Queueing Problems Research Articles

Stationary analysis of the shortest queue problem

A simple analytical solution is proposed for the stationary loss system of two parallel queues with finite capacity K, in which new customers join the shortest queue, or one of the two with equal probability if their lengths are equal. The arrival process is Poisson, service times at each queue have exponential distributions with the same parameter, and both queues have equal capacity. Using standard generating function arguments, a simple expression for the blocking probability is derived, which as far as we know is original. Using coupling arguments and explicit formulas, comparisons with related loss systems are then provided. Bounds are similarly obtained for the average total number of customers, with the stationary distribution explicitly determined on $$\{K, \ldots , 2K \}$$ , and elsewhere upper bounded. Furthermore, from the balance equations, all stationary probabilities are obtained as explicit combinations of their values at states (0, k) for $$0 \le k \le K$$ . These expressions extend to the infinite capacity and asymmetric cases, i.e., when the queues have different service rates. For the initial symmetric finite capacity model, the stationary probabilities of states (0, k) can be obtained recursively from the blocking probability. In the other cases, they are implicitly determined through a functional equation that characterizes their generating function. The whole approach shows that the stationary distribution of the infinite capacity symmetric process is the limit of the corresponding finite capacity distributions. Finally, application of the results for limited capacity to mean-field models for large bike-sharing networks with a local JSQ policy is briefly discussed.

Establishing a three-step model of designing the polling stations for shorter queue and smaller waiting time: a case study using computer simulation

ABSTRACTThis article tries to address the issue of lengthy queues at the polling stations during elections using simulation. It is known that the long queues may harm the voting experience and turn voters away. Moreover, the queuing problems have been repeating in different countries. We tried to use computer simulation to address this problem, with a polling station in the 2016 Hong Kong Legislative Election as the study target. We found and addressed the bottlenecks of the station successfully by reallocating the resources in the polling station in the simulations. Based on our results, we establish a three-step model for shortening the polling stations queues and waiting time more generally.

Analysis of Queue System to Improve the Quality of Service in Gra PARI Telkomsel Banda Aceh

The problem of queue is how to balance the waiting costs and preventing cost of the queue to gain maximumprofit. Queuing analysis can be done by knowing arrival distribution, service time distribution, queue discipline, andqueuing model. The purpose of the paper is to calculate the optimal number of servers so users do not wait too longin line, know the queue model in accordance with queuing conditions, and improve the efficiency and performance ofservers. In processing data, we are using analysis of distribution and M/G/s queuing method. The result of queuingsystem performance based on analysis and calculation shows that the queue model is (M/ G/ 8) :( FIFO/∞/∞ ). Theaverage time the customer waits in the queue is 17.17 minutes and the average service time per customer is 14.39 minutes.Customer is served for 14.39 minutes but before being served it must wait for 17.17 minutes. This condition indicatesthat waiting time is more than serving time. The system utility level at Gra PARI Banda Aceh is 95.5%, it indicatesthat utility is so high that it should be repaired to optimize the utility. The waiting time in the queue is 17.17 minutes,the waiting time in the system is 31.66 minutes, and the queue length in the system is 17 people. This will make thebottleneck of customers who will queue before being served. Based on the analysis of the new design, it is known thatthe addition of 1 server from 8 to 9 servers is the most optimal solution. The addition of 1 server can reduce the systemutility up to 84.9% and waiting time in the queue is 2.91 minutes, waiting time in the system 17.4 minutes, and the queuelength in the system 9 people. Cost analysis also shows the solution can reduce the cost of queue, so the optimal modelhas been found in this study. Therefore, optimal queuing conditions can help companies to improve service quality.

EXPERIENCE IN IMPLEMENTATION OF THE PROJECT «POLYCLINIC WITHOUT QUEUES» IN THE TOMSK REGIONAL ONCOLOGY CENTER

The problem of queues in polyclinics and hospitals is a deterrent to ensuring access to oncological care. In order to optimize anti-cancer control there were shortened timelines both for the diagnosis and the beginning of the specific treatment. Since 2012, in the Tomsk Regional Oncology Center a new concept of the polyclinic organization on the profile of «oncology» was formed. The key aspects of this concept were: 1) standardization of the medical staff work; 2) the rules for the routing of patients with the execution of the first medical appointment booking for visiting doctor through the registry, for the second visit - by an oncologist and with the differentiation of the streams of patients for medical care in the framework of MHI and medical services on a fee basis; 3) intensification of the provision with outpatient specialized care with the staff reinforcement: the regime of the polyclinic is organized in two shifts and 6 days a week, the number of doctors and nurses is increased by 60.8%, the number of medical registrars - by 7 times. To coordinate their work, the position of the senior medical registrator was introduced; 4) modernization of all workplaces of doctors, nurses, medical registrars with the provision of modern medical equipment, communications and information support; 5) logistics of the registry: the division of its zone into a «front office» - were the office-medical registrator communicates with patients only as «face-to-face» and «call center» - with a dialogue by phone. 6) quality control of the clinic work with evaluation of video and audio recordings of interaction between registrars and patients, visitors questioning. 7) the reform of the oncological consultation on an ongoing basis regulations; 8) increasing the comfort of waiting for patients with the organization of comfortable seats, coolers with glasses, air conditioners, corporate identity and logo. The result of the implemented activities was a reduction in the start of specialized treatment by 68.3%, increased coverage of antitumor therapy by 16.4%, including among rural residents. This contributed to the improvement of the situation in a number of indices: the increase in the share of early forms of malignant neoplasms, active detectability by 21.6% and 164.7%, respectively, a decrease in one-year mortality rate, neglect by 25.2% and 8.6%, respectively. Population satisfaction with the provision of cancer care increased.

Reduction of Waiting Time in Logistics Centers by Trailer Yards

This paper provides a mathematical model and a contribution to the discussion of the problem of queues and waiting times at loading/unloading ramps as a part of transportation networks. As a central point, the paper investigates how the waiting time can be reduced by adding additional empty trailers to the logistics system, and under the assumption that the trailers can be exchanged by the drivers. The proposed model can be used for further investigations and estimates in the cost benefit analysis, on the reduction of CO2 emission and other related issues.

Forecasting Air-to-Ground Munitions Demand in Military Operations Using Markov-Modulated Poisson Process

In this paper, we examine the problem of modeling and forecasting the air-to-ground munitions demand in military operations. We consider a continuous state space time series approach and we model the munitions demand as a non-homogeneous Poisson process with intensity function that depends on a continuous-time Markovian operational tempo process. This approach is known in stochastic process as a Markov-Modulated Poisson Process (MMPP) and has successfully been applied to queuing and communication network problems. We consider four operational tempo states, corresponding to the different intensity levels of military operations. We apply the maximum likelihood estimation method to derive the MMPP model parameters, assuming that the Markov chain states are observed. We illustrate the method with an example using two time series data sets of different trends. This study provides military planners with a decision support method for forecasting munitions requirements in the face of abrupt changes in demand. An extension of the model would be to use Bayesian approach for inferring the MMPP parameters through application of a Forward-Backward type algorithm to capture potential hidden states.

Priority Systems at Theme Parks from the Perspective of Managers and Customers

Waiting times are becoming an increasingly important customer-experience challenge in theme parks. The seemingly ever-present problem of long queues for rides and attractions is being tackled by the development of priority systems. These innovations allow customers to join an alternative queue that bypasses the congestion faced by regular customers. In other words, by paying extra, customers can purchase the right to be served sooner. Such systems are becoming prevalent, but there is a lack of empirical research into priority systems at theme parks in the academic and management literature, which suggests that in-depth empirical analysis is necessary in order to understand the consumer decision-making process when making this purchase. This article examines priority systems at theme parks both from the viewpoint of park management and of customers. To address this gap, we surveyed nearly 1,000 customers at a major theme park in Spain and conducted semi-structured interviews with 10 theme park managers to assess both customer and manager attitudes towards waiting generally and priority systems specifically. Our results reveal that these priority systems facilitate market segmentation. When theme parks offer this or option, different groups of customers are identified based on their attitudes: those who wait in regular lines and those who are willing to pay to avoid lines. Thus, this innovative system creates an important source of new revenue while also improving the customer experience by reducing waiting times and minimizing congestion. Following a discussion of our results, we offer practical recommendations to managers who need to address the challenges of waiting times in theme parks and wish to improve both profits and customer experiences by implementing a priority system. People nowadays like to be together not in the oldfashioned way of, say, mingling on the piazza of an Italian Renaissance city, but, instead, huddled together in traffic jams, bus queues, on escalators and so on. It's a new kind of togetherness which may seem totally alien, but it's the togetherness of modern technology.

Detect the Sybil Attack by using GPSR Protocol

is a vehicular ad hoc network. This is a part of mobile ad hoc network. VANETs also called as intelligent transportation system (ITS) in which vehicles convey to give auspicious data. Their point is to give security, information and management of network. Rather than of their numerous advantages vehicular network is inclined to various attacks. Like prankster attack, denial of service attack, black hole attack, alteration attack, fabrication attack, man in the middle attack, timing attack, illusion attack and so forth. In this research we will attempt to uproot Sybil attack in which node creates its multiple identities and it can be affected by various ways. In previous research researcher judge the estimated physical measurement on the bases of three parameter but it may also be the case that message delay occur due to various another reasons like queue problem, congestion problem, accidental problem, so this approach is not accurate due to absence of GPS. According to this work GPSR protocol will be used through which physical measurement of vehicle can be verified at any time and GPS coordinates will be compared. If GPS coordinate matched then there is no attack. KeywordsVanet's, WSN, GPSR, GPS

Long queue estimation for signalized intersections using mobile data

Queue length is one of the key measures in assessing arterial performances. Under heavy congestion, queues are difficult to estimate from either fixed-location sensors (such as loop detectors) or mobile sensors since they may exceed the region of detection, which is defined as long queue in the literature. While the long queue problem has been successfully addressed in the past using fixed-location sensors, whether this can be done using mobile traffic sensors remains unclear. In this paper, a queue length estimation method is proposed to solve this long queue problem using short vehicle trajectories obtained from mobile sensors. The method contains vehicle trajectory reconstruction models to estimate the missing deceleration or acceleration process of a vehicle. Long queue estimation models are then developed using the reconstructed vehicle trajectories. The proposed method can provide estimates of the queue profile and the maximum queue length of a cycle. The method is tested in a field experiment with reasonable results.

Economic Solutions to Medical Queuing: A Policy Model with Random Sampling

The paper shows that the formulation of economic criteria and their application to facilitate resolving social queues in the health sector can bring about higher social welfare levels and can be superior to, current practices of allocating scarce public services on the many demanders of the service. The model makes use of the Quality Adjusted Life Years, QALY, as an indication of the effectiveness of medical attention in terms of gained life years in good health after treatment. The model introduces the lifetime earnings of patients and links them to the QALY. Selection of patients to be treated is based on productivity as represented by the prospective income earnings of the queuing patients. Random sampling simulation (i.e. Monte Carlo method) show that patient selection based on maximizing discounted lifetime earnings would release resources that can be used for treating more patients and thus reduce waiting time, and reduce the overall cost pressures. The results will show a convergence between efficiency and fairness goals.Although the application is for the health sector in the Netherlands around 2000, the problem of social queues is not unique for health services, or developed countries. Social queues can be observed in specific educations, subsidised housing, unemployment retraining, poverty alleviation, and for many public goods in predominantly centrally planned economies. The model is sufficiently general so as to apply to more areas of social queuing than health services and to various countries and periods as well.

Simulation-Based Approximate Policy Iteration with Generalized Logistic Functions

We present an approximate dynamic programming method based on simulation, policy iteration, a postdecision state formulation, and a logistic value function approximation. This method was developed as part of our efforts to determine whether nonlinear value function approximations could provide cost-effective policies for advance patient scheduling problems, and as a way of identifying the main advantages and disadvantages of using simulation versus linear programming to approximately solve dynamic capacity allocation problems. We first apply the proposed method to a queueing problem and then study a more practical application based on an advance multipriority patient scheduling problem. We investigate the quality and practical implications of the resulting appointment scheduling policies using simulation, and compare their performance to that of four other policies. Patient scheduling policies obtained by the new method not only depend on the number of appointments already booked on each day but also on the overall system workload. In particular, these policies provide lower discounted cost values and shorter average wait times for higher priority patients than policies directly obtained using linear programming and an affine value function approximation in the predecision state variables.

Distributed Queuing in Dynamic Networks

We consider the problem of forming a distributed queue in the synchronous dynamic network model of Kuhn, Lynch, and Oshman (STOC 2010) in which the network topology changes from round to round but the network stays connected. Queue requests may arrive over rounds at network nodes and the goal is to eventually enqueue them in a distributed queue. We show that in 1-interval connected graphs, where the communication links change arbitrarily between every round, it is possible to solve the distributed queueing problem in [Formula: see text] rounds using [Formula: see text] size messages, where [Formula: see text] is the number of nodes in the network and [Formula: see text] is the number of queue requests. Further, we show that for more stable graphs, e.g. [Formula: see text]-interval connected graphs where the communication links change in every [Formula: see text] rounds, the distributed queuing problem can be solved in [Formula: see text] rounds using the same [Formula: see text] size messages, where [Formula: see text] is the concurrency level parameter that captures the minimum number of active queue requests in the system at any round. These results hold in any arbitrary arrival of queue requests and ensure correctness of the queue formed. To our best knowledge, these are the first solutions to the distributed queuing problem in highly dynamic networks.

Simulation Analysis and Improvement of the Vehicle Queuing System on Intersections Based on MATLAB

In order to reduce the traffic congestion and to enhance the capacity of urban road intersections, this paper builds a model of the vehicle queuing system for the intersection by queuing theory Based on Monte Carlo algorithm, this paper carries out simulation and analysis of the vehicle queuing system in the intersection by MATLAB, analyses, the status of vehicle queue to reduce the vehicle queue waiting time, and explores methods to solve the problem of vehicle queues at intersections. The optimal design for vehicle operating conditions has also been implemented from the perspec- tive of the queuing theory, facilities planning, Ergonomics and the management system. The results show that the analysis and improvement to the existing access program of the intersection can effectively relieve the vehicles queuing problem and promote the social service intensity of urban transportation system.

SIMULASI PENJADWALAN KAPAL TAMBAT UNTUK PENCAPAIAN ZERO WAITING TIME DI DERMAGA JAMRUD UTARA DENGAN OPTIMASI ALGORITMA SEQUENTIAL SEARCHING

Sea transportation is one of the main transportation in Indonesia. The flow of the ships and goods is increasing from year to year. If those increase is not supported by proper infrastructure and facilities and also good services, those would cause traffic problems on the voyage that resulted in queue problems in the port. The uneffective and unefficient of arrival and service pattern for berthing vessels make the queue problems becomes more difficult to be solved.Ship berthing services system on North Jamrud is still done manually by helding meeting every day to determine the berthing position. Designing a scheduling management system of ship berthing by simulating the ship schedule will help the service process for port management and agent. Sequential searching algorithm is used to search and collect the ship arrival data by minimizing the total service time of the ships.The simulation showed that the berthing process of ships can be done quickly by ensuring that the service time of the ships is in accordance with the standard operation procedure. The mean of waiting time for passanger ship is 41 hours, for cargo ship is 47 hours, and for the dry bulk type of ship is 70 hours with R = 0.9
 Keywords : Schedulling , Sequential Searching, Waiting time

Does a given vector–matrix pair correspond to a PH distribution?

The analysis of practical queueing problems benefits if realistic distributions can be used as parameters. Phase type (PH) distributions can approximate many distributions arising in practice, but their practical applicability has always been limited when they are described by a non-Markovian vector–matrix pair. In this case it is hard to check whether the non-Markovian vector–matrix pair defines a non-negative matrix-exponential function or not. In this paper we propose a numerical procedure for checking if the matrix-exponential function defined by a non-Markovian vector–matrix pair can be represented by a Markovian vector–matrix pair with potentially larger size. If so, then the matrix-exponential function is non-negative.The proposed procedure is based on O’Cinneide’s characterization result, which says that a non-Markovian vector–matrix pair with strictly positive density on (0,∞) and with a real dominant eigenvalue has a Markovian representation. Our method checks the existence of a potential Markovian representation in a computationally efficient way utilizing the structural properties of the applied representation transformation procedure.

Use of generalized birth and death process in solving queuing problems

The general procedure for determining the fluctuation in different phases of a population in which the changes take place either as functions of time or some parameter of the population is considered in this paper. It is indicated that the solution for most of the queuing problems can be obtained as special cases of the above procedure. Following this, the exact solutions for stable or unstable condition arising for some simple situations have been obtained.

Distribution of busy periods for the bulk-service queuing problem.

The distribution of busy periods for the bulk-service queuing problems ,in which the server on finding the systems empty, waits, has been obtained by using the phase technique. As particular cases, the results the classical queue have been derived.

Queuing Model For Effective Customer Service Delivery In The Banking Industry: A Study Of Union Bank PLC In Enugu Metropolis

The study highlights the imperativeness of maintaining an effective customer service delivery by attacking the notorious problem of long queue in service industry especially in Union Bank Plc. The following were the objectives: to highlight the cause(s) of clumsy service delivery in this bank which is manifested in long queues, to ascertain the usefulness of queuing model in ameliorating this problem, To examine the effects of long queue and poor service delivery on the customers, To examine the measures put in place by the bank to ameliorate the problem of long queue, to ascertain the usefulness of supervision of the tellers and facilities in ensuring the efficiency and effectiveness service delivery. The paper adopted a survey method with questionnaire and oral interviews as instruments of getting the data. The analysis of the study was presented in simple percentage in a table. The population of the study was 118 for staff (Junior/senior) and the population of customers being infinite, a sample size was derived using Williams and Freud formula to get a total of 462 customers. The data collected were analyzed with descriptive statistics. The findings indicate that the long queue is caused by poor supervision of tellers and facilities. The long queue has caused a high rate of drop of their customers to other banks. The bank has tried to embark on many strategies to attack this problem but it came late after many customers had gone. The study concludes that customer satisfaction is of prime importance to any enterprise that wants to control a high share of the market for their products. As all banks sell the same products but each bank's competitive advantage is its strategy for the satisfaction of her customers. Constant long queue in any service industry is an impediment to the realization of this goal. Proper supervision of queuing model is a panacea to this problem. The study recommends the following: proper and adequate supervision of tellers to maximize their efforts and show case the need for extra service points. There should be a constant appraisal of the staff to expose the trainable and un-trainable ones amongst them. The trainable ones should be sent for training while non-trainable ones will be laid off. There should be a proper examination of facilities and network system to keep them functional. Finally there should be regular promotional programmes to create the needed awareness to the public, informing them of the bank's re-engineering of its system to attract them back to the bank.

Distributed Queuing in Dynamic Networks

We consider the problem of forming a distributed queue in the adversarial dynamic network model of Kuhn, Lynch, and Oshman (STOC 2010) in which the network topology changes from round to round but the network stays connected. This is a synchronous model in which network nodes are assumed to be fixed, the communication links for each round are chosen by an adversary, and nodes do not know who their neighbors are for the current round before they broadcast their messages. Queue requests may arrive over rounds at arbitrary nodes and the goal is to eventually enqueue them in a distributed queue. We present two algorithms that give a total distributed ordering of queue requests in this model. We measure the performance of our algorithms through round complexity, which is the total number of rounds needed to solve the distributed queuing problem. We show that in 1-interval connected graphs, where the communication links change arbitrarily between every round, it is possible to solve the distributed queueing problem in O(nk) rounds using O(log n) size messages, where n is the number of nodes in the network and k <= n is the number of queue requests. Further, we show that for more stable graphs, e.g. T-interval connected graphs where the communication links change in every T rounds, the distributed queuing problem can be solved in O(n+ (nk/min(alpha,T))) rounds using the same O(log n) size messages, where alpha > 0 is the concurrency level parameter that captures the minimum number of active queue requests in the system in any round. These results hold in any arbitrary (sequential, one-shot concurrent, or dynamic) arrival of k queue requests in the system. Moreover, our algorithms ensure correctness in the sense that each queue request is eventually enqueued in the distributed queue after it is issued and each queue request is enqueued exactly once. We also provide an impossibility result for this distributed queuing problem in this model. To the best of our knowledge, these are the first solutions to the distributed queuing problem in adversarial dynamic networks.

OpenFlow-Based Flow-Level Bandwidth Provisioning for CICQ Switches

Flow-level bandwidth provisioning (FBP) achieves fine-grained bandwidth assurance for individual flows. It is especially important for virtualization-based computing environments such as data centers. However, existing flow-level bandwidth provisioning solutions suffer from a number of drawbacks, including high implementation complexity, poor performance guarantees, and inefficiency to process variable length packets. In this paper, we study flow-level bandwidth provisioning for Combined Input Crosspoint Queued (CICQ) switches in the OpenFlow context. First, we propose the Flow-level Bandwidth Provisioning algorithm for CICQ switches, which reduces the switch scheduling problem to multiple instances of fair queuing problems, each utilizing a well-studied fair queuing algorithm. We theoretically prove that FBP can closely emulate the ideal Generalized Processing Sharing model, and accurately guarantee the provisioned bandwidth. Furthermore, we implement FBP in the OpenFlow software switch to obtain realistic performance data by a prototype. Leveraging the capability of OpenFlow to define and manipulate flows, we experimentally demonstrate a practical flow-level bandwidth provisioning solution. Finally, we conduct extensive simulations and experiments to evaluate the design. The simulation data verify the correctness of the analytical results, and show that FBP achieves tight performance guarantees. The experiment results demonstrate that our OpenFlow-based prototype can conveniently and accurately provision bandwidth at the flow level.