Nonstationary Queueing Research Articles

Empowering the Capillary of the Urban Daily Commute: Battery Deployment Analysis for the Locker-Based E-bike Battery Swapping

In densely populated Asian countries, e-bikes have become a new supernova in daily urban transportation. To facilitate the operations of e-bike-based mobility, the present paper studies the management of the battery deployment for the e-bike battery-swapping system, where the unique features of e-bike riding are considered. Given the pedal-assisted mode, e-bike users could abandon waiting and return to the station later on without too much range anxiety. However, because of the time-varying nature of the customer arrival and the complicated user behaviors, the battery quantity at each station is altered to guarantee the designated service level. However, little research has been done on the operations management of the e-bike battery-swapping system. To bridge the gap, we propose a nonstationary queueing network model to characterize the customer behaviors during the battery-swapping service. Then we develop a closed-form delayed infinite-server fluid approximation for the battery deployment of the one-time-loop scenario under various quality-of-service targets. In addition, we handle the infinite-time-loop scenario with the simulation-based iterative staffing algorithm. In the simulation study, we observe that the proposed battery deployment algorithms can help stabilize the system performance in terms of abandonment probability and expected delay in the face of time-varying demand and complex customer behaviors. Moreover, we reveal that the number of return loops correlates with the service level targets on the battery deployment decision. Furthermore, a time gap exists between the demand and the optimal battery deployment, making proactive battery management in the system possible. Funding: This work was supported by the National Natural Science Foundation of China [Grants 72271222, 71871203, 71872093, 72271137, L1924063], and the National Social Science Fund of China [Grant 21&ZD128]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0132 .

An approximate approach to fuzzy stochastic differential equations under sub-fractional Brownian motion

In this paper, we introduce fuzzy stochastic differential equations (FSDEs) driven by sub-fractional Brownian motion (SFBM) which are applied to describe phenomena subjected to randomness and fuzziness simultaneously. The SFBM is an extension of the Brownian motion that retains many properties of fractional Brownian motion (FBM), but not the stationary increments. This property makes SFBM a possible candidate for models that include long-range dependence, self-similarity, and non-stationary increments which is suitable for the construction of stochastic models in finance and non-stationary queueing systems. We apply an approximation method to stochastic integrals, and a decomposition of the SFBM to find the existence and uniqueness of the solutions.

The “complex probabilities” balance principle for non-Markov processes modeling

This paper presents the principle of “complex probabilities” balance, based on the description of the stochastic process not in the time, but in the complex domain, which allows developing models of non-stationary queuing systems with arbitrary probabilities distributions of the requests and their servicing time, taking into account random or deterministic time delays. A system of balance equations in the complex domain was compiled and solved using Laplace images. Performed an inverse Laplace transform to move from images to probabilities in the time domain. Presented models for acyclic and cyclic stochastic processes with arbitrary distributions of time points between incoming requests and their service. Given calculation examples. Recommendations for the further application of the principle of balance of “complex probabilities” are given.

A Queuing Network Model of a Multi-Airport System Based on Point-Wise Stationary Approximation

A multiple-airport system (MAS) consists of more than two airports in a metropolitan area under a large block of terminal airspace that is managed by one or two air traffic control units. When the capacity of an airport or of the terminal airspace drops, flight delays occur in the MAS system. A quick estimation and predication of traffic congestion in the MAS is important yet challenging. This paper aims to develop a queuing network model of MAS using point-wise stationary queues. The model analyzes the changes of non-stationary queues under the principle of flow conservation to capture flight delay propagation in the system. Regression analyses are performed to examine the relationship between the arrival and departure efficiencies of different airports. The model is validated with the data of Guangdong–Hong Kong–Macao Greater Bay Area airports. Simulation results show that the model can effectively estimate flight delays in the MAS.

Calibrating nonstationary queueing network models

Calibrating nonstationary queueing network models

Dynamic Rebalancing Strategy in Free-Float Bicycle Sharing Systems: Orbit Queues and Two-Sided Matching

In populous metropolitan areas, the free-floating bicycle-sharing system (FFBSS) acts as an innovative urban mobility as a service, which provides an ease-of-use feature and extra flexibility in contrast to the traditional shared bicycles with docks. In consideration of customer behaviors, such as abandonment and retrial, which occur in FFBSS, a redistribution strategy for shared bicycles among different user-density locations is presented with an aim to diminish the total operational cost while enhancing the overall service level. To formulate the user and multitype shared bicycle–arrival patterns as nonhomogeneous queues, our results provide a tractable analytical paradigm for a time-varying balancing strategy for FFBSS. The bicycle variation at each virtual zone after each redistribution is determined via a nonstationary queueing model, in which the service time, patience time, and research delay are all subject to general distribution. Then, the bicycle-deployment strategy is evaluated with respect to average queueing length and abandonment rate during a normal workday based on a tailored nonhomogeneous probabilistic matching queue. To verify the efficacy and cost-effectiveness of the proposed bicycle-redistribution strategy, multiple simulation runs are conducted with respect to various times of the day. It shows that the resulting optimal rebalancing strategy is batch-based in synchrony with the time heterogeneity in the traffic demand. Furthermore, several managerial insights are provided to shed light on the rule of thumb in practical FFBSS redistribution coordination.

A non-stationary queuing approach and genetic algorithm for the optimisation of truck appointment system in a container terminal in Casablanca City

Due to the increasing container traffic, many terminals face a considerable number of truck arrivals. This situation leads to congestion problems at the gates and generates serious air pollution while decreasing terminal efficiency. To consider this issue, many terminals use a truck appointment system. However, the latter should take, necessarily, into account the terminal's local conditions to ensure a satisfying performance. In the present work, one proposes an appointment model to control truck arrivals in one of the busiest terminals in Morocco. The model is based on an improvement of the approximation approach related to the queue length estimation. The treatment adopts a genetic algorithm with a novel testing scenarios highlighting more the solution performances by crossing several basic existing scenarios. Then, some numerical experiments are conducted based on literature works data to calibrate the model and ensure its accuracy. Finally, the best configuration was approved for the local terminal.

Weighted Dyck paths and nonstationary queues

We consider a model for a queue in which only a fixed number N of customers can join. Each customer joins the queue independently at an exponentially distributed time. Assuming further that the service times are independent and follow an exponential distribution, this system can be described as a two-dimensional Markov chain on a finite triangular region of the square lattice. We interpret the resulting random walk on as a Dyck path that is weighted according to some state-dependent transition probabilities that are constant along one axis, but are rather general otherwise. We untangle the resulting intricate combinatorial structure by introducing appropriate generating functions that exploit the recursive structure of the model. This allows us to derive an explicit expression for the probability mass function of the number of customers served in any busy period (equivalently, of the length of any excursion of the Dyck path above the diagonal) as a weighted sum with alternating sign over a certain subclass of Dyck paths.

Strong Embeddings for Transitory Queueing Models

In this paper, we establish strong embedding theorems, in the sense of the Komlós-Major-Tusnády framework, for the performance metrics of a general class of transitory queueing models of nonstationary queueing systems. The nonstationary and non-Markovian nature of these models makes the computation of performance metrics hard. The strong embeddings yield error bounds on sample path approximations by diffusion processes in the form of functional strong approximation theorems.

Non-stationary poisson model of continuously functioning queuing system

The study of non-stationary queuing systems is related to their important applications in computing systems. Algorithms for calculating non-stationary queuing systems are quite complex. Nevertheless, the development of modelling of production processes and communications, trade processes and consumer services requires the development of methods for calculating such queuing systems. In this regard, we should mention the currently actively developing state programs ”Smart city”, ”Digitalization of the economy” which require the development and specification of methods for calculating non-stationary queuing systems. Therefore, it is necessary to build non-stationary queuing models in such a way that their calculation would be quite simple and convenient for computing. In this paper, this can be achieved by assuming that the service time is deterministic, the input non-stationary flow of customers is Poisson, and that there are an infinite number of devices that exclude the customers from being in the queue.

Research impact of queue choosing policy on macroscopic characteristics in multichannel non-stationary queue system

A multichannel non-stationary queuing system model of stadium checkpoint system studied. Input flow of model is based on statistical information of visitors flows from football matches in the Russian Federation. An algorithm choosing the shortest queue for implementing a policy of choosing a non-random queue presented. Result of comparing different policies described for input rate like real ones. The result is substantiated by comparing the functioning of the stationary QS with different queue selection policies in 3 modes: underload, load, overload.

Computational approach for researching visitor flow dynamics at public venues and mass gathering events

Visitor flow dynamics at public venues has been studied by using mathematical models of the non-stationary queuing system and discrete-event modelling. Computational approach for research visitor flows quantitative characteristics is described. The dependence of input rate from time in non-stationary queuing system model is like the dependencies of rate of visitors to football matches. Quantitative characteristics are waiting line length and waiting time (time spend in queue) from time for different parameters of the input rate and the service rate device. It is proven that the maximum values of the studied characteristics and the corresponding time values are described by deterministic functions that depend on the maximum intensity of visitor flow and the average service speed. The form of these functions is well described.

A non-stationary queuing approach and Genetic Algorithm for the optimization of Truck Appointment System in a Container Terminal in Casablanca City

A non-stationary queuing approach and Genetic Algorithm for the optimization of Truck Appointment System in a Container Terminal in Casablanca City

QoS-Aware Capacity Planning of Networked PEV Charging Infrastructure

Plug-in electric vehicle (PEV) charging infrastructure is necessary to accommodate the rapid increase in PEV penetration rate. Capacity planning of PEV charging infrastructure (EVCI) must ensure not only a satisfactory charging service for PEV users but also a reliable operation of the power grid. In this paper, we propose a quality-of-service (QoS) aware capacity planning of EVCI. In particular, the proposed framework accounts for the link between the charging QoS and the power distribution network (PDN) capability. Towards this end, we firstly optimize charging facility sizes to achieve a targeted QoS level. Then, we minimize the integration cost for the PDN by attaining the most cost-effective allocation of the energy storage systems (ESSs) and/or upgrading the PDN substation and feeders. Additionally, we capture the correlation between the occupation levels of neighboring charging facilities and the blocked PEV user behaviors. We model the EVCI as a queuing network with finite capacity, and utilize the non-stationary queuing models to study the temporal variability of the PEV charging demand. A network of charging facilities is used to demonstrate the effectiveness of the proposed framework.

IMPROVING THE SHIFT-SCHEDULING PROBLEM USING NON-STATIONARY QUEUEING MODELS WITH LOCAL HEURISTIC AND GENETIC ALGORITHM

We improve the shift-scheduling process by using nonstationary queueing models to evaluate schedules and two heuristics to generate schedules. Firstly, we improved the fitness function and the initial population generation method for a benchmark genetic algorithm in the literature. We also proposed a simple local search heuristic. The improved genetic algorithm found solutions that obey the delay probability constraint more often. The proposed local search heuristic also finds feasible solutions with a much lower computational expense, especially under low arrival rates. Differently from a genetic algorithm, the local search heuristic does not rely on random choices. Furthermore, it finds one final solution from one initial solution, rather than from a population of solutions. The developed local search heuristic works with only one well-defined goal, making it simple and straightforward to implement. Nevertheless, the code for the heuristic is simple enough to accept changes and cope with multiple objectives.

On the Rate of Convergence and Limiting Characteristics for a Nonstationary Queueing Model

Consideration is given to the nonstationary analogue of M / M / 1 queueing model in which the service happens only in batches of size 2, with the arrival rate λ ( t ) and the service rate μ ( t ) . One proposes a new and simple method for the study of the queue-length process. The main probability characteristics of the queue-length process are computed. A numerical example is provided.

Assessing uncertainty and risk in an expeditionary military logistics network

Uncertainty is rampant in military expeditionary operations spanning high-intensity combat to humanitarian operations. These missions require rapid planning and decision-support tools to address the logistical challenges involved in providing support in often austere environments. The US Army’s adoption of an enterprise resource planning system provides an opportunity to develop automated decision-support tools and other analytical models designed to take advantage of newly available logistical data. This research presents a tool that runs in near-real time to assess risk while conducting capacity planning and performance analysis designed for inclusion in a suite of applications dubbed the Military Logistics Network Planning System, which previously only evaluated the mean sample path. Logistical data from combat operations during Operation Iraqi Freedom drive supply requisition forecasts for a contingency scenario in a similar geographic environment. A nonstationary queueing network model is linked with a heuristic logistics scheduling methodology to provide a stochastic framework to account for uncertainty and assess risk.

Исследование влияния случайных вариаций интенсивности входного потока на макроскопические показатели нестационарной СМО

Исследование влияния случайных вариаций интенсивности входного потока на макроскопические показатели нестационарной СМО

Research of impact input rate random variations on macroscopic characteristics of non-stationary queuing system

The results of research of input stream rate random variations influence on the macroscopic characteristics of a nonstationary queuing system (NQS) are discussed in this paper. Statistical information obtained during the football match between the football clubs “Krylia Sovetov” and “Dynamo” at the stadium “Metallurg” in Samara is available. The characteristics of the stochastic component of the variation in the input rate were chosen on the basis of this information. The probability density function and the cumulative distribution function of random variations in the input rate of applications were estimated using the Rosenblatt-Parzen approximation. NQ’s characteristics was studied such as the maximum queue length, the maximum waiting time in the queue, the time point at which the maximum queue length is reached, and the time point at which waiting time in the queue the longest, the number of visitors who entered at the time of the match beginning, the time needed to service the entire queue. The results of the statistical simulation shown that taking into account the random component of the variation input rate does not affect this macroscopic characteristics.

About influence of input rate random part of nonstationary queue system on statistical estimates of its macroscopic indicators

A model of the non-stationary queuing system (NQS) is described. The input of this model receives a flow of requests with input rate λ = λdet(t) + λrnd(t), where λdet(t) is a deterministic function depending on time; λrnd(t) is a random function. The parameters of functions λdet(t), λrnd(t) were identified on the basis of statistical information on visitor flows collected from various Russian football stadiums. The statistical modeling of NQS is carried out and the average statistical dependences are obtained: the length of the queue of requests waiting for service, the average wait time for the service, the number of visitors entered to the stadium on the time. It is shown that these dependencies can be characterized by the following parameters: the number of visitors who entered at the time of the match; time required to service all incoming visitors; the maximum value; the argument value when the studied dependence reaches its maximum value. The dependences of these parameters on the energy ratio of the deterministic and random component of the input rate are investigated.