects on patient outcomes and can potentially lead to a longer length of stay (LOS) when the patient ultimately does receive care. This work sets out to understand these delay issues from an operational perspective. Using data of more than 57,000 emergency department (ED) visits, we use an instrumental variable approach to empirically measure the impact of delays in intensive care unit (ICU) admission, i.e., ED boarding, on the patient’s ICU LOS for multiple patient types. Capturing these empirically observed effects in a queueing model is challenging because the effect introduces potentially long-range correlations in service and interarrival times. We propose a queueing model that incorporates these measured delay effects and characterizes approximations to the expected work in the system when the service time of a job is adversely impacted by the delay experienced by that job. Our approximation demonstrates an effect of system load on work that grows much faster than the traditional 1/(1 − ρ ) relationship seen in most queueing systems. As such, it is imperative that the relationship of delays and LOS be better understood by hospital managers so that they can make capacity decisions that prevent even seemingly moderate delays from causing dire operational consequences. This paper was accepted by Yossi Aviv, operations management .

Yardstick competition is a regulatory scheme for local monopolists (e.g., hospitals), where the monopolist’s reimbursement is linked to performance relative to other equivalent monopolists. This regulatory scheme is known to provide cost-reduction incentives and serves as the theoretical underpinning behind the hospital prospective reimbursement system used throughout the developed world. This paper uses a game-theoretic queueing model to investigate how yardstick competition performs in service systems (e.g., hospital emergency departments), where in addition to incentivizing cost reduction the regulator wants to incentivize waiting time reduction. We first show that the form of cost-based yardstick competition used in practice results in inefficiently long waiting times. We then demonstrate how yardstick competition can be appropriately modified to achieve the dual goal of cost and waiting-time reduction. In particular, we show that full efficiency ( first-best ) can be restored if the regulator makes the providers’ reimbursement contingent on their service rates and is also able to charge a provider-specific “toll” to consumers. More important, if such a toll is not feasible, as may be the case in healthcare, we show that there exists an alternative and particularly simple yardstick-competition scheme, which depends on the average waiting time only, that can significantly improve system efficiency ( second-best ). This scheme is easier to implement because it does not require the regulator to have detailed knowledge of the queueing discipline. We conclude with a numerical investigation that provides insights on the practical implementation of yardstick competition for hospital emergency departments, and we also present a series of modelling extensions. The e-companion is available at https://doi.org/10.1287/mnsc.2018.3089 . This paper was accepted by Serguei Netessine, operations management.

In this paper, we consider a queueing-inventory system under continuous review with a random order size policy and lost sales. If the inventory is depleted after the service of a customer, a replenishment order is instantaneously triggered. The replenishment order size may be randomized according to a discrete probability distribution. Customers arrive in the system according to a Poisson process and require service from a server. The server takes multiple vacations once the inventory is depleted. The service time, the lead time, and the vacation time are all assumed to be distributed exponentially. We derive the stationary joint distribution of the queue length, the on-hand inventory level, and the status of the server in explicit product form. Furthermore, the conditional distributions of the on-hand inventory level when the server is off due to a vacation or depleted inventory, and when the server is on and working, are derived. Then, we calculate some of the system performance measures. The effect of the server’s vacation on the performance measures is investigated analytically. Finally, some numerical results are presented. The simulation study of the model in the context of more general arrival processes and service time distributions is presented.

A call center is a service network in which agents provide telephone-based services. Customers who seek these services are delayed in tele-queues. This article summarizes an analysis of a unique record of call center operations. The data comprise a complete operational history of a small banking call center, call by call, over a full year. Taking the perspective of queueing theory, we decompose the service process into three fundamental components: arrivals, customer patience, and service durations. Each component involves different basic mathematical structures and requires a different style of statistical analysis. Some of the key empirical results are sketched, along with descriptions of the varied techniques required. Several statistical techniques are developed for analysis of the basic components. One of these techniques is a test that a point process is a Poisson process. Another involves estimation of the mean function in a nonparametric regression with lognormal errors. A new graphical technique is introduced for nonparametric hazard rate estimation with censored data. Models are developed and implemented for forecasting of Poisson arrival rates. Finally, the article surveys how the characteristics deduced from the statistical analyses form the building blocks for theoretically interesting and practically useful mathematical models for call center operations.

This paper deals with the optimization of flight arrival and departure sequencing in a multi-airport terminal area, addressing the pressing challenge of escalating flight delays. A two-tiered scheduling intervention-stochastic queuing bi-level model is established, which includes both strategic and tactical levels while considering multiple factors. A genetic algorithm based on multi-waypoint rolling horizon control is developed to search for Pareto optimal solution sets to optimize flight scheduling. Experimental validation shows that, compared to the pre-optimization conditions and the traditional First-Come-First-Served model, the proposed method significantly reduces the total flight delay time and effectively promotes the optimal allocation and efficient utilization of airspace resources in the terminal area.

We consider a service system in which customers who arrive at a service station and place an order, are not involved in the processing of their order, which can therefore be executed in their absence. Consequently, customers may leave the service station for some period of time during the processing of their order (i.e., go to orbit), and then return. While the customers are in orbit, they can utilize their time efficiently. If the service is completed before the customer's return from orbit, the ready service (RS) is stored in a designated storage facility until the customer returns and retrieves the RS from the inventory. If, however, the service is not yet completed when the customer returns, the customer can leave to orbit again. Accordingly, the policy is called \"repeated orbit\" (during the service). We formulate and analyze the queueing-inventory-repeated-orbit (QIRO) system using the matrix geometric method. The optimal orbiting time is calculated by maximizing the customer's expected utility. In addition, the optimal RS storage capacity and the optimal investment in preservation technologies (to store the RSs) are derived, both of which serve to increase demand and thus maximize the system's expected profit.

This paper studies an emerging business model of line-sitting in which customers seeking service can hire others (line-sitters) to wait in line on behalf of them. We develop a queueing-game-theoretic model that captures the interaction among customers, the line-sitting firm, and the service provider to examine the impact of line-sitting on the service provider’s revenue and customer welfare. We also contrast line-sitting with the well-known priority purchasing scheme, as both allow customers to pay extra to skip the wait. Our main results are as follows. First, we find that both accommodating line-sitting and selling priority can bring in extra revenue for the service provider, although by different means—selling priority increases revenue mainly by allowing the service provider to practice price discrimination that extracts more customer surplus, whereas line-sitting does so through demand expansion, attracting customers who would not otherwise join. Second, the priority purchasing scheme tends to make the customer population worse off, whereas line-sitting can be a win–win proposition for both the service provider and the customers. Nevertheless, having the additional option of hiring line-sitters does not always benefit customers as a whole because the demand expansion effect also induces negative congestion externalities. Finally, despite the fact that the service provider collects the priority payment as revenue but not the line-sitting payment, which accrues to the third-party line-sitting firm, we demonstrate that, somewhat surprisingly, accommodating line-sitting can raise more revenue for the service provider than directly selling priority. This paper was accepted by Charles Corbett, operations management.