Stochastic Queueing Research Articles

Theoretical study of the working process of a multivariate cabbage harvester

BACKGROUND. A multi-variant cabbage harvester of a block-modular design is proposed for small-scale farming in vegetable growing. At the same time, it is planned to complete the cabbage harvester in three versions: with an elevator, with a lower longitudinal conveyor, with an elevator and an upper longitudinal conveyor. AIMS – modeling the working process of a multivariate cabbage harvester to identify its main technological parameters that ensure the efficiency of its operation. MATERIALS AND METHODS. The working process of a multivariate cabbage harvester is presented as the functioning of a certain physical system, the state of which changes during the technological process over time depending on stochastic factors. The process of sequential transition of a system from one state to another is considered on the basis of queuing theory depending on the intensity of movement of the flow of heads of cabbage λ in the technological line of the machine and the intensity of service μ of this flow. In this work, the limiting probabilities of the model states are determined and the stochastic indicators of its functioning are calculated. RESULTS AND DISCUSSION. Based on the results of calculations of stochastic indicators of the functioning of the model, the optimal number of service personnel people was established, when the maximum probability of servicing cabbage heads can be up to 0.934. CONCLUSIONS. The workflow of a multivariate cabbage harvester is modeled as a stationary stochastic queuing process. Based on the research results, it is recommended to take the number of service personnel at the combine refining table as .

Two-types of service facilities in interconnected stochastic queueing and queueing-inventory system with marked Markovian arrival process

This article explores the performance of interconnected queueing systems and queueing-inventory systems (IQSQIS) in stochastic modeling. IQSQIS features two types of service facilities with dual service stations: one providing non-commodity service with a multi-server, and another handling commodity sales with a single server. As directed, a customer type i,i=1,2 can approach the station i,i=1,2 whose arrival pattern follows the marked Markovian arrival process (MMAP) since we assume that both service stations have an equal arrival phase. The IQSQIS gives an offer to the type-2 customer to choose type-1 service at the end of their service completion. Numerical results suggest that this option reduces customer wait times, orbit size, and overall system costs. The comparative analysis of heterogeneous and homogeneous servers in station-1 and queue-dependent and non-queue-dependent service facilities in station-2 is presented and investigated using the numerical outputs.

Technical equipment of workshop production and logistics systems. Determination of organizational and production characteristics of equipment

Two approaches are considered for determination of the required volume of workshop logistics equipment and the requirements for its performance indicators. A volumetric-analytical calculation on a deterministic model and a calculation on a stochastic queuing model are proposed. Their capabilities and areas of rational application are studied. Keywords:workshop logistics, technological infrastructure, equipment, organizational characteristics a.g.lazarenko@yandex.ru

Traffic count estimation using crowd-sourced trajectory data in the absence of dedicated infrastructure

Traffic count (or link count) data represents the cumulative traffic in the lanes between two consecutive signalised intersections. Typically, dedicated infrastructure-based sensors are required for link count data collection. The lack of adequate data collection infrastructure leads to lack of link count data for numerous cities, particularly those in low- and middle-income countries. Here, we address the research problem of link count estimation using crowd-sourced trajectory data to reduce the reliance on any dedicated infrastructure. A stochastic queue discharge model is developed to estimate link counts at signalised intersections taking into account the sparsity and low penetration rate (i.e., the percentage of vehicles with known trajectory) brought on by crowdsourcing. The issue of poor penetration rate is tackled by constructing synthetic trajectories entirely from known trajectories. The proposed model further provides a methodology for estimating the delay resulting from the start-up loss time of the vehicles in the queue under unknown traffic conditions. The proposed model is implemented and validated with real-world data at a signalised intersection in Kolkata, India. Validation results demonstrate that the model can estimate link count with an average accuracy score of 82% with a very low penetration rate (not in the city, but at the intersection) of 5.09% in unknown traffic conditions, which is yet to be accomplished in the current state-of-the-art.

Modeling and evaluating the impact of variable bus lane on isolated signal intersection performance

Dedicated Bus Lane (DBL) is a typical strategy to ensure priority for public transportation. However, when the frequency of bus departures is low, the DBL often remains vacant, reducing the efficiency of traffic utilization. Variable bus lane (VBL) strategy allows for the provision of service to social vehicles in specific scenarios, aiming to alleviate traffic congestion and improve emission efficiency at intersections. To analyze the impact of this strategy on dynamic queuing behavior and traffic efficiency at an isolated intersection, this paper proposes a multidimensional stochastic queuing model. The model incorporates various factors such as traffic demand, signal timing, bus arrival time, and the length of the variable area at intersections. By examining the steady-state distribution of queue length and calculating performance indicators, the effectiveness of VBL in improving intersection performance is evaluated. Numerical simulations have demonstrated that the proposed model accurately describes the vehicle queuing process at intersections under different conditions. Theoretical analysis confirms that the implementation of VBL strategy can effectively improve traffic efficiency at intersections and minimize the queue length of vehicles.

Stochastic queue profile estimation using license plate recognition data

Queue profile has garnered significant attention for its precise description of queue formation and dissipation at signalized intersections. License Plate Recognition (LPR) systems, recording full-sample lane-based departure times of individual vehicles, offer an ideal data source for queue profile estimation. Thus, this paper presents a stochastic queue profile estimation method utilizing LPR data. It adopts the classic Input-Output model as a baseline to reconstruct arrival and departure curves using departure information from LPR detectors at successive intersections. A pseudo departure curve is then derived from the distribution of free-flow travel time. The stochastic queue profile is further reconstructed by analyzing the relationship among these curves, accounting for potential lane changes and overtaking behavior. The proposed method is validated through empirical and simulation cases. The empirical case achieves accurate queue length estimation with a Mean Absolute Error (MAE) of 5.38 m, while the simulation case yields precise stochastic queue profiles with an MAE of 5.95 m and an average deviation of 2.40 m for queue length. Sensitivity analysis demonstrates the method's robustness across parameters like demand-to-capacity ratio, miss detection ratio, and overtaking ratio. This work holds promise for real-time signal control optimization and vehicular trajectory reconstruction.

Chat service in a multichannel system under competition where customers are boundedly rational

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.

Revolutionizing Charging Efficiency: Charging Slot Prediction using Android

Abstract: With ever- adding pollution situations and its impact on the terrain, governments are looking for alternate energy options for transportation services. fleetly depleting global oil painting reserves and rising oil painting import bills of governments are also driving the need for alternate energy sources for the transport vehicles. Transportation as a total is undoing a transformational change worldwide and Electric vehicle are the stylish result to address both pollution and oil painting import bills. Electric vehicles are getting more and more common these days. With the growing demand for Electric vehicles, the charging structure is critical for sustaining theE-Mobility services. As EVs come more marketable, there will be a need to produce an effective niche reserving system as the charging process can be time consuming and the need for further stations will be demanding. Developed the Framework and Architecture of the Next- Generation Communication grounded Online Evs Charging niche reserving at Charging Station. We erected the stochastic queuing model for Evs in the charging station. We formulated the objective function of EV’s charging at charging points in charging stations to determine the optimal charging time, minimum charging cost, least distance, minimum queuing detention and optimal duration for particular charging places. The proposed model of the booking system is designed to produce a cost effective and effective system. The proposed garçon- grounded real- time cast charging structure avoids staying times and its scheduling operation efficiently prevents the EV from halting on the road due to battery drain out.

An integrated strategy-based game-theoretic model and decentralized queueing system for mobile multi-robot task coordination

Autonomous multi-robot systems are restricted by their coordination ability with one another. Coordination entails the simultaneous division of tasks, the assignment of tasks, the formation of teams, the scheduling of tasks, and the routing of tasks. These activities are called task planning. Task planning is essential for the execution of task allocation problems in multi-robot systems. This study investigates the application of a decentralized queuing mechanism for task coordination in the context of mobile robots. Heuristic and strategic coordination strategies are used in developing the proposed system. The completion time and the distance traveled to process a demand are the two metrics used to evaluate the performance of robots in their respective operation field. The robots that used the stochastic queueing strategy achieved competitive results with those of the other robots.

A matrix-analytic method for the steady state analysis of a Markovian queueing system with scrap items

This paper studies a mathematical analysis of scrap item-based single server stochastic queueing, which consists of storage space for the scrap items collected from the customers. The primary customers arrive in the finite waiting hall to sell scrap or recyclable products. The server collects the customer’s scrap items and stores them in the storage space. If the waiting hall is full whenever the primary customers arrive, they can join an infinite orbit or permanently leave the system under the Bernoulli trial. Whenever the orbital customers find at least one free space in the waiting hall, they can enter it. The server begins vacation once the storage reaches its maximum capacity or no more customers exist in the waiting hall. The server switches to regular mode whenever at least one free space exists in the storage, and one customer is in the waiting hall. Otherwise, he is not working in vacation mode. Customers in the waiting hall may lose their patience after waiting for a long time and may either enter orbit or leave the system permanently. Whenever the storage level (scrap item level) reaches a certain limit, the server places the procurement order for sending the items to the recycling unit or re-manufacturer. The system’s steady-state probability vector and stability condition have been derived by truncating the orbit at a point. Various system performances, such as expected total cost, profit cost, and waiting time for customers in the waiting hall, are defined, and a numerical study is carried out to analyze the performance of the proposed model. The numerical findings indicate that disabling working in vacation mode increases waiting time and total cost while working in vacation mode results in minimized waiting time and total cost.

Dynamic Routing in Stochastic Urban Air Mobility Networks: A Markov Decision Process Approach

Urban air mobility (UAM) is an emerging concept in short-range aviation transportation, where the aircraft will take off, land, and charge their batteries at a set of vertistops, and travel only through a set of flight corridors connecting these vertistops. We study the problem of routing an electric aircraft from its origin vertistop to its destination vertistop with the minimal expected total travel time. We first introduce a UAM network model that accounts for the limited battery capacity of aircraft, stochastic travel times of flight corridors, stochastic queueing delays, and a limited number of battery-charging stations at vertistops. Based on this model, we provide a sufficient condition for the existence of a routing strategy that avoids battery exhaustion. Furthermore, we show how to compute such a strategy by computing the optimal policy in a Markov decision process, a mathematical framework for decision-making in a stochastic dynamic environment. We illustrate our results using a case study with 29 vertistops and 137 flight corridors.

Health resource allocation method at cordon sanitaire for pandemic control and prevention

<p style='text-indent:20px;'>The outbreak of COVID-19 and its variants has profoundly disrupted our normal life. Many local authorities enforced cordon sanitaires for the protection of sensitive areas. Travelers can only cross the cordon after being tested. This paper aims to propose a method to determine the optimal deployment of cordon sanitaires in terms of minimum queueing delay time with available health testing resources. A sequential two-stage model is formulated where the first-stage model describes transportation system equilibrium to predict traffic flows. The second-stage model, a nonlinear integer programming, optimizes health resource allocation along the cordon sanitaire. This optimization aims to minimize the system's total delay time among all entry gates. Note that a stochastic queueing model is used to represent the queueing phenomenon at each entry link. A heuristic algorithm is designed to solve the proposed two-stage model where the Method of Successive Averages (MSA) is adopted for the first-stage model, and a genetic algorithm (GA) with elite strategy is adopted for the second-stage model. An experimental study is conducted to demonstrate the effectiveness of the proposed method and algorithm. The results show that these methods can find a good heuristic solution, and it is not cost-effective for authorities to keep adding health resources after reaching a certain limit. These methods are useful for policymakers to determine the optimal deployment of health resources at cordon sanitaires for pandemic control and prevention.</p>

Joint Learning and Control in Stochastic Queueing Networks with Unknown Utilities

We study the optimal control problem in stochastic queueing networks with a set of job dispatchers connected to a set of parallel servers with queues. Jobs arrive at the dispatchers and get routed to the servers following some routing policy. The arrival processes of jobs and the service processes of servers are stochastic with unknown arrival rates and service rates. Upon the completion of each job from dispatcher u n at server s m , a random utility whose mean is unknown is obtained. We seek to design a control policy that makes routing decisions at the dispatchers and scheduling decisions at the servers to maximize the total utility obtained by the end of a finite time horizon T . The performance of policies is measured by regret, which is defined as the difference in total expected utility with respect to the optimal dynamic policy that has access to arrival rates, service rates and underlying utilities. We first show that the expected utility of the optimal dynamic policy is upper bounded by T times the solution to a static linear program, where the optimization variables correspond to rates of jobs from dispatchers to servers and the feasibility region is parameterized by arrival rates and service rates. We next propose a policy for the optimal control problem that is an integration of a learning algorithm and a control policy. The learning algorithm seeks to learn the optimal extreme point solution to the static linear program based on the information available in the optimal control problem. The control policy, a mixture of priority-based and Joint-the-Shortest-Queue routing at the dispatchers and priority-based scheduling at the servers, makes decisions based on the graphical structure induced by the extreme point solutions provided by the learning algorithm. We prove that our policy achieves logarithmic regret whereas application of existing techniques to the optimal control problem would lead to Ω(√ T )-regret. The theoretical analysis is further complemented with simulations to evaluate the empirical performance of our policy.

Irrigation scheduling of pressurized irrigation networks for minimizing energy consumption

AbstractAlthough pressurized irrigation systems can increase water use efficiency, the energy requirements of these irrigation systems are much higher than those of gravity‐fed systems in water transport and distribution. To reduce irrigation energy consumption, this research introduces two factors influencing energy consumption: branch pipe assigned queue and branch pipe assigned times. The traditional single water distribution and sequential queue are optimized as multiple water distributions and stochastic queues. Combined with traditional motor frequency optimization, eight scheduling scenarios are established based on these three optimization factors and compared with the original scenario. Next, this study optimizes the discharge of all hydrants for each scenario using a genetic algorithm with the same framework and operational process. Predictions and experiments in a case study in eastern China indicated that only optimizing the branch pipe assigned queue or times cannot significantly reduce energy consumption, while an energy‐savings rate of 8% can be achieved by simultaneously optimizing the branch pipe assigned queue and times. In addition, the energy savings rate of only optimizing the motor operating frequency is 11%. However, an energy‐saving rate of 19% can be obtained by combining branch pipe‐assigned times optimization with motor frequency optimization.

K-Nearest Neighbor Queues with Delayed Information

In this paper, we analyze a model called the k-nearest neighbor queue with the possibility of having delayed queue length feedback. We prove fluid limits for the stochastic queueing model and show that the fluid limit converges to a system of delay differential equations. Using the properties of circulant matrices, we derive a closed form expression for the value of the critical delay, which governs whether the delayed information will induce oscillations or a Hopf bifurcation in our queueing system.

Ride-hail to ride rail: Learning to balance supply and demand in ride-hailing services with intermodal mobility options

Growing spatiotemporal imbalance in supply and demand in ride-hailing services has been arousing concern. A variety of measures in the perspective of ride-hailing services per se is studied. However, approaching the imbalance problem in the broader perspective of intermodal mobility, which integrates different modes of passenger transportation in a single trip and aims to overcome limitations of any unimodal mobility, remains to be explored. This paper aims to investigate the potential of introducing intermodal mobility options to balance ride-hailing services. We first identify the importance of the availability decision on intermodal mobility options. Then we formulate the availability decision problem as a Markov decision process (MDP). Due to its convoluted system dynamics and large state space, we cast the intractable MDP into a reinforcement learning (RL) problem to approximately learn the availability policy. To stabilize the learning processes, we model the intermodal ride-hailing services as a stochastic queueing network and tailor a family of state-of-the-art RL algorithms to iteratively evaluate and improve the availability policy. Lastly, we test this optimization framework in a large-scale intermodal mobility scenario calibrated with real-world trip data. Results show that the learned availability policy can significantly dissipate riders’ queue and improve the service rates towards more balanced supply and demand.

Modelling vaccination capacity at mass vaccination hubs and general practice clinics: a simulation study

BackgroundCOVID-19 mass vaccination programs place an additional burden on healthcare services. We aim to model the queueing process at vaccination sites to inform service delivery.MethodsWe use stochastic queue network models to simulate queue dynamics in larger mass vaccination hubs and smaller general practice (GP) clinics. We estimate waiting times and daily capacity based on a range of assumptions about appointment schedules, service times and staffing and stress-test these models to assess the impact of increased demand and staff shortages. We also provide an interactive applet, allowing users to explore vaccine administration under their own assumptions.ResultsBased on our assumed service times, the daily throughput for an eight-hour clinic at a mass vaccination hub ranged from 500 doses for a small hub to 1400 doses for a large hub. For GP clinics, the estimated daily throughput ranged from about 100 doses for a small practice to almost 300 doses for a large practice. What-if scenario analysis showed that sites with higher staff numbers were more robust to system pressures and mass vaccination sites were more robust than GP clinics.ConclusionsWith the requirement for ongoing COVID-19 booster shots, mass vaccination is likely to be a continuing feature of healthcare delivery. Different vaccine sites are useful for reaching different populations and maximising coverage. Stochastic queue networks offer a flexible and computationally efficient approach to simulate vaccination queues and estimate waiting times and daily throughput to inform service delivery.

Utilizing partial flexibility to improve emergency department flow: Theory and implementation

AbstractEmergency departments (EDs) typically have multiple areas where patients of different acuity levels receive treatments. In practice, different areas often operate with fixed nurse staffing levels. When there are substantial imbalances in congestion among different areas, it could be beneficial to deviate from the original assignment and reassign nurses. However, reassignments typically are only feasible at the beginning of 8–12‐h shifts, providing partial flexibility in adjusting staffing levels. In this work, we propose a stochastic queueing network model of patient flow in the ED and study an associated fluid control problem to guide the reassignment decision for two types of nursing staff. We propose a heuristic solution approach and investigate its performance both analytically and using simulation. Analytical results and simulation experiments suggest a significant reduction of waiting times in parameter regimes relevant to the ED setting. We further implement the staffing approach at a large ED. This pilot study highlights several challenges of implementing operational interventions in the ED, including the difficulty of establishing a clean statistical environment in such setting. Despite these challenges, we find that guiding reassignment decisions using our approach is associated with significant improvements to patient flow including a reduction in average total ED length‐of‐stay of 1.7 h.

TauSSA

In this paper, we present TauSSA, a discrete-event simulation tool for stochastic queueing networks integrated in the LINE solver. TauSSA combines Gillespie's stochastic simulation algorithm with tau leaping, a methodology for optimistic simulation acceleration. Although tau leaping is frequently used in chemical reaction network simulation, it has so far found limited application in queueing theory. TauSSA offers one of the very first attempts to make this method broadly applicable to analyze extended queueing network models, which include class switching, fork-join, and non-exponential service and arrival distributions. We conceptualize various strategies for handling ordering and illegal states in tau leaping that arise specifically within queueing network models, and compare their performance through numerical experiments. Our main finding is that strategies that sort events based on the network topological order incur a better trade-off between speedup and approximation error.

Characterizing the dynamics and uncertainty of queues at signalized intersections with left-turn bay

In most signalized intersections, in order to solve the problem of insufficient road space, left-turn bays are commonly set up at intersections with a shared through and left-turn lane. However, this design tends to result in the potential queue overflow and blockage problems, which further make the discharge process of either left-turn vehicles or through vehicles at the intersections to be interrupted unexpectedly during their respective green phase. As a result, the queueing processes of vehicles present high nonlinearity and uncertainty during a signal cycle. In this paper, a stochastic queueing model is proposed to characterize the dynamics and uncertainty of queues at signalized intersections with a left-turn bay. The proposed model takes full account of the random interaction between the through movement and the left-turn movement under the influence of overflow and blockage of queues. We obtain some average performance indicators as well as the signal-state-dependent dynamic performance measure of queues and its variance at any given time point within a signal cycle. The proposed analytical model is validated against the VISSIM simulation model under different scenarios; the results show a good degree of agreement. In addition, in order to systematically determine the queue dynamics and uncertainty, we also conduct a series of numerical simulations to quantitatively capture the queue characteristics of vehicles at signalized intersections with left-turn bay by considering possible factors.