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Journal articles on the topic 'Markov queueing model'

Author: Grafiati

Published: 6 September 2023

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1

GAWRON, PIOTR, DARIUSZ KURZYK, and ZBIGNIEW PUCHAŁA. "A MODEL FOR QUANTUM QUEUE." International Journal of Quantum Information 11, no. 02 (March 2013): 1350023. http://dx.doi.org/10.1142/s0219749913500238.

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We consider an extension of discrete time Markov chain queueing model to the quantum domain by use of discrete time quantum Markov chain. We introduce methods for numerical analysis of such models. Using these tools we show that quantum model behaves fundamentally different from the classical one.

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2

Tanackov, Prentkovskis, Jevtić, Stojić, and Ercegovac. "A New Method for Markovian Adaptation of the Non-Markovian Queueing System Using the Hidden Markov Model." Algorithms 12, no. 7 (June 28, 2019): 133. http://dx.doi.org/10.3390/a12070133.

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This manuscript starts with a detailed analysis of the current solution for the queueing system M/Er/1/∞. In the existing solution, Erlang’s service is caused by Poisson’s arrival process of groups, but not individual clients. The service of individual clients is still exponentially distributed, contrary to the declaration in Kendall’s notation. From the related theory of the Hidden Markov Model (HMM), for the advancement of queueing theory, the idea of “hidden Markov states” (HMS) was taken. In this paper, the basic principles of application of HMS have first been established. The abstract HMS states have a catalytic role in the standard procedure of solving the non-Markovian queueing systems. The proposed solution based on HMS exceeds the problem of accessing identical client groups in the current solution of the M/Er/r queueing system. A detailed procedure for the new solution of the queueing system M/Er/1/∞ is implemented. Additionally, a new solution to the queueing system M/N/1/∞ with a normal service time N(μ,σ) based on HMS is also implemented.

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3

Böhm, W., and S. G. Mohanty. "Transient analysis of M/M/1 queues in discrete time by general server vacations." Journal of Applied Probability 31, A (1994): 115–29. http://dx.doi.org/10.2307/3214952.

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In this contribution we consider an M/M/1 queueing model with general server vacations. Transient and steady state analysis are carried out in discrete time by combinatorial methods. Using weak convergence of discrete-parameter Markov chains we also obtain formulas for the corresponding continuous-time queueing model. As a special case we discuss briefly a queueing system with a T-policy operating.

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Böhm, W., and S. G. Mohanty. "Transient analysis of M/M/1 queues in discrete time by general server vacations." Journal of Applied Probability 31, A (1994): 115–29. http://dx.doi.org/10.1017/s0021900200107028.

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In this contribution we consider an M/M/1 queueing model with general server vacations. Transient and steady state analysis are carried out in discrete time by combinatorial methods. Using weak convergence of discrete-parameter Markov chains we also obtain formulas for the corresponding continuous-time queueing model. As a special case we discuss briefly a queueing system with a T-policy operating.

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5

Balea, Paraschiv, and Gheorghe Potcovaru. "A QUEUEING MODEL FOR SOME CATALYTIC REACTIONS." SOUTHERN BRAZILIAN JOURNAL OF CHEMISTRY 9, no. 10 (December 20, 2001): 23–30. http://dx.doi.org/10.48141/sbjchem.v9.n10.2001.26_2001.pdf.

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The waiting model associated to the catalytical process given by the chemical eq_uation C + S ↔ CS ↔ C + P (1), is described by the Markov process: {Xi(t); t≥O}, (i = 1, 2, 3, 4), where the random variables are the concentrations of the species C (the catalyst), S (the substrate}, CS (the intermediate complex formed by the substrate S and the catalyst) and P (the reaction product) at time t. The equations, that describe the evolution of the process, have been obtained.

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6

Tiến, Đỗ Văn, and Csaba Rotter. "A CLOSED-FORM SOLUTION FOR A QUEUEING MODEL OF ENERGY EFFICIENT ETHERNET LINKS." Journal of Computer Science and Cybernetics 37, no. 4 (October 12, 2021): 453–64. http://dx.doi.org/10.15625/1813-9663/37/4/16126.

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To save energy consumption of Ethernet switches, IEEE has standardized a new energy-efficient operation for Ethernet links with a low-power state and transition mechanisms between the high-power state for transporting traffic and the low-power state.In this paper, we propose a queueing model with the Markov Modulated Compound Poisson Process that is able to characterize backbone packet traffic. We derive a closed-form solution for the stationary distribution of the proposed queueing model. We show that our model can capture an entire system where the transition times are constant.

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7

Baek, Jung Woo, Ho Woo Lee, Se Won Lee, and Soohan Ahn. "A Markov-modulated fluid flow queueing model under D -policy." Numerical Linear Algebra with Applications 18, no. 6 (November 2011): 993–1010. http://dx.doi.org/10.1002/nla.811.

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8

Van Dijk, Nico M. "Perturbation theory for unbounded Markov reward processes with applications to queueing." Advances in Applied Probability 20, no. 1 (March 1988): 99–111. http://dx.doi.org/10.2307/1427272.

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Consider a perturbation in the one-step transition probabilities and rewards of a discrete-time Markov reward process with an unbounded one-step reward function. A perturbation estimate is derived for the finite horizon and average reward function. Results from [3] are hereby extended to the unbounded case. The analysis is illustrated for one- and two-dimensional queueing processes by an M/M/1-queue and an overflow queueing model with an error bound in the arrival rate.

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9

Van Dijk, Nico M. "Perturbation theory for unbounded Markov reward processes with applications to queueing." Advances in Applied Probability 20, no. 01 (March 1988): 99–111. http://dx.doi.org/10.1017/s0001867800017961.

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Consider a perturbation in the one-step transition probabilities and rewards of a discrete-time Markov reward process with an unbounded one-step reward function. A perturbation estimate is derived for the finite horizon and average reward function. Results from [3] are hereby extended to the unbounded case. The analysis is illustrated for one- and two-dimensional queueing processes by an M/M/1-queue and an overflow queueing model with an error bound in the arrival rate.

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10

Bäuerle, Nicole, and Ulrich Rieder. "Comparison Results for Markov-Modulated Recursive Models." Probability in the Engineering and Informational Sciences 11, no. 2 (April 1997): 203–17. http://dx.doi.org/10.1017/s0269964800004769.

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We consider a general discrete-time stochastic recursive model that is influenced by an external Markov chain. Our aim is to investigate the effect that the transition matrix of the external process has on the system states of the model. To answer this question, we use new stochastic ordering concepts. Especially interesting are the results for infinite-stage Markov-modulated models. We illustrate our main results by three applications: an inventory model, a consumption model, and a queueing model for a time division multiplexing system.

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11

Aalto, Samuli. "Characterization of the Output Rate Process for a Markovian Storage Model." Journal of Applied Probability 35, no. 1 (March 1998): 184–99. http://dx.doi.org/10.1239/jap/1032192561.

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We consider storage models where the input rate and the demand are modulated by a Markov jump process. One particular example from teletraffic theory is a fluid model of a multiplexer loaded by exponential on-off sources. Although the storage level process has been widely studied, little attention has been paid to the output rate process. We will show that, under certain assumptions, there exists another Markov jump process that modulates the output rate. The modulating process is explicitly constructed. It turns out to be a modification of a GI/G/1 queueing process

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12

Aalto, Samuli. "Characterization of the Output Rate Process for a Markovian Storage Model." Journal of Applied Probability 35, no. 01 (March 1998): 184–99. http://dx.doi.org/10.1017/s0021900200014777.

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We consider storage models where the input rate and the demand are modulated by a Markov jump process. One particular example from teletraffic theory is a fluid model of a multiplexer loaded by exponential on-off sources. Although the storage level process has been widely studied, little attention has been paid to the output rate process. We will show that, under certain assumptions, there exists another Markov jump process that modulates the output rate. The modulating process is explicitly constructed. It turns out to be a modification of a GI/G/1 queueing process

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13

Liu, Yuanyuan, Wendi Li, and Xiuqin Li. "On geometric and algebraic transience for block-structured Markov chains." Journal of Applied Probability 57, no. 4 (November 23, 2020): 1313–38. http://dx.doi.org/10.1017/jpr.2020.69.

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AbstractBlock-structured Markov chains model a large variety of queueing problems and have many important applications in various areas. Stability properties have been well investigated for these Markov chains. In this paper we will present transient properties for two specific types of block-structured Markov chains, including M/G/1 type and GI/M/1 type. Necessary and sufficient conditions in terms of system parameters are obtained for geometric transience and algebraic transience. Possible extensions of the results to continuous-time Markov chains are also included.

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14

Dshalalow, Jewgeni H., and Gary Russell. "On a single-server queue with fixed accumulation level, state dependent service, and semi-Markov modulated input flow." International Journal of Mathematics and Mathematical Sciences 15, no. 3 (1992): 593–600. http://dx.doi.org/10.1155/s0161171292000759.

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The authors study the queueing process in a single-server queueing system with state dependent service and with the input modulated by a semi-Markov process embedded in the queueing process. It is also assumed that the server capacity isr≥1and that any service act will not begin until the queue accumulates at leastrunits. In this model, therefore, idle periods also depend upon the queue length.The authors establish an ergodicity criterion for the queueing process and evaluate explicitly its stationary distribution and other characteristics of the system, such as the mean service cycle, intensity of the system, intensity of the input stream, distribution of the idle period, and the mean busy period. Various special cases are treated.

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15

Li, Kangrui, Xiang Ji, Zicong Huang, and Shujie Yang. "Age of information: in Systems with Multi-source, Limited Buffers, and LCFS-S." Journal of Networking and Network Applications 3, no. 1 (2023): 32–44. http://dx.doi.org/10.33969/j-nana.2023.030104.

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In recent years, an increasing number of real-time applications have become more sensitive to the freshness of information, which requires that packets reach the receiver as promptly as possible. As a measure of information freshness, it is of great interest to measure the age of information (AoI) on multi-source networks. In this paper, we propose a new queueing system: the systems with N sources, Single buffer, Non-source-aware, and LCFS-S (NSLS-Q system). To simplify the study, we first studied the queueing system for Two sources, Single buffer, Non-source-aware, and LCFS-S (TSLS-Q system). We then generalize the conclusions to the NSLS-Q system. We model the queueing system using a stochastic hybrid system (SHS) to solve for the age of information in the queueing system. In this, Markov chains are used to represent the state transitions. We then compared the system with other queueing systems through numerical results. The results show that the queue model performs better in terms of AoI compared to the traditional queue model.

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16

Dang Thanh, Chuong, Duc Trung Pham, and Thang Doan Van. "A Retrial Queueing model with FDL at OBS core node." Network Protocols and Algorithms 10, no. 3 (January 6, 2019): 1. http://dx.doi.org/10.5296/npa.v10i3.13431.

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Optical Burst Switching networks are considered as an important candidate for the future transport networks. Many analysis models of OBS node with FDLs have been proposed recently. In this paper, we propose a novel retrial queueing model at OBS core node architecture SPL - feed-forward. Blocking probability will be calculated based on Markov multi-dimensional models. Numerical solution values from the proposed analysis method are compared with simulation, as well as between these models.

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17

Last, Günter. "Ergodicity properties of stress release, repairable system and workload models." Advances in Applied Probability 36, no. 2 (June 2004): 471–98. http://dx.doi.org/10.1239/aap/1086957582.

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In this paper we derive some of the main ergodicity properties of a class of Markov renewal processes and the associated marked point processes. This class represents a generic model of applied probability and is of importance in earthquake modeling, reliability theory and queueing.

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18

Last, Günter. "Ergodicity properties of stress release, repairable system and workload models." Advances in Applied Probability 36, no. 02 (June 2004): 471–98. http://dx.doi.org/10.1017/s0001867800013574.

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In this paper we derive some of the main ergodicity properties of a class of Markov renewal processes and the associated marked point processes. This class represents a generic model of applied probability and is of importance in earthquake modeling, reliability theory and queueing.

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19

Lu, Yingdong. "Performance Analysis of A Queueing System with Server Arrival and Departure." ACM SIGMETRICS Performance Evaluation Review 49, no. 2 (January 17, 2022): 21–23. http://dx.doi.org/10.1145/3512798.3512807.

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In many systems, in order to fulfill demand (computing or other services) that varies over time, service capacities often change accordingly. In this paper, we analyze a simple two dimensional Markov chain model of a queueing system in which multiple servers can arrive to increase service capacity, and depart if a server has been idle for too long. It is well known that multi-dimensional Markov chains are in general difficult to analyze. Our focus is on an approximation method of stationary performance of the system via the Stein method. For this purpose, innovative methods are developed to estimate the moments of the Markov chain, as well as the solution to the Poisson equation with a partial differential operator.

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20

Evdokimova, Ekaterina, Sabine Wittevrongel, and Dieter Fiems. "A Taylor Series Approach for Service-Coupled Queueing Systems with Intermediate Load." Mathematical Problems in Engineering 2017 (2017): 1–10. http://dx.doi.org/10.1155/2017/3298605.

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This paper investigates the performance of a queueing model with multiple finite queues and a single server. Departures from the queues are synchronised or coupled which means that a service completion leads to a departure in every queue and that service is temporarily interrupted whenever any of the queues is empty. We focus on the numerical analysis of this queueing model in a Markovian setting: the arrivals in the different queues constitute Poisson processes and the service times are exponentially distributed. Taking into account the state space explosion problem associated with multidimensional Markov processes, we calculate the terms in the series expansion in the service rate of the stationary distribution of the Markov chain as well as various performance measures when the system is (i) overloaded and (ii) under intermediate load. Our numerical results reveal that, by calculating the series expansions of performance measures around a few service rates, we get accurate estimates of various performance measures once the load is above 40% to 50%.

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21

Andrzej Korzeniowski, Joshua Patterson,. "M/M/1 Model with Unreliable Service." International Journal of Statistics and Probability 7, no. 1 (December 29, 2017): 125. http://dx.doi.org/10.5539/ijsp.v7n1p125.

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We define a new term ”unreliable service” and construct the corresponding embedded Markov Chain to an M/M/1 queue with so defined protocol. Sufficient conditions for positive recurrence and closed form of stationary distribution are provided. Furthermore, we compute the probability generating function of the stationary queue length and Laplace-Stieltjes transform of the stationary waiting time. In the course of the analysis an interesting decomposition of both the queue length and waiting time has emerged. A number of queueing models can be recovered from our work by taking limits of certain parameters.

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22

Hou, Fei, Yao Yu Li, and Jun Wu. "Queueing Netwoks Theory Based Analysis Approach for Aircraft Sortie Generation." Applied Mechanics and Materials 411-414 (September 2013): 1727–31. http://dx.doi.org/10.4028/www.scientific.net/amm.411-414.1727.

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This paper concentrates the carrier aircraft sortie generation evaluation problem. Based on the analysis of aircraft sortie process, we construct a Markov queueing network based aircraft sortie evaluation model, which contains the whole evaluation system and details. Finally, a simulation experiment is given to test our method and model, and simulation result proves its veracity and can be used to provide suggestion to commanders.

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23

KLIMENOK, VALENTINA I., DMITRY S. ORLOVSKY, and ALEXANDER N. DUDIN. "A BMAP/PH/N SYSTEM WITH IMPATIENT REPEATED CALLS." Asia-Pacific Journal of Operational Research 24, no. 03 (June 2007): 293–312. http://dx.doi.org/10.1142/s0217595907001310.

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A multi-server queueing model with a Batch Markovian Arrival Process, phase-type service time distribution and impatient repeated customers is analyzed. After any unsuccessful attempt, the repeated customer leaves the system with the fixed probability. The behavior of the system is described in terms of continuous time multi-dimensional Markov chain. Stability condition and an algorithm for calculating the stationary state distribution of this Markov chain are obtained. Main performance measures of the system are calculated. Numerical results are presented.

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24

Coutin, L., L. Decreusefond, and J. S. Dhersin. "A Markov Model for the Spread of Viruses in an Open Population." Journal of Applied Probability 47, no. 4 (December 2010): 976–96. http://dx.doi.org/10.1239/jap/1294170513.

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Inspired by methods of queueing theory, we propose a Markov model for the spread of viruses in an open population with an exogenous flow of infectives. We apply it to the diffusion of AIDS and hepatitis C diseases among drug users. From a mathematical point of view, the difference between the two viruses is shown in two parameters: the probability of curing the disease (which is 0 for AIDS but positive for hepatitis C) and the infection probability, which seems to be much higher for hepatitis. This model bears some resemblance to the M/M/∞ queueing system and is thus rather different from the models based on branching processes commonly used in the epidemiological literature. We carry out an asymptotic analysis (large initial population) and show that the Markov process is close to the solution of a nonlinear autonomous differential system. We prove both a law of large numbers and a functional central limit theorem to determine the speed of convergence towards the limiting system. The deterministic system itself converges, as time tends to ∞, to an equilibrium point. We then show that the sequence of stationary probabilities of the stochastic models shrinks to a Dirac measure at this point. This means that in a large population and for long-term analysis, we may replace the individual-based microscopic stochastic model with the macroscopic deterministic system without loss of precision. Moreover, we show how to compute the sensitivity of any functional of the Markov process with respect to a slight variation of any parameter of the model. This approach is applied to the spread of diseases among drug users, but could be applied to many other case studies in epidemiology.

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Coutin, L., L. Decreusefond, and J. S. Dhersin. "A Markov Model for the Spread of Viruses in an Open Population." Journal of Applied Probability 47, no. 04 (December 2010): 976–96. http://dx.doi.org/10.1017/s0021900200007300.

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Inspired by methods of queueing theory, we propose a Markov model for the spread of viruses in an open population with an exogenous flow of infectives. We apply it to the diffusion of AIDS and hepatitis C diseases among drug users. From a mathematical point of view, the difference between the two viruses is shown in two parameters: the probability of curing the disease (which is 0 for AIDS but positive for hepatitis C) and the infection probability, which seems to be much higher for hepatitis. This model bears some resemblance to the M/M/∞ queueing system and is thus rather different from the models based on branching processes commonly used in the epidemiological literature. We carry out an asymptotic analysis (large initial population) and show that the Markov process is close to the solution of a nonlinear autonomous differential system. We prove both a law of large numbers and a functional central limit theorem to determine the speed of convergence towards the limiting system. The deterministic system itself converges, as time tends to ∞, to an equilibrium point. We then show that the sequence of stationary probabilities of the stochastic models shrinks to a Dirac measure at this point. This means that in a large population and for long-term analysis, we may replace the individual-based microscopic stochastic model with the macroscopic deterministic system without loss of precision. Moreover, we show how to compute the sensitivity of any functional of the Markov process with respect to a slight variation of any parameter of the model. This approach is applied to the spread of diseases among drug users, but could be applied to many other case studies in epidemiology.

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26

Hordijk, Arie, and Flos Spieksma. "Constrained admission control to a queueing system." Advances in Applied Probability 21, no. 2 (June 1989): 409–31. http://dx.doi.org/10.2307/1427167.

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We consider an exponential queue with arrival and service rates depending on the number of jobs present in the queue. The queueing system is controlled by restricting arrivals. Typically, a good policy should provide a proper balance between throughput and congestion. A mathematical model for computing such a policy is a Markov decision chain with rewards and a constrained cost function. We give general conditions on the reward and cost function which guarantee the existence of an optimal threshold or thinning policy. An efficient algorithm for computing an optimal policy is constructed.

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27

Hordijk, Arie, and Flos Spieksma. "Constrained admission control to a queueing system." Advances in Applied Probability 21, no. 02 (June 1989): 409–31. http://dx.doi.org/10.1017/s0001867800018619.

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We consider an exponential queue with arrival and service rates depending on the number of jobs present in the queue. The queueing system is controlled by restricting arrivals. Typically, a good policy should provide a proper balance between throughput and congestion. A mathematical model for computing such a policy is a Markov decision chain with rewards and a constrained cost function. We give general conditions on the reward and cost function which guarantee the existence of an optimal threshold or thinning policy. An efficient algorithm for computing an optimal policy is constructed.

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28

Gbenga-ilori, Abiodun, and Olufunmilayo Sanusi. "Markovian Queueing Model for Throughput Maximization in D2D-Enabled Cellular Networks." International Journal of Electrical and Computer Engineering (IJECE) 8, no. 5 (October 1, 2018): 3767. http://dx.doi.org/10.11591/ijece.v8i5.pp3767-3777.

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Device-to-Device (D2D) communication has been considered a key enabling technology that can facilitate spectrum sharing in 4G and 5G cellular networks. In order to meet the high data rate demands of these new generation cellular networks, this paper considers the optimization of available spectrum resource through dynamic spectrum access. The utilization of continuous-time Markov chain (CTMC) model for efficient spectrum access in D2D-enabled cellular networks is investigated for the purpose of determining the impact of this model on the capacity improvement of cellular networks. The paper considers the use of CTMC model with both queueing and non-queueing cases called 13-Q CTMC and 6-NQ CTMC respectively with the aim of improving the overall capacity of the cellular network under a fairness constraint among all users. The proposed strategy consequently ensures that spectrum access for cellular and D2D users is optimally coordinated by designing optimal spectrum access probabilities. Numerical simulations are performed to observe the impact of the proposed Markovian queueing model on spectrum access and consequently on the capacity of D2D-enabled cellular networks. Results showed that the proposed 13-Q CTMC provide a more spectrum-efficient sharing scheme, thereby enabling better network performances and larger capabilities to accommodate more users.

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29

Zhang, Zhicong, Shuai Li, and Xiaohui Yan. "Online Self-Organizing Network Control with Time Averaged Weighted Throughput Objective." Discrete Dynamics in Nature and Society 2018 (2018): 1–11. http://dx.doi.org/10.1155/2018/4184805.

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We study an online multisource multisink queueing network control problem characterized with self-organizing network structure and self-organizing job routing. We decompose the self-organizing queueing network control problem into a series of interrelated Markov Decision Processes and construct a control decision model for them based on the coupled reinforcement learning (RL) architecture. To maximize the mean time averaged weighted throughput of the jobs through the network, we propose a reinforcement learning algorithm with time averaged reward to deal with the control decision model and obtain a control policy integrating the jobs routing selection strategy and the jobs sequencing strategy. Computational experiments verify the learning ability and the effectiveness of the proposed reinforcement learning algorithm applied in the investigated self-organizing network control problem.

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30

Zhang, Feng, and Zhifeng Zhu. "A Discrete-TimeGeo/G/1Retrial Queue withJVacations and Two Types of Breakdowns." Journal of Applied Mathematics 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/834731.

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This paper is concerned with a discrete-timeGeo/G/1retrial queueing model withJvacations and two types of breakdowns. If the orbit is empty, the server takes at mostJvacations repeatedly until at least one customer appears in the orbit upon returning from a vacation. It is assumed that the server is subject to two types of different breakdowns and is sent immediately for repair. We analyze the Markov chain underlying the considered queueing system and derive the system state distribution as well as the orbit size and the system size distributions in terms of their generating functions. Then, we obtain some performance measures through the generating functions. Moreover, the stochastic decomposition property and the corresponding continuous-time queueing system are investigated. Finally, some numerical examples are provided to illustrate the effect of vacations and breakdowns on several performance measures of the system.

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31

Chaudhry, Mohan, and Jing Gai. "Analytic and Computational Analysis of GI/Ma,b/c Queueing System." Mathematics 10, no. 19 (September 22, 2022): 3445. http://dx.doi.org/10.3390/math10193445.

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Bulk-service queueing systems have been widely applied in many areas in real life. While single-server queueing systems work in some cases, multi-servers can efficiently handle most complex applications. Bulk-service, multi-server queueing systems (compared to well-developed single-server queueing systems) are more complex and harder to deal with, especially when the inter-arrival time distributions are arbitrary. This paper deals with analytic and computational analyses of queue-length distributions for a complex bulk-service, multi-server queueing system GI/Ma,b/c, wherein inter-arrival times follow an arbitrary distribution, a is the quorum, and b is the capacity of each server; service times follow exponential distributions. The introduction of quorum a further increases the complexity of the model. In view of this, a two-dimensional Markov chain has to be involved. Currently, it appears that this system has not been addressed so far. An elegant analytic closed-form solution and an efficient algorithm to obtain the queue-length distributions at three different epochs, i.e., pre-arrival epoch (p.a.e.), random epoch (r.e.), and post-departure epoch (p.d.e.) are presented, when the servers are in busy and idle states, respectively.

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32

Melikov, Agassi, Sevinj Aliyeva, and Janos Sztrik. "Analysis of Queueing System MMPP/M/K/K with Delayed Feedback." Mathematics 7, no. 11 (November 18, 2019): 1128. http://dx.doi.org/10.3390/math7111128.

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The model of multi-channel queuing system with Markov modulated Poisson process (MMPP) flow and delayed feedback is considered. After the customer is served completely, they will decide either to join the retrial group again for another service (feedback) with some state-dependent probability or to leave the system forever with complimentary probability. Feedback calls organize an orbit of repeated calls (r-calls). If upon arrival of an r-call all the channels of the system are busy, then it either leaves the system with some state-dependent probability or with a complementary probability returns to orbit. Methods to calculate the steady-state probabilities of the appropriate three-dimensional Markov chain as well as performance measures of investigated system are developed. Results of numerical experiments are demonstrated.

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33

Percus, Ora E., and J. K. Percus. "Queue length distributions in a markov model of a multistage clocked queueing network." Communications on Pure and Applied Mathematics 43, no. 5 (July 1990): 685–93. http://dx.doi.org/10.1002/cpa.3160430506.

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Chương, Đặng Thanh, and Phạm Trung Đức. "Mô hình hàng đợi retrial cho đường trễ quang FDL tại nút lõi OBS xét chất lượng dịch vụ QoS." Hue University Journal of Science: Techniques and Technology 127, no. 2A (February 1, 2019): 131–46. http://dx.doi.org/10.26459/hueuni-jtt.v127i2a.5099.

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Optical Burst Switching networks are considered as an important candidate for future transport networks. Many analysis models of the OBS core node with FDLs have been proposed recently. Our paper proposes a novel retrial queueing model at OBS core node architecture SPL - feed-forward with QoS. Blocking probability will be calculated based on Markov multi-dimensional models. Numerical results from the proposed analysis method are compared with simulation, as well as between these model.

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Zhao, Yiqiang Q., Wei Li, and Attahiru Sule Alfa. "Duality results for block-structured transition matrices." Journal of Applied Probability 36, no. 4 (December 1999): 1045–57. http://dx.doi.org/10.1239/jap/1032374754.

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In this paper, we consider a certain class of Markov renewal processes where the matrix of the transition kernel governing the Markov renewal process possesses some block-structured property, including repeating rows. Duality conditions and properties are obtained on two probabilistic measures which often play a key role in the analysis and computations of such a block-structured process. The method used here unifies two different concepts of duality. Applications of duality are also provided, including a characteristic theorem concerning recurrence and transience of a transition matrix with repeating rows and a batch arrival queueing model.

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Zhao, Yiqiang Q., Wei Li, and Attahiru Sule Alfa. "Duality results for block-structured transition matrices." Journal of Applied Probability 36, no. 04 (December 1999): 1045–57. http://dx.doi.org/10.1017/s002190020001785x.

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In this paper, we consider a certain class of Markov renewal processes where the matrix of the transition kernel governing the Markov renewal process possesses some block-structured property, including repeating rows. Duality conditions and properties are obtained on two probabilistic measures which often play a key role in the analysis and computations of such a block-structured process. The method used here unifies two different concepts of duality. Applications of duality are also provided, including a characteristic theorem concerning recurrence and transience of a transition matrix with repeating rows and a batch arrival queueing model.

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Hordijk, A., G. M. Koole, and J. A. Loeve. "Analysis of a Customer Assignment Model with No State Information." Probability in the Engineering and Informational Sciences 8, no. 3 (July 1994): 419–29. http://dx.doi.org/10.1017/s0269964800003508.

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In this paper we analyze a queueing network consisting of parallel queues and arriving customers that have to be assigned to one of the queues. The assignment rule may not depend on the numbers of customers in the queues. Our goal is to find a policy that is optimal with respect to the long-run average cost. We will consider two cases: holding costs and waiting times. A recently developed algorithm for Markov decision chains with partial state information is applied. It turns out that the periodic policies found by this algorithm are close, if not equal, to the optimal ones.

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Kempa, Wojciech M., and Iwona Paprocka. "Transient Behavior of a Queueing Model with Hyper-Exponentially Distributed Processing Times and Finite Buffer Capacity." Sensors 22, no. 24 (December 16, 2022): 9909. http://dx.doi.org/10.3390/s22249909.

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In the paper, a finite-capacity queueing model is considered in which jobs arrive according to a Poisson process and are being served according to hyper-exponential service times. A system of equations for the time-sensitive queue-size distribution is established by applying the paradigm of embedded Markov chain and total probability law. The solution of the corresponding system written for Laplace transforms is obtained via an algebraic approach in a compact form. Numerical illustration results are attached as well.

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Rosson, Hong-Tham T., and Jewgeni H. Dshalalow. "A non-Markovian queueing system with a variable number of channels." Journal of Applied Mathematics and Stochastic Analysis 16, no. 4 (January 1, 2003): 375–95. http://dx.doi.org/10.1155/s1048953303000297.

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In this paper we study a queueing model of type GI/M/m˜a/∞ with m parallel channels, some of which may suspend their service at specified random moments of time. Whether or not this phenomenon occurs depends on the queue length. The queueing process, which we target, turns out to be semi-regenerative, and we fully explore this utilizing semi-regenerative techniques. This is contrary to the more traditional supplementary variable approach and the less popular approach of combination semi-regenerative and supplementary variable technique. We pass to the limiting distribution of the continuous time parameter process through the embedded Markov chain for which we find the invariant probability measure. All formulas are analytically tractable.

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Kondrashova, Elizaveta. "Controlled optimization model for traffic zones during road repair periods." E3S Web of Conferences 164 (2020): 03007. http://dx.doi.org/10.1051/e3sconf/202016403007.

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The aim of the research is construct a model that allows to make the best decisions while carrying out repairs on the road. These decisions can be made taking into account both the interests of the participants of the traffic and taking into account the costs spent on repair. This paper presents optimization model for traffic zones using queueing controlled models in searching for an optimal management strategy. This optimal strategy is based on the theory of controlled semi-Markov processes. As a result we have controlled model for use during road repair periods. The model can be complicated and varied depending on the conditions.

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Kim, Song-Kyoo, and Chan Yeob Yeun. "A Versatile Queuing System For Sharing Economy Platform Operations." Mathematics 7, no. 11 (October 23, 2019): 1005. http://dx.doi.org/10.3390/math7111005.

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The paper deals with a sharing economy system with various management factors by using a bulk input G/M/1 type queuing model. The effective management of operating costs is vital for controlling the sharing economy platform and this research builds the theoretical background to understand the sharing economy business model. Analytically, the techniques include a classical Markov process of the single channel queueing system, semi-Markov process and semi-regenerative process. It uses the stochastic congruent properties to find the probability distribution of the number of contractors in the sharing economy platform. The obtained explicit formulas demonstrate the usage of functional for the main stochastic characteristics including sharing expenses due to over contracted resources and optimization of their objective function.

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Usar, I. Ya, I. A. Makushenko, and Iu O. Protopop. "The convergense rate of stationary distribution of retrial queueing system with queue." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 3 (2019): 52–55. http://dx.doi.org/10.17721/1812-5409.2019/3.7.

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This paper describes a steady state behavior of the retrial system in the case of one server, one place in the queue and an infinity orbit. We research Markov`s models of retrial systems and variable rate of input flow controlled by threshold strategy. We defined stationary regime existence conditions and investigated probability characteristics of process for two-dimension Markov process with continuous time which we took as a main model of the specified system. In stationary regime for probability characteristics of the service process were found explicit formulas. Research methods which we used are based on the initial process approximation by the process with bounded state space. Results of the research allow us to evaluate convergence rates of stationary distribution of finite systems with repeated calls to stationary distribution of infinite systems. Method of probability flow equating is used for obtain explicit expressions for stationary system probabilities through the closed path which are defined in a special way. We considered model for one service devices and one place in the queue, which are controlled by threshold strategies.

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Al-Begain, Khalid, Alexander N. Dudin, and Vilena V. Mushko. "Novel Queueing Model for Multimedia Over Downlink in 3.5G Wireless Network." Journal of Communications Software and Systems 2, no. 2 (April 5, 2017): 68. http://dx.doi.org/10.24138/jcomss.v2i2.290.

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In this paper, a model for multimedia transmission over downlink shared channel in 3.5G wireless network is presented. The multimedia stream consists of multiplesubstreams that are aggregated into one real-time and onenonreal-time flows. Correlation with each flow and between flows is assumed. Additionally, we propose a combined time-space priority buffer management scheme to optimise quality of service requirements for each flow. The problem is formulated in terms of a queue with two priority classes, one of which has time priority while the another has space priority. The input is described by the Batch Marked Markovian Arrival Process (BMMAP). Service time distributions are of PH (phase) type dependent on the class of a customer. The buffer is finite, but the customers of a class having higher priority for taking into the service from a buffer (time priority) can occupy only a part of this buffer. Queueing system's behavior is described in terms ofmulti-dimensional continuous time skip-free to the left Markov chain. It allows to exploit an effective algorithm for calculation of the stationary distribution of the queueing system. Loss probability for customers of both classes is calculated. Waiting time distribution for priority customers is calculated.

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Alam, M., and V. Mani. "Queueing model of a bi-level Markov service-system and its solution using recursion." IEEE Transactions on Reliability 37, no. 4 (1988): 427–33. http://dx.doi.org/10.1109/24.9853.

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Pearce, C. E. M. "Extended continued fractions, recurrence relations and two-dimensional Markov processes." Advances in Applied Probability 21, no. 2 (June 1989): 357–75. http://dx.doi.org/10.2307/1427164.

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Connections between Markov processes and continued fractions have long been known (see, for example, Good [8]). However the usefulness of extended continued fractions in such a context appears not to have been explored. In this paper a convergence theorem is established for a class of extended continued fractions and used to provide well-behaved solutions for some general order linear recurrence relations such as arise in connection with the equilibrium distribution of state for some Markov processes whose natural state spaces are of dimension 2. Specific application is made to a multiserver version of a queueing problem studied by Neuts and Ramalhoto [13] and to a model proposed by Cohen [5] for repeated call attempts in teletraffic.

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Pearce, C. E. M. "Extended continued fractions, recurrence relations and two-dimensional Markov processes." Advances in Applied Probability 21, no. 02 (June 1989): 357–75. http://dx.doi.org/10.1017/s0001867800018589.

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Connections between Markov processes and continued fractions have long been known (see, for example, Good [8]). However the usefulness of extended continued fractions in such a context appears not to have been explored. In this paper a convergence theorem is established for a class of extended continued fractions and used to provide well-behaved solutions for some general order linear recurrence relations such as arise in connection with the equilibrium distribution of state for some Markov processes whose natural state spaces are of dimension 2. Specific application is made to a multiserver version of a queueing problem studied by Neuts and Ramalhoto [13] and to a model proposed by Cohen [5] for repeated call attempts in teletraffic.

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Efrosinin, Dmitry, Natalia Stepanova, and Janos Sztrik. "Algorithmic Analysis of Finite-Source Multi-Server Heterogeneous Queueing Systems." Mathematics 9, no. 20 (October 18, 2021): 2624. http://dx.doi.org/10.3390/math9202624.

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The paper deals with a finite-source queueing system serving one class of customers and consisting of heterogeneous servers with unequal service intensities and of one common queue. The main model has a non-preemptive service when the customer can not change the server during its service time. The optimal allocation problem is formulated as a Markov-decision one. We show numerically that the optimal policy which minimizes the long-run average number of customers in the system has a threshold structure. We derive the matrix expressions for performance measures of the system and compare the main model with alternative simplified queuing systems which are analysed for the arbitrary number of servers. We observe that the preemptive heterogeneous model operating under a threshold policy is a good approximation for the main model by calculating the mean number of customers in the system. Moreover, using the preemptive and non-preemptive queueing models with the faster server first policy the lower and upper bounds are calculated for this mean value.

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Sun, Feng, Li Sun, Shao-wei Sun, and Dian-hai Wang. "Study on the Calculation Models of Bus Delay at Bays Using Queueing Theory and Markov Chain." Computational Intelligence and Neuroscience 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/750304.

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Traffic congestion at bus bays has decreased the service efficiency of public transit seriously in China, so it is crucial to systematically study its theory and methods. However, the existing studies lack theoretical model on computing efficiency. Therefore, the calculation models of bus delay at bays are studied. Firstly, the process that buses are delayed at bays is analyzed, and it was found that the delay can be divided into entering delay and exiting delay. Secondly, the queueing models of bus bays are formed, and the equilibrium distribution functions are proposed by applying the embedded Markov chain to the traditional model of queuing theory in the steady state; then the calculation models of entering delay are derived at bays. Thirdly, the exiting delay is studied by using the queueing theory and the gap acceptance theory. Finally, the proposed models are validated using field-measured data, and then the influencing factors are discussed. With these models the delay is easily assessed knowing the characteristics of the dwell time distribution and traffic volume at the curb lane in different locations and different periods. It can provide basis for the efficiency evaluation of bus bays.

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Chakravarthy, S. R., and S. Thiagarajan. "Two parallel finite queues with simultaneous services and Markovian arrivals." Journal of Applied Mathematics and Stochastic Analysis 10, no. 4 (January 1, 1997): 383–405. http://dx.doi.org/10.1155/s1048953397000439.

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In this paper, we consider a finite capacity single server queueing model with two buffers, A and B, of sizes K and N respectively. Messages arrive one at a time according to a Markovian arrival process. Messages that arrive at buffer A are of a different type from the messages that arrive at buffer B. Messages are processed according to the following rules: 1. When buffer A(B) has a message and buffer B(A) is empty, then one message from A(B) is processed by the server. 2. When both buffers, A and B, have messages, then two messages, one from A and one from B, are processed simultaneously by the server. The service times are assumed to be exponentially distributed with parameters that may depend on the type of service. This queueing model is studied as a Markov process with a large state space and efficient algorithmic procedures for computing various system performance measures are given. Some numerical examples are discussed.

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Dshalalow, Jewgeni. "On the multiserver queue with finite waiting room and controlled input." Advances in Applied Probability 17, no. 2 (June 1985): 408–23. http://dx.doi.org/10.2307/1427148.

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In this paper we study a multi-channel queueing model of type with N waiting places and a non-recurrent input flow dependent on queue length at the time of each arrival. The queue length is treated as a basic process. We first determine explicitly the limit distribution of the embedded Markov chain. Then, by introducing an auxiliary Markov process, we find a simple relationship between the limiting distribution of the Markov chain and the limiting distribution of the original process with continuous time parameter. Here we simultaneously combine two methods: solving the corresponding Kolmogorov system of the differential equations, and using an approach based on the theory of semi-regenerative processes. Among various applications of multi-channel queues with state-dependent input stream, we consider a closed single-server system with reserve replacement and state-dependent service, which turns out to be dual (in a certain sense) in relation to our model; an optimization problem is also solved, and an interpretation by means of tandem systems is discussed.

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