Journal articles: 'Single-Server Queue System'

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Liang, Huei-Mei, and V. G. Kulkarni. "Stability condition for a single-server retrial queue." Advances in Applied Probability 25, no. 03 (1993): 690–701. http://dx.doi.org/10.1017/s0001867800025611.

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A single-server retrial queue consists of a primary queue, an orbit and a single server. Assume the primary queue capacity is 1 and the orbit capacity is infinite. Customers can arrive at the primary queue either from outside the system or from the orbit. If the server is busy, the arriving customer joins the orbit and conducts a retrial later. Otherwise, he receives service and leaves the system. We investigate the stability condition for a single-server retrial queue. Let λ be the arrival rate and 1/μ be the mean service time. It has been proved that λ / μ &lt; 1 is a sufficient stability condition for the M/G /1/1 retrial queue with exponential retrial times. We give a counterexample to show that this stability condition is not valid for general single-server retrial queues. Next we show that λ /μ &lt; 1 is a sufficient stability condition for the stability of a single-server retrial queue when the interarrival times and retrial times are finite mixtures of Erlangs.

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Takagi, Hideaki. "Analysis of finite-capacity polling systems." Advances in Applied Probability 23, no. 2 (1991): 373–87. http://dx.doi.org/10.2307/1427754.

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We consider a system of N finite-capacity queues attended by a single server in cyclic order. For each visit by the server to a queue, the service is given continuously until that queue becomes empty (exhaustive service), given continuously only to those customers present at the visiting instant (gated service), or given to only a single customer (limited service). The server then switches to the next queue with a random switchover time, and administers the same type of service there similarly. For such a system where each queue has a Poisson arrival process, general service time distribution, and finite capacity, we find the distribution of the waiting time at each queue by utilizing the known results for a single M/G/1/K queue with multiple vacations.

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Takagi, Hideaki. "Analysis of finite-capacity polling systems." Advances in Applied Probability 23, no. 02 (1991): 373–87. http://dx.doi.org/10.1017/s0001867800023557.

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We consider a system of N finite-capacity queues attended by a single server in cyclic order. For each visit by the server to a queue, the service is given continuously until that queue becomes empty (exhaustive service), given continuously only to those customers present at the visiting instant (gated service), or given to only a single customer (limited service). The server then switches to the next queue with a random switchover time, and administers the same type of service there similarly. For such a system where each queue has a Poisson arrival process, general service time distribution, and finite capacity, we find the distribution of the waiting time at each queue by utilizing the known results for a single M/G/1/K queue with multiple vacations.

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Liang, Huei-Mei, and V. G. Kulkarni. "Stability condition for a single-server retrial queue." Advances in Applied Probability 25, no. 3 (1993): 690–701. http://dx.doi.org/10.2307/1427530.

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A single-server retrial queue consists of a primary queue, an orbit and a single server. Assume the primary queue capacity is 1 and the orbit capacity is infinite. Customers can arrive at the primary queue either from outside the system or from the orbit. If the server is busy, the arriving customer joins the orbit and conducts a retrial later. Otherwise, he receives service and leaves the system.We investigate the stability condition for a single-server retrial queue. Let λ be the arrival rate and 1/μ be the mean service time. It has been proved that λ/μ < 1 is a sufficient stability condition for the M/G/1/1 retrial queue with exponential retrial times. We give a counterexample to show that this stability condition is not valid for general single-server retrial queues. Next we show that λ /μ < 1 is a sufficient stability condition for the stability of a single-server retrial queue when the interarrival times and retrial times are finite mixtures of Erlangs.

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DUAN, ZHE, and MELIKE BAYKAL-GÜRSOY. "A NOTE ON INFINITE-SERVER MARKOV MODULATED AND SINGLE-SERVER RETRIAL QUEUES." Asia-Pacific Journal of Operational Research 31, no. 02 (2014): 1440003. http://dx.doi.org/10.1142/s021759591440003x.

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We reconsider the M/M/∞ queue with two-state Markov modulated arrival and service processes and the single-server retrial queue analyzed in Keilson and Servi [Keilson, J and L Servi (1993). The matrix M/M/∞ system: Retrial models and Markov modulated sources. Advances in Applied Probability, 25, 453–471]. Fuhrmann and Cooper type stochastic decomposition holds for the stationary occupancy distributions in both queues [Keilson, J and L Servi (1993). The matrix M/M/∞ system: Retrial models and Markov modulated sources. Advances in Applied Probability, 25, 453–471; Baykal-Gürsoy, M and W Xiao (2004). Stochastic decomposition in M/M/∞ queues with Markov-modulated service rates. Queueing Systems, 48, 75–88]. The main contribution of the present paper is the derivation of the explicit form of the stationary system size distributions. Numerical examples are presented visually exhibiting the effect of various parameters on the stationary distributions.

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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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Chydzinski, Andrzej, Marek Barczyk, and Dominik Samociuk. "The Single-Server Queue with the Dropping Function and Infinite Buffer." Mathematical Problems in Engineering 2018 (October 9, 2018): 1–12. http://dx.doi.org/10.1155/2018/3260428.

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We present an analysis of queues with the dropping function and infinite buffer. In such queues, the arriving packet (job, customer, etc.) can be dropped with the probability which is a function of the queue size. Currently, the main application area of the dropping function is active queue management in routers, but it is applicable also in many other queueing systems. So far, queues with the dropping function have been analyzed with finite buffers only, which led to complicated, computationally demanding formulas. Assuming infinite buffers enabled us herein to obtain formulas in compact, easy to use forms. Moreover, a model with the infinite buffer can often be used as a good approximation of the real queue, in which the buffer is large. We start with noticing that the classic stability condition, ρ<1, cannot be used for queues with the dropping function and infinite buffer. For this reason, we prove a few new, easy to use conditions, which guarantee system stability or instability. Then we prove several theorems on popular performance characteristics, including the queue size, busy period, loss ratio, output rate, and system response time. Additionally, we derive a special, very important characteristic called the burst ratio, which may influence severely the quality of real-time multimedia transmissions. All the theorems are illustrated with numerical examples, demonstrating in particular how the system stability may be tested and how the shape of the dropping function may affect different performance characteristics.

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Lee, Thomas Y. S. "Analysis of Single Buffer Random Polling System With State-Dependent Input Process and Server/Station Breakdowns." International Journal of Operations Research and Information Systems 9, no. 1 (2018): 22–50. http://dx.doi.org/10.4018/ijoris.2018010102.

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Models and analytical techniques are developed to evaluate the performance of two variations of single buffers (conventional and buffer relaxation system) multiple queues system. In the conventional system, each queue can have at most one customer at any time and newly arriving customers find the buffer full are lost. In the buffer relaxation system, the queue being served may have two customers, while each of the other queues may have at most one customer. Thomas Y.S. Lee developed a state-dependent non-linear model of uncertainty for analyzing a random polling system with server breakdown/repair, multi-phase service, correlated input processes, and single buffers. The state-dependent non-linear model of uncertainty introduced in this paper allows us to incorporate correlated arrival processes where the customer arrival rate depends on the location of the server and/or the server's mode of operation into the polling model. The author allows the possibility that the server is unreliable. Specifically, when the server visits a queue, Lee assumes that the system is subject to two types of failures: queue-dependent, and general. General failures are observed upon server arrival at a queue. But there are two possibilities that a queue-dependent breakdown (if occurs) can be observed; (i) is observed immediately when it occurs and (ii) is observed only at the end of the current service. In both cases, a repair process is initiated immediately after the queue-dependent breakdown is observed. The author's model allows the possibility of the server breakdowns/repair process to be non-stationary in the number of breakdowns/repairs to reflect that breakdowns/repairs or customer processing may be progressively easier or harder, or that they follow a more general learning curve. Thomas Y.S. Lee will show that his model encompasses a variety of examples. He was able to perform both transient and steady state analysis. The steady state analysis allows us to compute several performance measures including the average customer waiting time, loss probability, throughput and mean cycle time.

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Renisagayaraj M, Roja R, Bhuvaneswari S, Suganthi P, and Sujatha R. "A Study of Multiserver Retrial Queues With Different Stages of Homogeneous Service." Journal of Computational Mathematica 7, no. 1 (2023): 017–22. http://dx.doi.org/10.26524/cm159.

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We discuss a queuing system with retrial of customers. Two models are discussed. First, we investigate single server queues in parallel, when the customer going to search and join the shorter of the two queues and in the second model we introduce the multiserver queue to multiserver retrial queue system. Multiserver provides different stages of homogeneous service in succession.

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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 (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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Yang, Ya Wei, Hong Wei Ding, Jia Guo, Yong Wang, and Qian Lin Liu. "The Analysis of the Loss Rate of Information Packet of Multi-Queue Single Server Polling System in Bi-Directional Cable TV Network." Applied Mechanics and Materials 543-547 (March 2014): 3013–16. http://dx.doi.org/10.4028/www.scientific.net/amm.543-547.3013.

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In this paper, the authors employ the multi-queue single-server system for information packets to calculate the theoretical value and computer simulation in the Bi-directional cable TV network. 3-queues single server polling system is used for example in the paper. And the simulation results show that the theoretical analysis and computer simulation are consistent.

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Deng, Yonglu, and Jiqing Tan. "Priority queueing model with changeover times and switching threshold." Journal of Applied Probability 38, A (2001): 263–73. http://dx.doi.org/10.1239/jap/1085496608.

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The paper studies a single-server two-queue priority system with changeover times and switching threshold. The server serves queue 1 exhaustively and does not remain at an empty queue if the other one is non-empty. It immediately switches from queue 2 to queue 1 when the length of the latter reaches some level M. Whenever service is changed from one queue to the other a changeover time is required. Arrivals are Poisson, service times and changeover times are independent and exponentially distributed. Using an analytic method we obtain the steady-state joint probability generating function of the lengths of the two queues. By means of this probability generating function some performance measures of the system such as mean length of queue and mean delay can be calculated.

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Deng, Yonglu, and Jiqing Tan. "Priority queueing model with changeover times and switching threshold." Journal of Applied Probability 38, A (2001): 263–73. http://dx.doi.org/10.1017/s0021900200112847.

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The paper studies a single-server two-queue priority system with changeover times and switching threshold. The server serves queue 1 exhaustively and does not remain at an empty queue if the other one is non-empty. It immediately switches from queue 2 to queue 1 when the length of the latter reaches some level M. Whenever service is changed from one queue to the other a changeover time is required. Arrivals are Poisson, service times and changeover times are independent and exponentially distributed. Using an analytic method we obtain the steady-state joint probability generating function of the lengths of the two queues. By means of this probability generating function some performance measures of the system such as mean length of queue and mean delay can be calculated.

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Dimitriou, Ioannis. "A TWO-CLASS RETRIAL SYSTEM WITH COUPLED ORBIT QUEUES." Probability in the Engineering and Informational Sciences 31, no. 2 (2017): 139–79. http://dx.doi.org/10.1017/s0269964816000528.

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We consider a single server system accepting two types of retrial customers, which arrive according to two independent Poisson streams. The service station can handle at most one customer, and in case of blocking, typeicustomer,i=1, 2, is routed to a separate typeiorbit queue of infinite capacity. Customers from the orbits try to access the server according to the constant retrial policy. We consider coupled orbit queues, and thus, when both orbit queues are non-empty, the orbit queueitries to re-dispatch a blocked customer of typeito the main service station after an exponentially distributed time with rate μi. If an orbit queue empties, the other orbit queue changes its re-dispatch rate from μito$\mu_{i}^{\ast}$. We consider both exponential and arbitrary distributed service requirements, and show that the probability generating function of the joint stationary orbit queue length distribution can be determined using the theory of Riemann (–Hilbert) boundary value problems. For exponential service requirements, we also investigate the exact tail asymptotic behavior of the stationary joint probability distribution of the two orbits with either an idle or a busy server by using the kernel method. Performance metrics are obtained, computational issues are discussed and a simple numerical example is presented.

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Sivasamy, Ramasamy. "A finite state Markovian queue to let in impatient customers only during K-vacations." Statistics in Transition new series 25, no. 3 (2024): 187–96. http://dx.doi.org/10.59170/stattrans-2024-035.

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We investigate a matrix analysis study for a single-server Markovian queue with finite capacity, i.e. an M/M/1/N queue, where the single server can go for a maximum, i.e. a K number of consecutive vacation periods. During these vacation periods of the server, every customer becomes impatient and leaves the queues. If the server detects that the system is idle during service startup, the server rests. If the vacation server finds a customer after the vacation ends, the server immediately returns to serve the customer. Otherwise, the server takes consecutive vacations until the server takes a maximum number of vacation periods, e.g. K, after which the server is idle and waits to serve the next arrival. During vacation, customers often lose patience and opt for scheduled deadlines independently. If the customer’s service is not terminated before the customer’s timer expires, the customer is removed from the queue and will not return. Matrix analysis provides a computational form for a balanced queue length distribution and several other performance metrics. We design a ‘no-loss; no-profit cost model’ to determine the appropriate value for the maximum value of K consecutive vacation periods and provide a solution with a numerical illustration.

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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 (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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Ojirobe, Yunusa, Abubakar Yahaya, and Muhammad Abdulkarim. "AN ANALYSES ON PATIENTS’ QUEUING SYSTEM AT MUHAMMAD ABDULLAHI WASE SPECIALIST HOSPITAL, KANO." FUDMA JOURNAL OF SCIENCES 5, no. 2 (2021): 344–50. http://dx.doi.org/10.33003/fjs-2021-0502-578.

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A major cause for concern in hospitals is congestion, which brings about untoward hardship to patients due to long queues and delay in service delivery. This paper seeks to minimize the waiting time of patients by comparing the performance indicators of a single server and multi-server model at the Paediatrics Department of Muhammad Abdullahi Wase Specialist Hospital Kano (MAWSHK). In order to achieve this, primary data was obtained through direct observation which in turn is subjected to the test of goodness of fit to ascertain the distribution that best describes the data. The performance indicators comprising utilization factor, average number of patients in the queue, average number of patients in the system, average waiting time in queue and average waiting time in system for a single server and multi-server model were computed and analyzed respectively. Our findings indicate that the G/G/4 model performs better compared to the G/G/1 model as it minimizes the waiting time of patients

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Xie, Runhan, and Ziv Scully. "Reducing Heavy-Traffic Response Time with Asymmetric Dispatching." ACM SIGMETRICS Performance Evaluation Review 51, no. 2 (2023): 36–38. http://dx.doi.org/10.1145/3626570.3626584.

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Reducing mean response time has always been a desirable goal in queueing systems. If job sizes (a.k.a. service times) are known to the scheduler, the policy that minimizes mean response time of a single-server queue is SRPT (Shortest Remaining Processing Time). This is true even for queues that are part of a larger system, such as immediate-dispatch systems where jobs are sent to one of multiple single-server queues upon arrival.

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B. Janani. "Time-Dependent Analysis of a Single-Server Queueing System with Disasters and Unreliable Repairs: A Probabilistic Approach to System Resilience." Advances in Nonlinear Variational Inequalities 28, no. 4s (2025): 48–71. https://doi.org/10.52783/anvi.v28.3225.

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A single server Markovian queueing paradigm is studied. The server is prone to disaster when delivering service or during idle periods. When the server encountered problems, all waiting customers will be flushed away and the repair procedure began immediately. Arrivals are allowed to join the queue during the repair time. The likelihood of restoring the server is p(p<1) after an exponential repair time. All waiting users leave the system if the server cannot be fixed. The time-dependent likelihood for a single server queue with disaster and an unreliable repairer is explicitly estimated for the first time. To demonstrate the significance of parameter values, performance measures and numerical figures were also supplied.

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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 (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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Ben, Sidiq Okwudili. "Single-Server Queue System of Shuttle Bus Performance: Federal University of Technology Akure as Case Study." American International Journal of Multidisciplinary Scientific Research 5, no. 3 (2019): 9–14. http://dx.doi.org/10.46281/aijmsr.v5i3.372.

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This study has examined the performance of University transport bus shuttle based on utilization using a Single-server queue system which occur if arrival and service rate is Poisson distributed (single queue) (M/M/1) queue. In the methodology, Single-server queue system was modelled based on Poisson Process with the introduction of Laplace Transform. It is concluded that the performance of University transport bus shuttle is 96.6 percent which indicates a very good performance such that the supply of shuttle bus in FUTA is capable of meeting the demand.

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Ansell, P. S., K. D. Glazebrook, and I. Mitrani. "THRESHOLD POLICIES FOR A SINGLE-SERVER QUEUING NETWORK." Probability in the Engineering and Informational Sciences 15, no. 1 (2001): 15–33. http://dx.doi.org/10.1017/s0269964801151028.

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We consider a single-server queuing system with two job classes under service policies of threshold type. The server switches from type 1 to type 2 when either the former queue is empty or the latter reaches size T; it switches from type 2 to type 1 when the former queue size drops below T and the latter is not empty. The joint queue-length distribution is determined for preemptive and nonpreemptive implementations using both analytic techniques and the power series algorithm.

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Sonia, Kalra, and Singla Neelam. "An Analysis of a Two-State Markovian Retrial Queueing Model with Priority Customers." Indian Journal of Science and Technology 15, no. 10 (2022): 428–41. https://doi.org/10.17485/IJST/v15i10.2017.

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Abstract Objective: This study considered a system of retrial queues with two types of customers: high-priority and low-priority. This study deals to find the time dependent probabilities of exact number of arrivals and departures from the system when server is free or busy. Numerical solution and graphical representation will also be presented. Method: For this model, we solved difference differential equations recursively and used Laplace transformation to obtain the transient state probabilities of exact number of arrivals and departures from the system when server is free or busy. Findings: Timedependent probabilities of exact number of arrivals (primary arrivals, arrivals in high priority queue, arrivals in low priority queue) in the system and exact number of departures (primary departures, departures from high priority queue, departures from low priority queue) from the system by a given time for when the server is idle and when the server is busy are obtained. Various interesting performance measures along with some special cases are also obtained. Conversion of two state model into single state model was discussed. Numerical illustrations are also presented using MATLAB programming along with the busy period probabilities of the system and server. Novelty: In past research, models considered arrivals and departures from the orbit whereas in present model arrivals and departures from the system are studied along with the concept of retrial and priority customers. Applications: Priority retrial queues are used in many applications like real time systems, operating systems, manufacturing system, simulation and medical service systems. Keywords: Arrivals; Departures; Probability; Priority; Retrial

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Zulfianndari, Irmawati,, and Rini Nur. "EVALUASI KINERJA LOAD BALANCING DENGAN ALGORITMA SCHEDULLING NEVER QUEUE." Journal of Informatics and Computer Engineering Research 1, no. 2 (2024): 42–49. https://doi.org/10.31963/jicer.v1i2.5176.

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Load balancing is used as a technique to handle large loads that cannot be carried out by a single server, so that the server does not experience overload. In handling load sharing, Load balancing uses a scheduling algorithm (Scheduling). The scheduling algorithm that is generally used is Round Robin which works by dividing requests evenly and then creating a queue for the server so that unfinished processes wait in the queue for quite a long time. In the Load balancing system there is an algorithm that adopts two speed models, which works by looking at the server status and the smallest connection delay, namely the Never Queue Algorithm. This study aims to determine the performance of Load balancing when the Schedulling Never Queue Algorithm is applied, based on predetermined scenarios and parameters. This study succeeded in implementing the Never Queue Algorithm in a Load balancing system for the Apache web server where the Time Per Request value will be lower if the Request received is larger when compared to using the Round Robin Algorithm. The Request Per Second value increases when the Requests sent are getting bigger. In terms of sharing server connections, the load balancer will share the load on the number of Requests based on the Shortest Expected Delay (SED) Algorithm, so several web servers receive different numbers of connections, so that processes don't stay in queues for a long time.

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Li, Tao, Liyuan Zhang, and Shan Gao. "An M/G/1 retrial queue with single working vacation under Bernoulli schedule." RAIRO - Operations Research 54, no. 2 (2020): 471–88. http://dx.doi.org/10.1051/ro/2019008.

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In this paper, an M/G/1 retrial queue with general retrial times and single working vacation is considered. We assume that the customers who find the server busy are queued in the orbit in accordance with a first-come-first-served (FCFS) discipline and only the customer at the head of the queue is allowed access to the server. During the normal period, if the orbit queue is not empty at a service completion instant, the server begins a working vacation with specified probability q (0 ≤ q ≤ 1), and with probability 1 − q, he waits for serving the next customer. During the working vacation period, customers can be served at a lower service rate. We first present the necessary and sufficient condition for the system to be stable. Using the supplementary variable method, we deal with the generating functions of the server state and the number of customers in the orbit. Various interesting performance measures are also derived. Finally, some numerical examples and cost optimization analysis are presented.

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Niranjan, Subramani Palani, Suthanthira Raj Devi Latha, and Sorin Vlase. "Cost Optimization in Sintering Process on the Basis of Bulk Queueing System with Diverse Services Modes and Vacation." Mathematics 12, no. 22 (2024): 3535. http://dx.doi.org/10.3390/math12223535.

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This research investigated a single bulk server queuing model where service modes and server vacations are dependent on the number of clients. The server operates in three different service modes: single service, fixed batch service, and variable batch service. Modes will be determined by queue length. The service starts only when the minimum number of customers, say ‘a’, has accumulated in the queue. At this point, the server selects one of three service modes. Transitions between duty modes are permitted only at the beginning of a duty period. At the end of the service, the server can go on vacation if the queue length drops below ‘a’. When returning from vacation, if threshold ‘a’ is not reached, the server will remain inactive until it is reached. A special technique called the Supplementary Variables Technique (SVT) was used to determine the probability-generating function when estimating the queue size at a given time. Appropriate numerical examples exemplify the method developed in the paper. An optimal cost analysis was performed to set the threshold values for different server modes with the intention of minimizing the aggregate average cost.

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Shin, Yang Woo, and Chareles E. M. Pearce. "The BMAP/G/1 vacation queue with queue-length dependent vacation schedule." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 40, no. 2 (1998): 207–21. http://dx.doi.org/10.1017/s0334270000012479.

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AbstractWe treat a single-server vacation queue with queue-length dependent vacation schedules. This subsumes the single-server vacation queue with exhaustive service discipline and the vacation queue with Bernoulli schedule as special cases. The lengths of vacation times depend on the number of customers in the system at the beginning of a vacation. The arrival process is a batch-Markovian arrival process (BMAP). We derive the queue-length distribution at departure epochs. By using a semi-Markov process technique, we obtain the Laplace-Stieltjes transform of the transient queue-length distribution at an arbitrary time point and its limiting distribution

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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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Hermanto, Koko, Cici Putri Sakina, Silvia Firda Utami, and Harizahayu Harizahayu. "Evaluasi Sistem Antrian Pada Loket Pendaftaran Puskesmas Unter Iwes Kecamatan Sumbawa." Unisda Journal of Mathematics and Computer Science (UJMC) 10, no. 2 (2024): 1–8. https://doi.org/10.52166/ujmc.v10i2.6866.

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The best service includes providing fast service so that customers can arrive quickly. The service here can be in the form of improving the queuing system. Queues can occur if the need for a service exceeds the available demand. One service sector with a queuing system is the Community Health Center. The Community Health Center is a functional implementing unit that is a health development center for fostering community participation in the health sector. So, research was carried out to evaluate the queuing system at the Unter Iwes Health Center registration counter in Sumbawa District to optimize queuing services. The study results show that the queuing system currently used at the registration counter at the Unter Iwes Health Center, Sumbawa sub-district, namely Single Channel-Single Phase, is still optimal, as indicated by a steady state value of less than one. On Monday, it was found that the average queue in the system (????s) was one person, the average queue in the queue (????q) was one person, while the probability that the number of patients in the queue would not occur (????o) was 0%. The average waiting time in the system (????s) is 0.24 minutes, while the average waiting time in the queue (????q) is 0.15 minutes, the server busy level (K) is 64%, and the server unemployment level (W) is 36%.

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Ott, Teunis J. "The single-server queue with independent GI/G and M/G input streams." Advances in Applied Probability 19, no. 1 (1987): 266–86. http://dx.doi.org/10.2307/1427383.

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This paper studies the single-server queueing system with two independent input streams: a GI/G and an M/G stream. A new proof is given of an old result which shows how this system can be transformed into an equivalent ‘single input stream’ GI/G/1 queue, and methods to study that equivalent system numerically are given. As part of the numerical analysis, algorithms are given to compute the moments and the distribution function of busy periods in the M/G/1 queue, and of other related busy periods. Special attention is given to the single-server queue with independent D/G and M/G input streams.This work is to be used in the modeling of real-time computer systems, which can often be described as a single-server queueing system with independent D/G and M/G input streams, see for example Ott (1984b).

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Ott, Teunis J. "The single-server queue with independent GI/G and M/G input streams." Advances in Applied Probability 19, no. 01 (1987): 266–86. http://dx.doi.org/10.1017/s0001867800016487.

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This paper studies the single-server queueing system with two independent input streams: a GI/G and an M/G stream. A new proof is given of an old result which shows how this system can be transformed into an equivalent ‘single input stream’ GI/G/1 queue, and methods to study that equivalent system numerically are given. As part of the numerical analysis, algorithms are given to compute the moments and the distribution function of busy periods in the M/G/1 queue, and of other related busy periods. Special attention is given to the single-server queue with independent D/G and M/G input streams. This work is to be used in the modeling of real-time computer systems, which can often be described as a single-server queueing system with independent D/G and M/G input streams, see for example Ott (1984b).

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Mukherjee, Debankur, Sem C. Borst, Johan S. H. van Leeuwaarden, and Philip A. Whiting. "Universality of load balancing schemes on the diffusion scale." Journal of Applied Probability 53, no. 4 (2016): 1111–24. http://dx.doi.org/10.1017/jpr.2016.68.

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Abstract We consider a system of N parallel queues with identical exponential service rates and a single dispatcher where tasks arrive as a Poisson process. When a task arrives, the dispatcher always assigns it to an idle server, if there is any, and to a server with the shortest queue among d randomly selected servers otherwise (1≤d≤N). This load balancing scheme subsumes the so-called join-the-idle queue policy (d=1) and the celebrated join-the-shortest queue policy (d=N) as two crucial special cases. We develop a stochastic coupling construction to obtain the diffusion limit of the queue process in the Halfin‒Whitt heavy-traffic regime, and establish that it does not depend on the value of d, implying that assigning tasks to idle servers is sufficient for diffusion level optimality.

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Bambos, Nicholas, and Jean Walrand. "On stability of state-dependent queues and acyclic queueing networks." Advances in Applied Probability 21, no. 3 (1989): 681–701. http://dx.doi.org/10.2307/1427642.

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We consider a single server first-come-first-served queue with a stationary and ergodic input. The service rate is a general function of the workload in the queue. We provide the necessary and sufficient conditions for the stability of the system and the asymptotic convergence of the workload process to a finite stationary process at large times. Then, we consider acyclic networks of queues in which the service rate of any queue is a function of the workloads of this and of all the preceding queues. The stability problem is again studied. The results are then extended to analogous systems with periodic inputs.

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Bambos, Nicholas, and Jean Walrand. "On stability of state-dependent queues and acyclic queueing networks." Advances in Applied Probability 21, no. 03 (1989): 681–701. http://dx.doi.org/10.1017/s0001867800018875.

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We consider a single server first-come-first-served queue with a stationary and ergodic input. The service rate is a general function of the workload in the queue. We provide the necessary and sufficient conditions for the stability of the system and the asymptotic convergence of the workload process to a finite stationary process at large times. Then, we consider acyclic networks of queues in which the service rate of any queue is a function of the workloads of this and of all the preceding queues. The stability problem is again studied. The results are then extended to analogous systems with periodic inputs.

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Federgruen, Awi, and Kut C. So. "Optimality of threshold policies in single-server queueing systems with server vacations." Advances in Applied Probability 23, no. 2 (1991): 388–405. http://dx.doi.org/10.2307/1427755.

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In this paper we consider a class of single-server queueing systems with compound Poisson arrivals, in which, at service completion epochs, the server has the option of taking off for one or several vacations of random length. The cost structure consists of a holding cost rate specified by a general non-decreasing function of the queue size, fixed costs for initiating and terminating service, and a variable operating cost incurred for each unit of time that the system is in operation. We show under some weak conditions with respect to the holding cost rate function and the service time, vacation time and arrival batch size distributions that it is either optimal among all feasible (stationary and non-stationary) policies never to take a vacation, or it is optimal to take a vacation when the system empties out and to resume work when, upon completion of a vacation, the queue size is equal to or in excess of a critical threshold. These optimality results are generalized for several variants of this model.

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Federgruen, Awi, and Kut C. So. "Optimality of threshold policies in single-server queueing systems with server vacations." Advances in Applied Probability 23, no. 02 (1991): 388–405. http://dx.doi.org/10.1017/s0001867800023569.

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In this paper we consider a class of single-server queueing systems with compound Poisson arrivals, in which, at service completion epochs, the server has the option of taking off for one or several vacations of random length. The cost structure consists of a holding cost rate specified by a general non-decreasing function of the queue size, fixed costs for initiating and terminating service, and a variable operating cost incurred for each unit of time that the system is in operation. We show under some weak conditions with respect to the holding cost rate function and the service time, vacation time and arrival batch size distributions that it is either optimal among all feasible (stationary and non-stationary) policies never to take a vacation, or it is optimal to take a vacation when the system empties out and to resume work when, upon completion of a vacation, the queue size is equal to or in excess of a critical threshold. These optimality results are generalized for several variants of this model.

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Wang, Fang, Jinting Wang, and Feng Zhang. "Equilibrium Customer Strategies in the Geo/Geo/1 Queue with Single Working Vacation." Discrete Dynamics in Nature and Society 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/309489.

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This paper is concerned with the equilibrium balking strategies of customers in a Geo/Geo/1 queue with single working vacation. Instead of completely stopping service, the server works with a small probability during the working vacation period. As soon as no customers exist in the system, the server takes a single vacation. The customers decide for themselves whether to enter the system or balk based on a natural reward-cost structure, the information available about the status of the server, and the queue length on hand upon arrival. We obtain the equilibrium balking strategies in two cases: fully observable and fully unobservable cases, which depend on whether the customers know both the queue length and the state of the server or none of them. Finally, we present several numerical experiments that demonstrate the effect of some parameters on the equilibrium behavior.

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Al-Matar, Najeeb, and Jewgeni H. Dshalalow. "Maintenance in Single-Server Queues: A Game-Theoretic Approach." Mathematical Problems in Engineering 2009 (2009): 1–23. http://dx.doi.org/10.1155/2009/857871.

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We use antagonistic stochastic games and fluctuation analysis to examine a single-server queue with bulk input and secondary work during server's multiple vacations. When the buffer contents become exhausted the server leaves the system to perform some diagnostic service of a minimum ofLjobs clustered in packets of random sizes (event A). The server is not supposed to stay longer thanTunits of time (event B). The server returns to the system when A or B occurs, whichever comes first. On the other hand, he may not break service of a packet in a middle even if A or B occurs. Furthermore, the server waits for batches of customers to arrive if upon his return the queue is still empty. We obtain a compact and explicit form functional for the queueing process in equilibrium.

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Dshalalow, Jewgeni H. "A single-server queue with random accumulation level." Journal of Applied Mathematics and Stochastic Analysis 4, no. 3 (1991): 203–10. http://dx.doi.org/10.1155/s1048953391000163.

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The author studies the queueing process in a single-server bulk queueing system. Upon completion of a previous service, the server can take a group of random size from customers that are available. Or, the server can wait until the queue attains a desired level. The author establishes an ergodicity criterion for both the queueing process with continuous time parameter and the imbedded process. Under this criterion, the author obtains explicit formulas for the stationary distributions of both processes by using semi-regenerative techniques.

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Shin, Yang Woo. "Sojourn time distributions in a Markovian G-queue with batch arrival and batch removal." Journal of Applied Mathematics and Stochastic Analysis 12, no. 4 (1999): 339–56. http://dx.doi.org/10.1155/s1048953399000301.

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We consider a single server Markovian queue with two types of customers; positive and negative, where positive customers arrive in batches and arrivals of negative customers remove positive customers in batches. Only positive customers form a queue and negative customers just reduce the system congestion by removing positive ones upon their arrivals. We derive the LSTs of sojourn time distributions for a single server Markovian queue with positive customers and negative customers by using the first passage time arguments for Markov chains.

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Suresh, S., M. Ramachandran, and Sathiyaraj Chinnasamy. "Evaluation of Unreliable Retrial G-queue Using Fuzzy ARAS Method." Data Analytics and Artificial Intelligence 2, no. 2 (2022): 97–108. http://dx.doi.org/10.46632/daai/2/2/5.

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A Regular busy server crashes due to negative customer traffic, and holiday interruption is being considered. If the orbit empties at the end of a positive customer service, the server worked Going on vacation. A working vacation (WV) server at a low service rate works. If there are clients on the computer at the end of each holiday, the server the probability that a new visitor is inactive and on vacation is p (single WV) or with probability q (multiple WVs). Substantial variable technique, constant state probability for the system and its orbit we found the generating function. System performance measures, reliability measures and random decay law are discussed. Finally, Some numerical examples and cost optimization analysis provided. Alternative: Single-Server Review G- Sequence, Incredible Review G-Series, Volume Visit Review G-Series. Evaluation Preference: Working vacation, Bernoulli feedback, Random vacations, single vacation. Unreliable retrial G-queue, Batch arrival Retrial G-queue, single server iteration is taken as a G-sequence alternative and working vacations, random vacations, single vacation, and Bernoulli vacation is taken evaluation parameters. In this from analysis Fuzzy ARAS method the best solution determines the solution with the shortest distance and the longest distance from the negative-best solution, but comparison of these distances is not considered significant. As a result it seems unreliable retrial G-queue got the first rank where as is the Batch arrival Retrial G-queue is having the lowest rank.

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Baruah, Monita, Kailash C. Madan, and Tillal Eldabi. "A Batch Arrival Single Server Queue with Server Providing General Service in Two Fluctuating Modes and Reneging during Vacation and Breakdowns." Journal of Probability and Statistics 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/319318.

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We study the behavior of a batch arrival queuing system equipped with a single server providing general arbitrary service to customers with different service rates in two fluctuating modes of service. In addition, the server is subject to random breakdown. As soon as the server faces breakdown, the customer whose service is interrupted comes back to the head of the queue. As soon as repair process of the server is complete, the server immediately starts providing service in mode 1. Also customers waiting for service may renege (leave the queue) when there is breakdown or when server takes vacation. The system provides service with complete or reduced efficiency due to the fluctuating rates of service. We derive the steady state queue size distribution. Some special cases are discussed and numerical illustration is provided to see the effect and validity of the results.

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He, Shuangchi. "Diffusion Approximation for Efficiency-Driven Queues When Customers Are Patient." Operations Research 68, no. 4 (2020): 1265–84. http://dx.doi.org/10.1287/opre.2019.1917.

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The analysis of queues with multiple servers is typically challenging when the service time distribution is general. Such analysis usually involves an infinite-dimensional process for tracking service ages or residual service times. In “Diffusion Approximation for Efficiency-Driven Queues When Customers Are Patient,” He demonstrates from a macroscopic perspective that, if customers are relatively patient and the system is overloaded, the dynamics of a many-server queue could be as simple as the dynamics of a single-server queue. In particular, the virtual waiting time process can be captured by a one-dimensional diffusion process, which enables us to obtain simple formulas for performance measures, such as service levels and effective abandonment fractions. To justify this diffusion model, a functional central limit theorem is established for the superposition of stationary renewal processes.

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NI WAYAN EKANTARI, NI WAYAN, NI KETUT TARI TASTRAWATI, and KARTIKA SARI. "PENERAPAN MODEL ANTREAN MULTI CHANNEL SINGLE PHASE PADA SISTEM PELAYANAN RESTORAN CEPAT SAJI." E-Jurnal Matematika 10, no. 3 (2021): 163. http://dx.doi.org/10.24843/mtk.2021.v10.i03.p337.

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A queue will occur if the average number of arrivals exceeds the capacity of service facilities. Fast food restaurants are one of the places that usually have long queues at lunchtime and dinner time. KFC in Bali, located in the village of Sanur, is a fast food restaurant that is experiencing long queues. This is because this restaurant is located in a tourism area and the only KFC outlet on the Ngurah Rai Sanur bypass line and does not yet have a drive-thru service. The current condition at KFC Sanur is that there is more than one service facility, disciplined first come first service (FCFS) queues according to the multi channel single phase queuing model. After being analyzed with data taken before the pandemic period on November 18, 2019 to December 1, 2019 for 14 days during weekdays and weekends, it was found that the performance of the KFC Sanur queue system would have a smaller utility level if there were 3 active server. The total cost per customer if there are 2 active server is IDR 78,692.38 and if there are 3 server is IDR 75,788.45. Based on the results of this analysis, it can be concluded that it will be more optimal if there are 3 active server.

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Artalejo, J. R., and A. Gomez-Corral. "On a single server queue with negative arrivals and request repeated." Journal of Applied Probability 36, no. 3 (1999): 907–18. http://dx.doi.org/10.1239/jap/1032374643.

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There is a growing interest in queueing systems with negative arrivals; i.e. where the arrival of a negative customer has the effect of deleting some customer in the queue. Recently, Harrison and Pitel (1996) investigated the queue length distribution of a single server queue of type M/G/1 with negative arrivals. In this paper we extend the analysis to the context of queueing systems with request repeated. We show that the limiting distribution of the system state can still be reduced to a Fredholm integral equation. We solve such an equation numerically by introducing an auxiliary ‘truncated’ system which can easily be evaluated with the help of a regenerative approach.

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Artalejo, J. R., and A. Gomez-Corral. "On a single server queue with negative arrivals and request repeated." Journal of Applied Probability 36, no. 03 (1999): 907–18. http://dx.doi.org/10.1017/s0021900200017666.

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There is a growing interest in queueing systems with negative arrivals; i.e. where the arrival of a negative customer has the effect of deleting some customer in the queue. Recently, Harrison and Pitel (1996) investigated the queue length distribution of a single server queue of type M/G/1 with negative arrivals. In this paper we extend the analysis to the context of queueing systems with request repeated. We show that the limiting distribution of the system state can still be reduced to a Fredholm integral equation. We solve such an equation numerically by introducing an auxiliary ‘truncated’ system which can easily be evaluated with the help of a regenerative approach.

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M, Varalakshmi, Chandrasekaran V M, and Saravanarajan M C. "A Single Server Queue with Immediate Feedback, Working Vacation and Server Breakdown." International Journal of Engineering & Technology 7, no. 4.10 (2018): 476. http://dx.doi.org/10.14419/ijet.v7i4.10.21044.

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This paper deals with analyze of a single server queueing system with immediate feedbacks and working vacation. Upon arrival if the customer sees the server to be busy then it joins the tail end of queue. Otherwise if server is idle, the customer gets into service. After completion of service, the customer is allowed to make an immediate feedback in finite number. Busy server may fail for a short interval of time. Using supplementary variable technique the steady state results are deduced. Some system performance measures are discussed

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Noraprilia, Karina, and Atina Ahdika. "ANALISIS ANTRIAN SINGLE CHANNEL SINGLE SERVER DENGAN LAYANAN BERKELOMPOK PADA KONEKSI INTERNET DI UNIVERSITAS ISLAM INDONESIA." Jurnal Ilmiah Matematika dan Pendidikan Matematika 10, no. 1 (2018): 53. http://dx.doi.org/10.20884/1.jmp.2018.10.1.2837.

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Internet is very important to support students in getting knowledge. However, internet access in college is sometimes not proportional to the number of users. Current speed of wireless network connection in Universitas Islam Indonesia (UII), named UIIAccess, is also not proportional to the number of users. Based on these problems, this research was conducted to study UIIAccess performance in providing internet service. The analysis used is single channel single server queuing model with bulk service. The result shows that traffic intensity of the system is 0.9694 indicating that the intensity of UIIAccess service is very solid. The queue performance shows that the average number of users in the system and waiting in the queue are respectively 32 and 11 users per minute, the average time spent by a user in the system and in the queue are consecutively 10.45574 and 3.63663 minutes. It indicates that the queue on UIIAccess is very crowded because of the imbalance between access speed and the number of users

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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 (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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Bounkhel, Messaoud, Lotfi Tadj, and Ramdane Hedjar. "Steady-State Analysis of a Flexible Markovian Queue with Server Breakdowns." Entropy 21, no. 3 (2019): 259. http://dx.doi.org/10.3390/e21030259.

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A flexible single-server queueing system is considered in this paper. The server adapts to the system size by using a strategy where the service provided can be either single or bulk depending on some threshold level c. If the number of customers in the system is less than c, then the server provides service to one customer at a time. If the number of customers in the system is greater than or equal to c, then the server provides service to a group of c customers. The service times are exponential and the service rates of single and bulk service are different. While providing service to either a single or a group of customers, the server may break down and goes through a repair phase. The breakdowns follow a Poisson distribution and the breakdown rates during single and bulk service are different. Also, repair times are exponential and repair rates during single and bulk service are different. The probability generating function and linear operator approaches are used to derive the system size steady-state probabilities.

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Journal articles on the topic 'Single-Server Queue System'

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