Journal articles on the topic 'Queues'
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1
Baek, Seung Jun, and Joon-Sang Park. "Delay-Optimal Scheduling for Two-Hop Relay Networks with Randomly Varying Connectivity: Join the Shortest Queue-Longest Connected Queue Policy." Mathematical Problems in Engineering 2017 (2017): 1–15. http://dx.doi.org/10.1155/2017/4362652.
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We consider a scheduling problem for a two-hop queueing network where the queues have randomly varying connectivity. Customers arrive at the source queue and are later routed to multiple relay queues. A relay queue can be served only if it is in connected state, and the state changes randomly over time. The source queue and relay queues are served in a time-sharing manner; that is, only one customer can be served at any instant. We propose Join the Shortest Queue-Longest Connected Queue (JSQ-LCQ) policy as follows: (1) if there exist nonempty relay queues in connected state, serve the longest queue among them; (2) if there are no relay queues to serve, route a customer from the source queue to the shortest relay queue. For symmetric systems in which the connectivity has symmetric statistics across the relay queues, we show that JSQ-LCQ is strongly optimal, that is, minimizes the delay in the stochastic ordering sense. We use stochastic coupling and show that the systems under coupling exist in two distinct phases, due to dynamic interactions among source and relay queues. By careful construction of coupling in both phases, we establish the stochastic dominance in delay between JSQ-LCQ and any arbitrary policy.
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Tu, Rungting, Wenting Feng, Cheryl Lin, and Pikuei Tu. "Read into the lines: the positive effects of queues." Journal of Service Theory and Practice 28, no. 5 (September 10, 2018): 661–81. http://dx.doi.org/10.1108/jstp-07-2017-0119.
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PurposeCompanies work hard to reduce queue lengths due to the common belief that queues in general are undesirable. Extant literature mainly has focused on the negative consequences of queues and overlooked the potential positive effects. The purpose of this paper is to address the benefits of queues by examining how consumers of different segments may read into the lines (queues) as well as why and when positive effects occur.Design/methodology/approachApplying and integrating psychology and marketing theories, the study develops a model with several propositions to identify and explain the mechanism and conditions under which queues have positive effects.FindingsContrary to conventional belief, queues may serve as positive signs. In certain segments, consumers can perceive a queue as a reflection of superior service/product quality, an opportunity to fulfill the need(s) for self-uniqueness or social inclusion or an avenue to avoid social exclusion. In addition, the benefits of long queues may come from consumers’ joining a line to seek desirable outcomes/gains based on their attribution of the queue, and consumers’ prefactual thinking that regards “not joining” the queue as potential losses. Furthermore, the magnitude of such effects depends on queue distinctiveness, choice heterogeneity, consumption hedonism and performance uncertainty.Originality/valueThis paper explains how, why and when a long queue can be read as positive cues and benefits both the firms and target/potential consumers. The authors demonstrate the psychological mechanisms of joining a queue based on attribution and prefactual thinking, and identify conditions under which positive queue effects are most likely to occur.
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Spicer, Scott, and Ilze Ziedins. "User-Optimal State-Dependent Routeing in Parallel Tandem Queues with Loss." Journal of Applied Probability 43, no. 1 (March 2006): 274–81. http://dx.doi.org/10.1239/jap/1143936259.
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We consider a system of parallel, finite tandem queues with loss. Each tandem queue consists of two single-server queues in series, with capacities C1 and C2 and exponential service times with rates μ1 and μ2 for the first and second queues, respectively. Customers that arrive at a queue that is full are lost. Customers arriving at the system can choose which tandem queue to enter. We show that, for customers choosing a queue to maximise the probability of their reaching the destination (or minimise their individual loss probability), it will sometimes be optimal to choose queues with more customers already present and/or with greater residual service requirements (where preceding customers are further from their final destination).
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Dao-Thi, Thu-Ha, and Jean Mairesse. "Zero-automatic queues and product form." Advances in Applied Probability 39, no. 2 (June 2007): 429–61. http://dx.doi.org/10.1239/aap/1183667618.
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We introduce and study a new model: zero-automatic queues. Roughly, zero-automatic queues are characterized by a special buffering mechanism evolving like a random walk on some infinite group or monoid. The salient result is that all stable zero-automatic queues have a product form stationary distribution and a Poisson output process. When considering the two simplest and extremal cases of zero-automatic queues, we recover the simple M/M/1 queue and Gelenbe's G-queue with positive and negative customers.
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Dao-Thi, Thu-Ha, and Jean Mairesse. "Zero-automatic queues and product form." Advances in Applied Probability 39, no. 02 (June 2007): 429–61. http://dx.doi.org/10.1017/s000186780000183x.
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We introduce and study a new model:zero-automatic queues. Roughly, zero-automatic queues are characterized by a special buffering mechanism evolving like a random walk on some infinite group or monoid. The salient result is that all stable zero-automatic queues have a product form stationary distribution and a Poisson output process. When considering the two simplest and extremal cases of zero-automatic queues, we recover the simple M/M/1 queue and Gelenbe'sG-queue with positive and negative customers.
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Zheng, Guan, Yang Zhijun, Qian Wenhua, and He Min. "On Two-Level State-Dependent Routing Polling Systems with Mixed Service." Mathematical Problems in Engineering 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/109325.
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Based on priority differentiation and efficiency of the system, we consider anN+1queues’ single-server two-level polling system which consists of one key queue andNnormal queues. The novel contribution of the present paper is that we consider that the server just polls active queues with customers waiting in the queue. Furthermore, key queue is served with exhaustive service and normal queues are served with 1-limited service in a parallel scheduling. For this model, we derive an expression for the probability generating function of the joint queue length distribution at polling epochs. Based on these results, we derive the explicit closed-form expressions for the mean waiting time. Numerical examples demonstrate that theoretical and simulation results are identical and the new system is efficient both at key queue and normal queues.
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Spicer, Scott, and Ilze Ziedins. "User-Optimal State-Dependent Routeing in Parallel Tandem Queues with Loss." Journal of Applied Probability 43, no. 01 (March 2006): 274–81. http://dx.doi.org/10.1017/s0021900200001522.
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We consider a system of parallel, finite tandem queues with loss. Each tandem queue consists of two single-server queues in series, with capacities C 1 and C 2 and exponential service times with rates μ1 and μ2 for the first and second queues, respectively. Customers that arrive at a queue that is full are lost. Customers arriving at the system can choose which tandem queue to enter. We show that, for customers choosing a queue to maximise the probability of their reaching the destination (or minimise their individual loss probability), it will sometimes be optimal to choose queues with more customers already present and/or with greater residual service requirements (where preceding customers are further from their final destination).
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Lemeshko, Oleksandr, Oleksandra Yeremenko, Larysa Titarenko, and Alexander Barkalov. "Hierarchical Queue Management Priority and Balancing Based Method under the Interaction Prediction Principle." Electronics 12, no. 3 (January 29, 2023): 675. http://dx.doi.org/10.3390/electronics12030675.
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This work is devoted to improving a two-level hierarchical queue management method based on priority and balancing under the interaction prediction principle. The lower level of calculations was connected with the problem optimization solution and was responsible for two tasks. Firstly, the packet flow aggregation and distribution among the macro-queues and sub-queues organized on the router interface must solve the congestion management problem. Secondly, the resource allocation problem solution was related to the balanced allocation of interface bandwidth among the sub-queues, which were weighted relative to their priorities under the traffic-engineering queues. The method’s lower-level functions were recommended to be placed on a set of processors of a routing device responsible for servicing the packets of individual macro-queues. At the same time, the processor coordinator could perform the functions of the upper-level calculations, providing interface bandwidth allocation among the macro-queues. The numerical research results of the proposed two-level hierarchical queue management method confirmed its effectiveness in ensuring high scalability. Balanced, priority-based packet flow distribution and interface bandwidth allocation among the macro-queues and sub-queues were implemented. In addition, the time was reduced for solving tasks related to queue management. The method demonstrated high convergence of the coordination procedure and the quality of the centralized calculations. The proposed approach can be used in various embedded systems.
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Boxma, Onno, Mayank Saxena, Stella Kapodistria, and Rudesindo Núñez Queija. "Two queues with random time-limited polling." Probability and Mathematical Statistics 37, no. 2 (May 14, 2018): 257–89. http://dx.doi.org/10.19195/0208-4147.37.2.4.
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TWO QUEUES WITH RANDOM TIME-LIMITED POLLINGIn this paper, we analyse a single server polling model withtwo queues. Customers arrive at the two queues according to two independent Poisson processes. There is a single server that serves both queues withgenerally distributed service times. The server spends an exponentially distributed amount of time in each queue. After the completion of this residing time, the server instantaneously switches to the other queue, i.e., there is noswitch-over time. For this polling model we derive the steady-state marginal workload distribution, as well as heavy traffic and heavy tail asymptotic results. Furthermore, we also calculate the joint queue length distribution for the special case of exponentially distributed service times using singular perturbation analysis.
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Pedarsani, Ramtin, and Jean Walrand. "Stability of multiclass queueing networks under longest-queue and longest-dominating-queue scheduling." Journal of Applied Probability 53, no. 2 (June 2016): 421–33. http://dx.doi.org/10.1017/jpr.2016.10.
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Abstract We consider the stability of robust scheduling policies for multiclass queueing networks. These are open networks with arbitrary routeing matrix and several disjoint groups of queues in which at most one queue can be served at a time. The arrival and potential service processes and routeing decisions at the queues are independent, stationary, and ergodic. A scheduling policy is called robust if it does not depend on the arrival and service rates nor on the routeing probabilities. A policy is called throughput-optimal if it makes the system stable whenever the parameters are such that the system can be stable. We propose two robust policies: longest-queue scheduling and a new policy called longest-dominating-queue scheduling. We show that longest-queue scheduling is throughput-optimal for two groups of two queues. We also prove the throughput-optimality of longest-dominating-queue scheduling when the network topology is acyclic, for an arbitrary number of groups and queues.
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Comte, Céline, and Jan-Pieter Dorsman. "Pass-and-swap queues." Queueing Systems 98, no. 3-4 (April 12, 2021): 275–331. http://dx.doi.org/10.1007/s11134-021-09700-3.
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AbstractOrder-independent (OI) queues, introduced by Berezner et al. (Queueing Syst 19(4):345–359, 1995), expanded the family of multi-class queues that are known to have a product-form stationary distribution by allowing for intricate class-dependent service rates. This paper further broadens this family by introducing pass-and-swap (P&S) queues, an extension of OI queues where, upon a service completion, the customer that completes service is not necessarily the one that leaves the system. More precisely, we supplement the OI queue model with an undirected graph on the customer classes, which we call a swapping graph, such that there is an edge between two classes if customers of these classes can be swapped with one another. When a customer completes service, it passes over customers in the remainder of the queue until it finds a customer it can swap positions with, that is, a customer whose class is a neighbor in the graph. In its turn, the customer that is ejected from its position takes the position of the next customer it can be swapped with, and so on. This is repeated until a customer can no longer find another customer to be swapped with; this customer is the one that leaves the queue. After proving that P&S queues have a product-form stationary distribution, we derive a necessary and sufficient stability condition for (open networks of) P&S queues that also applies to OI queues. We then study irreducibility properties of closed networks of P&S queues and derive the corresponding product-form stationary distribution. Lastly, we demonstrate that closed networks of P&S queues can be applied to describe the dynamics of new and existing load-distribution and scheduling protocols in clusters of machines in which jobs have assignment constraints.
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Zhang, Shu Li, and Sheng Hui Liu. "Research on Job Shop Scheduling Technique in Small-Scale Machine Production." Applied Mechanics and Materials 380-384 (August 2013): 726–29. http://dx.doi.org/10.4028/www.scientific.net/amm.380-384.726.
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According to the characteristics of the small-scale machine production, a job shop scheduling technique was given in this paper. In the technique, two classes of queues were built. The job queue expresses the procedures of a job. The machine queue expresses the actual processing sequence of the jobs on a machine. At first, all job queues could be built and the sequence of the operations in them should not be changed forever; all machine queues are null. The completion rate of each operation is defined. The core task of the technique are prioritizing the operation which the completion rate is the smallest of the job queues inserting into a machine queue, and minimize the finish time of the last operation in all machine. The technique could always achieve good job shop schedules. The feasibility and availability of the technique is verified through an example.
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HANSSON, SVEN OVE. "Medical Ethics and New Public Management in Sweden." Cambridge Quarterly of Healthcare Ethics 23, no. 3 (June 2, 2014): 261–67. http://dx.doi.org/10.1017/s0963180113000868.
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Abstract:In order to shorten queues to healthcare, the Swedish government has introduced a yearly “queue billion” that is paid out to the county councils in proportion to how successful they are in reducing queues. However, only the queues for first visits are covered. Evidence has accumulated that queues for return visits have become longer. This affects the chronically and severely ill. Swedish physicians, and the Swedish Medical Association, have strongly criticized the queue billion and have claimed that it conflicts with medical ethics. Instead they demand that their professional judgments on priority setting and medical urgency be respected. This discussion provides an interesting illustration of some of the limitations of new public management and also more generally of the complicated relationships between medical ethics and public policy.
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Margaret, Fredlina, Sofwan Ali Fakhrudin, Ariska Dithya Pratiwi, and Fergyanto E. Gunawan. "ANALYZE QUEUE PERFORMANCE USING ARENA 16.0 SOFTWARE (Z Cinema Case Study)." JARES (Journal of Academic Research and Sciences) 8, no. 1 (March 10, 2023): 40–44. http://dx.doi.org/10.35457/jares.v8i1.2737.
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Queues are often found in everyday life, such as waiting for cinema counters, check-in queues at airports and self-service cashier queues. Service facilities for a long time cause queues because they cannot meet the needs or capacity, so facility users have to wait. As in the example of the case of Cinema Z in Solo City has a maximum queue time of 13.6 minutes with a maximum number of queues of 11 people until served. This can cause customers to wait long enough to get movie tickets. This problem can be overcome by the need to manage the counter operator so that it can regulate when to open a new counter so that there is no queue. This research discusses the problem of queuing models at Cinema Z in Solo, Central Java Province. From the results of the analysis that can be known the performance values of the queuing system such as waiting time, number in, number out, dan number waiting.
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Miyazawa, Masakiyo, and Ronald W. Wolff. "Symmetric queues with batch departures and their networks." Advances in Applied Probability 28, no. 1 (March 1996): 308–26. http://dx.doi.org/10.2307/1427923.
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Batch departures arise in various applications of queues. In particular, such models have been studied recently in connection with production systems. For the most part, however, these models assume Poisson arrivals and exponential service times; little is known about them under more general settings. We consider how their stationary queue length distributions are affected by the distributions of interarrival times, service times and departing batch sizes of customers. Since this is not an easy problem even for single departure models, we first concentrate on single-node queues with a symmetric service discipline, which is known to have nice properties. We start with pre-emptive LIFO, a special case of the symmetric service discipline, and then consider symmetric queues with Poisson arrivals. Stability conditions and stationary queue length distributions are obtained for them, and several stochastic order relations are considered. For the symmetric queues and Poisson arrivals, we also discuss their network. Stability conditions and the stationary joint queue length distribution are obtained for this network.
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Miyazawa, Masakiyo, and Ronald W. Wolff. "Symmetric queues with batch departures and their networks." Advances in Applied Probability 28, no. 01 (March 1996): 308–26. http://dx.doi.org/10.1017/s0001867800027385.
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Batch departures arise in various applications of queues. In particular, such models have been studied recently in connection with production systems. For the most part, however, these models assume Poisson arrivals and exponential service times; little is known about them under more general settings. We consider how their stationary queue length distributions are affected by the distributions of interarrival times, service times and departing batch sizes of customers. Since this is not an easy problem even for single departure models, we first concentrate on single-node queues with a symmetric service discipline, which is known to have nice properties. We start with pre-emptive LIFO, a special case of the symmetric service discipline, and then consider symmetric queues with Poisson arrivals. Stability conditions and stationary queue length distributions are obtained for them, and several stochastic order relations are considered. For the symmetric queues and Poisson arrivals, we also discuss their network. Stability conditions and the stationary joint queue length distribution are obtained for this network.
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Hindriani, Nelli, Narwen ., and Hazmira Yozza. "IMPLEMENTASI AN TRIAN DENGAN MENGGUNAKAN ARRAY." Jurnal Matematika UNAND 3, no. 4 (December 1, 2014): 147. http://dx.doi.org/10.25077/jmu.3.4.147-151.2014.
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In a multiprogramming computer, the queues are a data set where additionof elements could only done on a tip on the back side is called rear and the elementshad done through the end of the front sides which is called front. Due the queue is adata set, then the appropriate data type for presenting the queue is to use the array.The advantage of using an array as a data type is ability to which can collect multipledata of the same type within a single variable, thus within making the program consistsfrom the several of similar types does not require a lot of variables. In a queues systemthere are some models of queues that may could be done include queuing model byshifting the position of the element to the previous element, the queues front modelswere occupied by a new element entered, the queue model in which the move is madeby random element, and a queuing model random element position.
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Jhunjhunwala, Prakirt Raj, and Siva Theja Maguluri. "Heavy Traffic Queue Length Distribution without Resource Pooling in an Input-Queued Switch." ACM SIGMETRICS Performance Evaluation Review 50, no. 4 (April 26, 2023): 26–28. http://dx.doi.org/10.1145/3595244.3595254.
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This paper studies the heavy-traffic joint distribution of queue lengths of an input-queued switch operating under the MaxWeight scheduling policy. Input-queued switch acts as a representative of SPNs that do not satisfy the so-called complete resource pooling (CRP) condition, and consequently exhibit a multidimensional state space collapse. Except in special cases, only mean queue lengths of such non-CRP systems have been obtained in the literature. In this paper, we develop the transform method to study the steady state distribution of non-CRP systems. The key challenge is in solving an implicit functional equation involving the Laplace transform of the heavy-traffic limiting distribution. We then consider the general n - n input-queued switch that has n2 queues. Under a conjecture on uniqueness of the solution of the functional equation, we obtain an exact joint distribution of the heavy-traffic limiting queue-lengths in terms of a nonlinear transformation of 2n iid exponentials.
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Wijayanti, Esti. "Perangkat Lunak untuk Antrian pada Badan Pengelolaan Keuangan dan Aset Daerah Kabupaten Pati." Jurnal Disprotek 11, no. 2 (December 20, 2020): 88–92. http://dx.doi.org/10.34001/jdpt.v11i2.1425.
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Badan Pengelolaan Keuangan dan Asset Daerah Pati (BPKAD) a government agency that serves the public in a manual way that requires its employees to remember the queues that previously walked. So automatic painting for bpkad queue system pati regency takes a lot of time because only relying on employees and humans can also be wrong or forget expected with the computerized system reduces errors in long queues because without remembering the previous queue. Therefore, a bpkad queue system must be applied in Pati Regency. The Software is a system for Printing Queues. Because typing the number is still manual so the creation of this application because it feels less effective. In this application the author uses Netbeans in its creation.
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Tandra, Rahul, N. Hemachandra, and D. Manjunath. "JOIN MINIMUM COST QUEUE FOR MULTICLASS CUSTOMERS: STABILITY AND PERFORMANCE BOUNDS." Probability in the Engineering and Informational Sciences 18, no. 4 (October 2004): 445–72. http://dx.doi.org/10.1017/s0269964804184027.
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We consider a system of K parallel queues providing different grades of service through each of the queues and serving a multiclass customer population. Service differentiation is achieved by specifying different join prices to the queues. Customers of class j define a cost function ψij(ci,xi) for taking service from queue i when the join price for queue i is ci and congestion in queue i is xi and join the queue that minimizes ψij(·,·). Such a queuing system will be called the “join minimum cost queue” (JMCQ) and is a generalization of the join shortest queue (JSQ) system. Non-work-conserving (called Paris Metro pricing system) and work-conserving (called the Tirupati system) versions of the JMCQ are analyzed when the cost to an arrival of joining a queue is a convex combination of the join price for that queue and the expected waiting time in that queue at the arrival epoch. Our main results are for a two-queue system.We obtain stability conditions and performance bounds. To obtain the lower and upper performance bounds, we propose two quasi-birth–death (QBD) processes that are derived from the original systems by suitably truncating the state space. The state space truncation in the non-work-conserving JMCQ follows the method of van Houtum and colleagues. We then show that this method is not applicable to the work-conserving JMCQ and provide sample-path-based proofs to show that the number in each queue is bounded by the number in the corresponding queues of these QBD processes. These sample-path proof techniques might also be of independent interest. We then show that the performance measures like mean queue length and revenue rate of the system are also bounded by the corresponding quantities of these QBD processes. Numerical examples show that these bounds are fairly tight. Finally, we generalize some of these results to systems with more queues.
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Knessl, Charles. "A diffusion model for two parallel queues with processor sharing: transient behavior and asymptotics." Journal of Applied Mathematics and Stochastic Analysis 12, no. 4 (January 1, 1999): 311–38. http://dx.doi.org/10.1155/s1048953399000295.
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We consider two identical, parallel M/M/1 queues. Both queues are fed by a Poisson arrival stream of rate λ and have service rates equal to μ. When both queues are non-empty, the two systems behave independently of each other. However, when one of the queues becomes empty, the corresponding server helps in the other queue. This is called head-of-the-line processor sharing. We study this model in the heavy traffic limit, where ρ=λ/μ→1. We formulate the heavy traffic diffusion approximation and explicitly compute the time-dependent probability of the diffusion approximation to the joint queue length process. We then evaluate the solution asymptotically for large values of space and/or time. This leads to simple expressions that show how the process achieves its stead state and other transient aspects.
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Rolski, Tomasz. "Approximation of periodic queues." Advances in Applied Probability 19, no. 3 (September 1987): 691–707. http://dx.doi.org/10.2307/1427413.
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In this paper we demonstrate how some characteristics of queues with the periodic Poisson arrivals can be approximated by the respective characteristics in queues with Markov modulated input. These Markov modulated queues were recently studied by Regterschot and de Smit (1984). The approximation theorems are given in terms of the weak convergence of some characteristics and their uniform integrability. The approximations are applicable for the following characteristics: mean workload, mean workload at the time of day, mean delay, mean queue size.
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Rolski, Tomasz. "Approximation of periodic queues." Advances in Applied Probability 19, no. 03 (September 1987): 691–707. http://dx.doi.org/10.1017/s0001867800016827.
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In this paper we demonstrate how some characteristics of queues with the periodic Poisson arrivals can be approximated by the respective characteristics in queues with Markov modulated input. These Markov modulated queues were recently studied by Regterschot and de Smit (1984). The approximation theorems are given in terms of the weak convergence of some characteristics and their uniform integrability. The approximations are applicable for the following characteristics: mean workload, mean workload at the time of day, mean delay, mean queue size.
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Turner, Stephen R. E. "The Effect of Increasing Routing Choice on Resource Pooling." Probability in the Engineering and Informational Sciences 12, no. 1 (January 1998): 109–24. http://dx.doi.org/10.1017/s0269964800005088.
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We consider a network of N identical /M/l or /M/∞ queues. There are two types of arriving customers, those that have no routing choice, and those that first pick r queues at random, and are then routed to the least busy of those queues. We derive the limiting distribution of queue lengths as N→∞, and investigate how this distribution varies with r. We show that even a small amount of routing choice can lead to substantial gains in performance through resource pooling. We corroborate these conclusions by carrying out some simulations of a related model, from which the previous model can be derived by an exchangeable queue simplification. We also observe that the exchangeable queue simplification results in a performance gain for some parameters, in contrast to earlier work.
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Szczotka, Władysław. "Exponential approximation of waiting time and queue size for queues in heavy traffic." Advances in Applied Probability 22, no. 1 (March 1990): 230–40. http://dx.doi.org/10.2307/1427606.
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An exponential approximation for the stationary waiting time distribution and the stationary queue size distribution for single-server queues in heavy traffic is given for a wide class of queues. This class contains for example not only queues for which the generic sequence, i.e. the sequence of service times and interarrival times, is stationary but also such queues for which the generic sequence is asymptotically stationary in some sense. The conditions ensuring the exponential approximation of the characteristics considered in heavy traffic are expressed in terms of the invariance principle for the stationary representation of the generic sequence and its first two moments.
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Szczotka, Władysław. "Exponential approximation of waiting time and queue size for queues in heavy traffic." Advances in Applied Probability 22, no. 01 (March 1990): 230–40. http://dx.doi.org/10.1017/s000186780001942x.
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An exponential approximation for the stationary waiting time distribution and the stationary queue size distribution for single-server queues in heavy traffic is given for a wide class of queues. This class contains for example not only queues for which the generic sequence, i.e. the sequence of service times and interarrival times, is stationary but also such queues for which the generic sequence is asymptotically stationary in some sense. The conditions ensuring the exponential approximation of the characteristics considered in heavy traffic are expressed in terms of the invariance principle for the stationary representation of the generic sequence and its first two moments.
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Ishizaki, Fumio. "Decomposition property in a discrete-time queue with multiple input streams and service interruptions." Journal of Applied Probability 41, no. 2 (June 2004): 524–34. http://dx.doi.org/10.1239/jap/1082999083.
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This paper studies a discrete-time single-server queue with two independent inputs and service interruptions. One of the inputs to the queue is an independent and identically distributed process. The other is a much more general process and it is not required to be Markov nor is it required to be stationary. The service interruption process is also general and it is not required to be Markov or to be stationary. This paper shows that a stochastic decomposition property for the virtual waiting-time process holds in the discrete-time single-server queue with service interruptions. To the best of the author's knowledge, no stochastic decomposition results for virtual waiting-time processes in non-work-conserving queues, such as queues with service interruptions, have been obtained before and only work-conserving queues have been studied in the literature.
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Ishizaki, Fumio. "Decomposition property in a discrete-time queue with multiple input streams and service interruptions." Journal of Applied Probability 41, no. 02 (June 2004): 524–34. http://dx.doi.org/10.1017/s0021900200014479.
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This paper studies a discrete-time single-server queue with two independent inputs and service interruptions. One of the inputs to the queue is an independent and identically distributed process. The other is a much more general process and it is not required to be Markov nor is it required to be stationary. The service interruption process is also general and it is not required to be Markov or to be stationary. This paper shows that a stochastic decomposition property for the virtual waiting-time process holds in the discrete-time single-server queue with service interruptions. To the best of the author's knowledge, no stochastic decomposition results for virtual waiting-time processes in non-work-conserving queues, such as queues with service interruptions, have been obtained before and only work-conserving queues have been studied in the literature.
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Devos, Arnaud, Joris Walraevens, Dieter Fiems, and Herwig Bruneel. "Heavy-Traffic Comparison of a Discrete-Time Generalized Processor Sharing Queue and a Pure Randomly Alternating Service Queue." Mathematics 9, no. 21 (October 27, 2021): 2723. http://dx.doi.org/10.3390/math9212723.
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This paper compares two discrete-time single-server queueing models with two queues. In both models, the server is available to a queue with probability 1/2 at each service opportunity. Since obtaining easy-to-evaluate expressions for the joint moments is not feasible, we rely on a heavy-traffic limit approach. The correlation coefficient of the queue-contents is computed via the solution of a two-dimensional functional equation obtained by reducing it to a boundary value problem on a hyperbola. In most server-sharing models, it is assumed that the system is work-conserving in the sense that if one of the queues is empty, a customer of the other queue is served with probability 1. In our second model, we omit this work-conserving rule such that the server can be idle in case of a non-empty queue. Contrary to what we would expect, the resulting heavy-traffic approximations reveal that both models remain different for critically loaded queues.
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Knessl, Charles, and Haishen Yao. "On the Nonsymmetric Longer Queue Model: Joint Distribution, Asymptotic Properties, and Heavy Traffic Limits." Advances in Operations Research 2013 (2013): 1–21. http://dx.doi.org/10.1155/2013/680539.
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We consider two parallel queues, each with independent Poisson arrival rates, that are tended by a single server. The exponential server devotes all of its capacity to the longer of the queues. If both queues are of equal length, the server devotesνof its capacity to the first queue and the remaining1−νto the second. We obtain exact integral representations for the joint probability distribution of the number of customers in this two-node network. Then we evaluate this distribution in various asymptotic limits, such as large numbers of customers in either/both of the queues, light traffic where arrivals are infrequent, and heavy traffic where the system is nearly unstable.
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Chou, Eva Shan. "“A Story about Hair”: A Curious Mirror of Lu Xun's Pre-Republican Years." Journal of Asian Studies 66, no. 2 (April 26, 2007): 421–59. http://dx.doi.org/10.1017/s0021911807000551.
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This article examines the subject of queues in the life and writings of Lu Xun (1881–1936), the most prominent figure in modern Chinese literature. The long-standing reluctance of readers and critics to associate this backward hairstyle with Lu Xun's iconic figure has restricted our understanding of the topic to two well-known satirical portraits in his short fiction, Ah Q and Sevenpounder. This article, however, proposes that the queue is of more than satiric interest—that the author's own experience raises fundamental questions about how he discloses and transmutes certain experiences in his writings. Starting from some little-studied events featuring queues in his pre-Republican years and a puzzling short story that recounts them, this essay analyzes the queue's autobiographical connections and their varied literary manifestations. It also makes a case for reexamining the uses of autobiography for a writer whose life story is an important part of his influence.
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Bambos, Nicholas, and George Michailidis. "ON PARALLEL QUEUING WITH RANDOM SERVER CONNECTIVITY AND ROUTING CONSTRAINTS." Probability in the Engineering and Informational Sciences 16, no. 2 (April 2002): 185–203. http://dx.doi.org/10.1017/s0269964802162048.
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We study systems of parallel queues with finite buffers, a single server with random connectivity to each queue, and arriving job flows with random or class-dependent accessibility to the queues. Only currently connected queues may receive (preemptive) service at any given time, whereas an arriving job can only join one of its accessible queues. Using the coupling method, we study three key models, progressively building from simpler to more complicated structures.In the first model, there are only random server connectivities. It is shown that allocating the server to the Connected queue with the Fewest Empty Spaces (C-FES) stochastically minimizes the number of lost jobs due to buffer overflows, under conditions of independence and symmetry.In the second model, we additionally consider random accessibility of queues by arriving jobs. It is shown that allocating the server to the C-FES and routing each arriving job to the currently Accessible queue with the Most Empty Spaces (C-FES/A-MES) minimizes the loss flow stochastically, under similar assumptions.In the third model (addressing a target application), we consider multiple classes of arriving job flows, each allowed access to a deterministic subset of the queues. Under analogous assumptions, it is again shown that the C-FES/A-MES policy minimizes the loss flow stochastically.The random connectivity/accessibility aspect enhances significantly the structure and application scope of the classical parallel queuing model. On the other hand, it introduces essential additional dynamics and considerable complications. It is interesting that a simple policy like FES/MES, known to be optimal for the classical model, extends to the C-FES/A-MES in our case.
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Gupta, Amit Kumar, Narendra Singh Yadav, and Dinesh Goyal. "Design and Performance Evaluation of Smart Job First Multilevel Feedback Queue (SJFMLFQ) Scheduling Algorithm with Dynamic Smart Time Quantum." International Journal of Multimedia Data Engineering and Management 8, no. 2 (April 2017): 50–64. http://dx.doi.org/10.4018/ijmdem.2017040106.
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Multilevel feedback queue scheduling (MLFQ) algorithm is based on the concept of several queues in which a process moves. In earlier scenarios there are three queues defined for scheduling. The two higher level queues are running on Round Robin scheduling and last level queue is running on FCFS (First Come First Serve). A fix time quantum is defined for RR scheduling and scheduling of process depends upon the arrival time in ready queue. Previously a lot of work has been done in MLFQ. In our propose algorithm Smart Job First Multilevel feedback queue (SJFMLFQ) with smart time quantum (STQ), the processes are arranged in ascending order of their CPU execution time and calculate a Smart Priority Factor SPF on which processes are scheduled in queue. The process which has lowest SPF value will schedule first and the process which has highest SF value will schedule last in queue. Then a smart time quantum (STQ) is calculated for each queue. As a result, we found decreasing in turnaround time, average waiting time and increasing throughput as compared to the previous approaches and hence increase in the overall performance.
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Rahmanizar, Cut Sarah, and Rusdi. "Penerapan Metode Antrian pada Layanan Kepengurusan Paspor di Kantor Imigrasi Kelas I TPI Banda Aceh." Regress: Journal of Economics & Management 2, no. 2 (November 13, 2022): 223–28. http://dx.doi.org/10.57251/reg.v2i2.673.
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This article describes the queuing system for passport management services at the Immigration Office Class I TPI Banda Aceh. Queue can be interpreted as a long queue of service recipients who need services from one or more service facilities. Queues occur because of an imbalance between those served and their services. Some community service users at the Immigration Office Class I TPI Banda Aceh were annoyed because of the long queues to receive immigration document services and sometimes canceled them. The purpose of this study is to optimize the queuing system in the passport management service at the Immigration Office Class I TPI Banda Aceh so that there are no long queues. The queuing system is optimized with a simulation approach using discrete event simulation. The simulation results show that the best value obtained in the proposed scenario simulation model is to add queue lines to the queuing system. The results obtained are by increasing the queue line from 1 to 2 so that the queue length is reduced from 91.2068 people per hour to 54.1520 and 50.8887 people per hour.
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Perel, Nir, and Uri Yechiali. "THE ISRAELI QUEUE WITH INFINITE NUMBER OF GROUPS." Probability in the Engineering and Informational Sciences 28, no. 1 (November 19, 2013): 1–19. http://dx.doi.org/10.1017/s0269964813000296.
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The so called “Israeli Queue” is a single server polling system with batch service of an unlimited size, where the next queue to be visited is the one in which the first customer in line has been waiting for the longest time. The case with finite number of queues (groups) was introduced by Boxma, Van der Wal and Yechiali [3]. In this paper we extend the model to the case with a (possibly) infinite number of queues. We analyze the M/M/1, M/M/c, and M/M/1/N—type queues, as well as a priority model with (at most) M high-priority classes and a single lower priority class. In all models we present an extensive probabilistic analysis and calculate key performance measures.
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Long, Gary. "Start-Up Delays of Queued Vehicles." Transportation Research Record: Journal of the Transportation Research Board 1934, no. 1 (January 2005): 125–31. http://dx.doi.org/10.1177/0361198105193400113.
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Start-up delays of queued vehicles have been studied in past research for evaluation of their impacts on saturation flow rates at downstream traffic signals. A more crucial issue, however, can be the effect of start-up delays of queued vehicles at upstream locations where queued vehicles back up from a traffic signal across a railroad crossing. The relationship between queue start-up delays and track clearance times is important in establishing traffic signal preemption settings. This paper presents models that are developed for prediction of the expected maximum time required to mobilize a queue of any length. The models consider not only the average delay times but also the limiting delay times that are expected to accommodate high proportions of queues. For design convenience, queue lengths are converted into distance from the leading edge of a queue rather than being described only by the number of vehicles in a queue. Because the variations in start-up times, in addition to the average times reported in the literature, are needed, two sets of field studies were used to obtain data for model calibration and to investigate various traffic operation effects. Other factors that might be expected to influence queue start-up times are also analyzed.
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Abu-Lebdeh, Ghassan, and Rahim F. Benekohal. "Genetic Algorithms for Traffic Signal Control and Queue Management of Oversaturated Two-Way Arterials." Transportation Research Record: Journal of the Transportation Research Board 1727, no. 1 (January 2000): 61–67. http://dx.doi.org/10.3141/1727-08.
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The formulation and solution of a dynamic signal control and queue management algorithm for two-way oversaturated arterials are presented. The algorithm is structured to find optimal control and queue management in at least one direction: the primary direction. The other direction is optimized only subject to the fulfillment of the constraints on the primary direction. The main idea of the procedure is to manage queue formation and dissipation through proper design of signal control parameters such that queues are always contained within respective links and that spillbacks are prevented. The two-way control procedure presented accounts for all possible traffic flow regimes that may form as a result of queue management schemes. Genetic algorithms were used to solve the problem. The results show that although the algorithm provides optimal control and queue management in the primary direction, it was also able to manage queues in the secondary direction so that the occurrence of queue spillbacks is prevented. Progression was attainable only in the primary direction. However, the algorithm was able to effectively deal with evolving traffic queues in both directions. In all but one link, traffic was successfully contained in the respective links, thus preventing spillback.
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Yurindra, Yurindra, Ari Amir Alkodri, Anisah Anisah, and Supardi Supardi. "Aplikasi Client Server Berbasis Android pada Barbershop The Barbega Menggunakan Model Multi Channel - Single Phase." Jurnal Sisfokom (Sistem Informasi dan Komputer) 9, no. 1 (April 27, 2020): 138. http://dx.doi.org/10.32736/sisfokom.v9i1.837.
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A common problem that is often faced by almost most Barbershop is in terms of serving customer queues, for barbershops who have many customers and have many service chairs, then of course a good customer queue service management concept is needed as well. One of the concepts of queuing services for customers is how queue information can reach customers without queuing at the location. For this reason, a queue service concept for customers is needed based on Android. Android is preferred because almost all smartphone users are currently based on Android. The application will be built based on the concept of client server so that the queue service will occur in real time. The Queuing model used is Multi Channel Single Phase, because in the queue at barbershop there will only be one stage of the process, but it requires a lot of queue flow. This can be seen in the structure of the development diagram. By using an Android-based application based on a single phase multi channel model that will be built it is ensured that customers will find it helpful, without having to spend time in a queue customers can order queues and see queues in real time so they can rush to barbershop when it is close to the queue
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Zubeldia, Martin, and Michel Mandjes. "Large deviations for acyclic networks of queues with correlated Gaussian inputs." Queueing Systems 98, no. 3-4 (February 18, 2021): 333–71. http://dx.doi.org/10.1007/s11134-021-09689-9.
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AbstractWe consider an acyclic network of single-server queues with heterogeneous processing rates. It is assumed that each queue is fed by the superposition of a large number of i.i.d. Gaussian processes with stationary increments and positive drifts, which can be correlated across different queues. The flow of work departing from each server is split deterministically and routed to its neighbors according to a fixed routing matrix, with a fraction of it leaving the network altogether. We study the exponential decay rate of the probability that the steady-state queue length at any given node in the network is above any fixed threshold, also referred to as the ‘overflow probability’. In particular, we first leverage Schilder’s sample-path large deviations theorem to obtain a general lower bound for the limit of this exponential decay rate, as the number of Gaussian processes goes to infinity. Then, we show that this lower bound is tight under additional technical conditions. Finally, we show that if the input processes to the different queues are nonnegatively correlated, non-short-range dependent fractional Brownian motions, and if the processing rates are large enough, then the asymptotic exponential decay rates of the queues coincide with the ones of isolated queues with appropriate Gaussian inputs.
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Grishechkin, Sergei. "On a relationship between processor-sharing queues and Crump–Mode–Jagers branching processes." Advances in Applied Probability 24, no. 3 (September 1992): 653–98. http://dx.doi.org/10.2307/1427484.
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The M/G/1 queue with batch arrivals and a queueing discipline which is a generalization of processor sharing is studied by means of Crump–Mode–Jagers branching processes. A number of theorems are proved, including investigation of heavy traffic and overloaded queues. Most of the results obtained are also new for the M/G/1 queue with processor sharing. By use of a limiting procedure we also derive new results concerning M/G/1 queues with shortest residual processing time discipline.
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Grishechkin, Sergei. "On a relationship between processor-sharing queues and Crump–Mode–Jagers branching processes." Advances in Applied Probability 24, no. 03 (September 1992): 653–98. http://dx.doi.org/10.1017/s0001867800024459.
Full textAbstract:
The M/G/1 queue with batch arrivals and a queueing discipline which is a generalization of processor sharing is studied by means of Crump–Mode–Jagers branching processes. A number of theorems are proved, including investigation of heavy traffic and overloaded queues. Most of the results obtained are also new for the M/G/1 queue with processor sharing. By use of a limiting procedure we also derive new results concerning M/G/1 queues with shortest residual processing time discipline.
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Kella, Offer, and Ward Whitt. "Linear stochastic fluid networks." Journal of Applied Probability 36, no. 1 (March 1999): 244–60. http://dx.doi.org/10.1239/jap/1032374245.
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We introduce open stochastic fluid networks that can be regarded as continuous analogues or fluid limits of open networks of infinite-server queues. Random exogenous input may come to any of the queues. At each queue, a c.d.f.-valued stochastic process governs the proportion of the input processed by a given time after arrival. The routeing may be deterministic (a specified sequence of successive queue visits) or proportional, i.e. a stochastic transition matrix may govern the proportion of the output routed from one queue to another. This stochastic fluid network with deterministic c.d.f.s governing processing at the queues arises as the limit of normalized networks of infinite-server queues with batch arrival processes where the batch sizes grow. In this limit, one can think of each particle having an evolution through the network, depending on its time and place of arrival, but otherwise independent of all other particles. A key property associated with this independence is the linearity: the workload associated with a superposition of inputs, each possibly having its own pattern of flow through the network, is simply the sum of the component workloads. As with infinite-server queueing models, the tractability makes the linear stochastic fluid network a natural candidate for approximations.
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Kella, Offer, and Ward Whitt. "Linear stochastic fluid networks." Journal of Applied Probability 36, no. 01 (March 1999): 244–60. http://dx.doi.org/10.1017/s0021900200017009.
Full textAbstract:
We introduce open stochastic fluid networks that can be regarded as continuous analogues or fluid limits of open networks of infinite-server queues. Random exogenous input may come to any of the queues. At each queue, a c.d.f.-valued stochastic process governs the proportion of the input processed by a given time after arrival. The routeing may be deterministic (a specified sequence of successive queue visits) or proportional, i.e. a stochastic transition matrix may govern the proportion of the output routed from one queue to another. This stochastic fluid network with deterministic c.d.f.s governing processing at the queues arises as the limit of normalized networks of infinite-server queues with batch arrival processes where the batch sizes grow. In this limit, one can think of each particle having an evolution through the network, depending on its time and place of arrival, but otherwise independent of all other particles. A key property associated with this independence is the linearity: the workload associated with a superposition of inputs, each possibly having its own pattern of flow through the network, is simply the sum of the component workloads. As with infinite-server queueing models, the tractability makes the linear stochastic fluid network a natural candidate for approximations.
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Park, Jaesung, and Yujin Lim. "Online Service-Time Allocation Strategy for Balancing Energy Consumption and Queuing Delay of a MEC Server." Applied Sciences 12, no. 9 (April 29, 2022): 4539. http://dx.doi.org/10.3390/app12094539.
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MEC servers (MESs) support multiple queues to accommodate the delay requirements of tasks offloaded from end devices or transferred from other MESs. The service time assigned to each queue trades off the queue backlog and energy consumption. Because multiple queues share the computational resources of a MES, optimally scheduling the service time among them is important, reducing the energy consumption of a MES and ensuring the delay requirement of each queue. To achieve a balance between these metrics, we propose an online service-time allocation method that minimizes the average energy consumption and satisfies the average queue backlog constraint. We employ the Lyapunov optimization framework to transform the time-averaged optimization problem into a per-time-slot optimization problem and devise an online service-time allocation method whose time complexity is linear to the number of queues. This method determines the service time for each queue at the beginning of each time slot using the observed queue length and expected workload. We adopt a long short-term memory (LSTM) deep learning model to predict the workload that will be imposed on each queue during a time slot. Using simulation studies, we verify that the proposed method strikes a better balance between energy consumption and queuing delay than conventional methods.
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Schmidt, Volker. "On joint queue-length characteristics in infinite-server tandem queues with heavy traffic." Advances in Applied Probability 19, no. 2 (June 1987): 474–86. http://dx.doi.org/10.2307/1427428.
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For m infinite-server queues with Poisson input which are connected in a series, a simple proof is given of a formula derived in [3] for the generating function of the joint customer-stationary distribution of the successive numbers of customers a randomly chosen customer finds at his arrival epochs at two queues of the system. In this connection, a shot-noise representation of the queue-length characteristics under consideration is used. Moreover, using this representation, corresonding asymptotic formulas are derived for infinite-server tandem queues with general high-density renewal input.
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Schmidt, Volker. "On joint queue-length characteristics in infinite-server tandem queues with heavy traffic." Advances in Applied Probability 19, no. 02 (June 1987): 474–86. http://dx.doi.org/10.1017/s0001867800016633.
Full textAbstract:
For m infinite-server queues with Poisson input which are connected in a series, a simple proof is given of a formula derived in [3] for the generating function of the joint customer-stationary distribution of the successive numbers of customers a randomly chosen customer finds at his arrival epochs at two queues of the system. In this connection, a shot-noise representation of the queue-length characteristics under consideration is used. Moreover, using this representation, corresonding asymptotic formulas are derived for infinite-server tandem queues with general high-density renewal input.
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Vlasiou, M., and U. Yechiali. "M/G/∞ POLLING SYSTEMS WITH RANDOM VISIT TIMES." Probability in the Engineering and Informational Sciences 22, no. 1 (December 18, 2007): 81–106. http://dx.doi.org/10.1017/s0269964808000065.
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We consider a polling system where a group of an infinite number of servers visits sequentially a set of queues. When visited, each queue is attended for a random time. Arrivals at each queue follow a Poisson process, and the service time of each individual customer is drawn from a general probability distribution function. Thus, each of the queues comprising the system is, in isolation, anM/G/∞-type queue. A job that is not completed during a visit will have a new service-time requirement sampled from the service-time distribution of the corresponding queue. To the best of our knowledge, this article is the first in which anM/G/∞-type polling system is analyzed. For this polling model, we derive the probability generating function and expected value of the queue lengths and the Laplace–Stieltjes transform and expected value of the sojourn time of a customer. Moreover, we identify the policy that maximizes the throughput of the system per cycle and conclude that under the Hamiltonian-tour approach, the optimal visiting order isindependentof the number of customers present at the various queues at the start of the cycle.
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Baccelli, F., E. G. Coffman, and E. N. Gilbert. "Tandem Conveyor Queues." Probability in the Engineering and Informational Sciences 3, no. 4 (October 1989): 517–36. http://dx.doi.org/10.1017/s0269964800001364.
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This paper analyzes a queueing system in which a constant-speed conveyor brings new items for service and carries away served items. The conveyor is a sequence of cells each able to hold at most one item. At each integer time, a new cell appears at the queue's input position. This cell holds an item requiring service with probability a, holds a passerby requiring no service with probability b, and is empty with probability (1– a – b). Service times are integers synchronized with the arrival of cells at the input, and they are geometrically distributed with parameter μ. Items requiring service are placed in an unbounded queue to await service. Served items are put in a second unbounded queue to await replacement on the conveyor in cells at the input position. Two models are considered. In one, a served item can only be placed into a cell that was empty on arrival; in the other, the served item can be placed into a cell that was either empty or contained an item requiring service (in the latter case unloading and loading at the input position can take place in the same time unit). The stationary joint distribution of the numbers of items in the two queues is studied for both models. It is verified that, in general, this distribution does not have a product form. Explicit results are worked out for special cases, e.g., when b = 0, and when all service times are one time unit (μ = 1). It is shown how the analysis of the general problem can be reduced to the solution of a Riemann boundary-value problem.
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Lee, Ho Woo, Se Won Lee, and Jongwoo Jeon. "Using factorization in analyzing D-BMAP/G/1 queues." Journal of Applied Mathematics and Stochastic Analysis 2005, no. 2 (January 1, 2005): 119–32. http://dx.doi.org/10.1155/jamsa.2005.119.
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We demonstrate how one can use the factorization property to derive the queue-length distributions of the discrete-time BMAP/G/1 queues with complex operational behavior during the idle period. The procedure demonstrated in this paper can be applied to the analysis of many other discrete-time BMAP/G/1 queues with more behavioral complexities.
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Nababan, Marlince NK, Windania Purba, and Evta Indra. "The Tuition Payment Queuing System Uses Android-Based First in First Out (FIFO) Algorithm." IOP Conference Series: Earth and Environmental Science 748, no. 1 (April 1, 2021): 012038. http://dx.doi.org/10.1088/1755-1315/748/1/012038.
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Abstract Queuing is an important component of a process in service. Queues are formed in a company or institution due to customers. Disorderly queues are a big problem for all concerned. Where, disorderly queues occur at University Prima Indonesia at the time of tuition payment so that the campus has to carry out a crowded queue process and students have to stand waiting for the next call resulting in less effective and efficient even waste of energy for students and employees. This research designed a system of tuition payment queues using the First In First Out (FIFO) algorithm which aims to reduce the time students are queuing at the checkout at the time of tuition payment so as not to wait too long so that the time of students and campus employees is not wasted too much and reduce the crowded queue time. The result of this study is an android-based tuition payment system, which is useful for reducing student build up when paying tuition. Thus it can be said that the calculation result of P0 queue has a result of 0.25%, and the number of customers 3 people, the average customer in the queue has a value of 2.25, the total customer time is 20 minutes, and the average customer time in the row is 15 minutes, the server busy time is 0.75, and the server’s empty time is 0.25%.