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Journal articles on the topic 'Distributions à queues lourdes'

Author: Grafiati

Published: 26 October 2024

Last updated: 31 July 2025

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1

Tahiananirina, RAZAFINDRALAMBO Hasina, RAZAFIMANDIMBY Honoré, RAMAHAZOSOA Irrish Parker, RABEHARISOA Jean Marc, and RATIARISON Adolphe Andriamanga. "Estimations Des Quantiles Extrêmes Des Précipitations Convectives Avec Les Distributions des Valeurs Extrêmes Généralisées : Cas Des Plaines De La Basse Betsiboka." International Journal of Progressive Sciences and Technologies 40, no. 1 (2023): 308. http://dx.doi.org/10.52155/ijpsat.v40.1.5578.

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Résumé - L’objectif de cette étude est d’estimer la fréquence de retour des précipitations convectives extrêmes dans les plaines de la basse Betsiboka, Madagascar. L’approche méthodologique consiste à trouver les distributions statistiques des pluies convectives journalières maximales annuelles de 1959 à 2021 en les ajustant avec des distributions des valeurs extrêmes généralisées. Les paramètres des distributions des valeurs extrêmes généralisées ont été estimés par la méthode des moments pondérés. Les résultats obtenus montrent que l’ajustement des données étudiées avec les distributions des

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2

Chaudhry, Mohan L., Indra, and Vijay Rajan. "Analytically Simple and Computationally Efficient Solution to Geo/G/1 and Geo/G/1/N Queues Involving Heavy-tailed Distributions for Service Times." Calcutta Statistical Association Bulletin 70, no. 1 (2018): 74–85. http://dx.doi.org/10.1177/0008068318770566.

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The previous studies pertaining to the queues Geo/G/1 and Geo/G/1/N involve light-tailed distributions for service time. However, due to applications of heavy-tailed distributions in computer science and financial engineering, these distributions are used for service time. This article provides a simple and computationally efficient solution to the queues Geo/G/1 and Geo/G/1/N involving heavy-tailed distributions for service times.

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3

Szczotka, Władysław. "Stationary representation of queues. I." Advances in Applied Probability 18, no. 3 (1986): 815–48. http://dx.doi.org/10.2307/1427189.

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The paper deals with the asymptotic behaviour of queues for which the generic sequence is not necessarily stationary but is asymptotically stationary in some sense. The latter property is defined by an appropriate type of convergence of probability distributions of the sequences to the distribution of a stationary sequence We consider six types of convergence of to The main result is as follows: if the sequence of the distributions converges in one of six ways then the sequence of distributions of the sequences converges in the same way, independently of initial conditions. Furthermore the lim

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4

Szczotka, Władysław. "Stationary representation of queues. I." Advances in Applied Probability 18, no. 03 (1986): 815–48. http://dx.doi.org/10.1017/s0001867800016086.

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The paper deals with the asymptotic behaviour of queues for which the generic sequence is not necessarily stationary but is asymptotically stationary in some sense. The latter property is defined by an appropriate type of convergence of probability distributions of the sequences to the distribution of a stationary sequence We consider six types of convergence of to The main result is as follows: if the sequence of the distributions converges in one of six ways then the sequence of distributions of the sequences converges in the same way, independently of initial conditions. Furthermore the lim

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5

Karpelevitch, F. I., and A. Ya Kreinin. "Joint distributions in Poissonian tandem queues." Queueing Systems 12, no. 3-4 (1992): 273–86. http://dx.doi.org/10.1007/bf01158803.

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6

Taylor, Nicholas B., and Benjamin G. Heydecker. "Estimating probability distributions of dynamic queues." Transportation Planning and Technology 38, no. 1 (2014): 3–27. http://dx.doi.org/10.1080/03081060.2014.976987.

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7

Wang, P. Patrick, and Vicky F. Locker. "Steady-State Distributions Of Parallel Queues." INFOR: Information Systems and Operational Research 39, no. 1 (2001): 89–106. http://dx.doi.org/10.1080/03155986.2001.11732428.

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8

Miyazawa, Masakiyo, and Ronald W. Wolff. "Symmetric queues with batch departures and their networks." Advances in Applied Probability 28, no. 1 (1996): 308–26. http://dx.doi.org/10.2307/1427923.

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Batch departures arise in various applications of queues. In particular, such models have been studied recently in connection with production systems. For the most part, however, these models assume Poisson arrivals and exponential service times; little is known about them under more general settings. We consider how their stationary queue length distributions are affected by the distributions of interarrival times, service times and departing batch sizes of customers. Since this is not an easy problem even for single departure models, we first concentrate on single-node queues with a symmetri

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9

Miyazawa, Masakiyo, and Ronald W. Wolff. "Symmetric queues with batch departures and their networks." Advances in Applied Probability 28, no. 01 (1996): 308–26. http://dx.doi.org/10.1017/s0001867800027385.

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Batch departures arise in various applications of queues. In particular, such models have been studied recently in connection with production systems. For the most part, however, these models assume Poisson arrivals and exponential service times; little is known about them under more general settings. We consider how their stationary queue length distributions are affected by the distributions of interarrival times, service times and departing batch sizes of customers. Since this is not an easy problem even for single departure models, we first concentrate on single-node queues with a symmetri

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10

Hunter, Jeffrey J. "Filtering of Markov renewal queues, IV: Flow processes in feedback queues." Advances in Applied Probability 17, no. 2 (1985): 386–407. http://dx.doi.org/10.2307/1427147.

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This paper is a continuation of the study of a class of queueing systems where the queue-length process embedded at basic transition points, which consist of ‘arrivals’, ‘departures’ and ‘feedbacks’, is a Markov renewal process (MRP). The filtering procedure of Çinlar (1969) was used in [12] to show that the queue length process embedded separately at ‘arrivals’, ‘departures’, ‘feedbacks’, ‘inputs’ (arrivals and feedbacks), ‘outputs’ (departures and feedbacks) and ‘external’ transitions (arrivals and departures) are also MRP. In this paper expressions for the elements of each Markov renewal ke

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11

Hunter, Jeffrey J. "Filtering of Markov renewal queues, IV: Flow processes in feedback queues." Advances in Applied Probability 17, no. 02 (1985): 386–407. http://dx.doi.org/10.1017/s0001867800015032.

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This paper is a continuation of the study of a class of queueing systems where the queue-length process embedded at basic transition points, which consist of ‘arrivals’, ‘departures’ and ‘feedbacks’, is a Markov renewal process (MRP). The filtering procedure of Çinlar (1969) was used in [12] to show that the queue length process embedded separately at ‘arrivals’, ‘departures’, ‘feedbacks’, ‘inputs’ (arrivals and feedbacks), ‘outputs’ (departures and feedbacks) and ‘external’ transitions (arrivals and departures) are also MRP. In this paper expressions for the elements of each Markov renewal ke

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12

Tarasov, V. N. "Analysis of queues with hyperexponential arrival distributions." Problems of Information Transmission 52, no. 1 (2016): 14–23. http://dx.doi.org/10.1134/s0032946016010038.

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13

Harrison, Peter G., and Edwige Pitel. "Response time distributions in tandem G-networks." Journal of Applied Probability 32, no. 1 (1995): 224–46. http://dx.doi.org/10.2307/3214932.

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The Laplace transform of the probability distribution of the end-to-end delay in tandem networks is obtained where the first and/or second queue are G-queues, i.e. they have negative arrivals. For the most general case the method is based on the solution of a boundary value problem on a closed contour in the complex plane, which itself reduces to the solution of a Fredholm integral equation of the second kind. We also consider the dependence or independence of the sojourn times at each queue in the two special cases where only one of the queues is a G-queue, the other having no negative arriva

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14

Harrison, Peter G., and Edwige Pitel. "Response time distributions in tandem G-networks." Journal of Applied Probability 32, no. 01 (1995): 224–46. http://dx.doi.org/10.1017/s0021900200102682.

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The Laplace transform of the probability distribution of the end-to-end delay in tandem networks is obtained where the first and/or second queue are G-queues, i.e. they have negative arrivals. For the most general case the method is based on the solution of a boundary value problem on a closed contour in the complex plane, which itself reduces to the solution of a Fredholm integral equation of the second kind. We also consider the dependence or independence of the sojourn times at each queue in the two special cases where only one of the queues is a G-queue, the other having no negative arriva

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15

Ayesta, Urtzi. "A Unifying Conservation Law for Single-Server Queues." Journal of Applied Probability 44, no. 4 (2007): 1078–87. http://dx.doi.org/10.1239/jap/1197908826.

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We develop a conservation law for a multi-class GI/GI/1 queue operating under a general work-conserving scheduling discipline. For single-class single-server queues, conservation laws have been obtained for both nonanticipating and anticipating disciplines with general service time distributions. For multi-class single-server queues, conservation laws have been obtained for (i) nonanticipating disciplines with exponential service time distributions and (ii) nonpreemptive nonanticipating disciplines with general service time distributions. The unifying conservation law we develop generalizes al

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16

Ayesta, Urtzi. "A Unifying Conservation Law for Single-Server Queues." Journal of Applied Probability 44, no. 04 (2007): 1078–87. http://dx.doi.org/10.1017/s0021900200003752.

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We develop a conservation law for a multi-class GI/GI/1 queue operating under a general work-conserving scheduling discipline. For single-class single-server queues, conservation laws have been obtained for both nonanticipating and anticipating disciplines with general service time distributions. For multi-class single-server queues, conservation laws have been obtained for (i) nonanticipating disciplines with exponential service time distributions and (ii) nonpreemptive nonanticipating disciplines with general service time distributions. The unifying conservation law we develop generalizes al

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17

Gelenbe, Erol, Peter Glynn, and Karl Sigman. "Queues with negative arrivals." Journal of Applied Probability 28, no. 1 (1991): 245–50. http://dx.doi.org/10.2307/3214756.

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We study single-server queueing models where in addition to regular arriving customers, there are negative arrivals. A negative arrival has the effect of removing a customer from the queue. The way in which this removal is specified gives rise to several different models. Unlike the standard FIFOGI/GI/1 model, the stability conditions for these new models may depend upon more than just the arrival and service rates; the entire distributions of interarrival and service times may be involved.

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18

Gelenbe, Erol, Peter Glynn, and Karl Sigman. "Queues with negative arrivals." Journal of Applied Probability 28, no. 01 (1991): 245–50. http://dx.doi.org/10.1017/s0021900200039589.

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We study single-server queueing models where in addition to regular arriving customers, there are negative arrivals. A negative arrival has the effect of removing a customer from the queue. The way in which this removal is specified gives rise to several different models. Unlike the standard FIFO GI/GI/1 model, the stability conditions for these new models may depend upon more than just the arrival and service rates; the entire distributions of interarrival and service times may be involved.

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19

Chang, Cheng-Shang. "On the input-output map of a G/G/1 queue." Journal of Applied Probability 31, no. 4 (1994): 1128–33. http://dx.doi.org/10.2307/3215337.

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In this note, we consider G/G/1 queues with stationary and ergodic inputs. We show that if the service times are independent and identically distributed with unbounded supports, then for a given mean of interarrival times, the number of sequences (distributions) of interarrival times that induce identical distributions on interdeparture times is at most 1. As a direct consequence, among all the G/M/1 queues with stationary and ergodic inputs, the M/M/1 queue is the only queue whose departure process is identically distributed as the input process.

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20

Chang, Cheng-Shang. "On the input-output map of a G/G/1 queue." Journal of Applied Probability 31, no. 04 (1994): 1128–33. http://dx.doi.org/10.1017/s0021900200099654.

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In this note, we consider G/G/1 queues with stationary and ergodic inputs. We show that if the service times are independent and identically distributed with unbounded supports, then for a given mean of interarrival times, the number of sequences (distributions) of interarrival times that induce identical distributions on interdeparture times is at most 1. As a direct consequence, among all the G/M/1 queues with stationary and ergodic inputs, the M/M/1 queue is the only queue whose departure process is identically distributed as the input process.

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21

Li, Junping, and Anyue Chen. "Decay property of stopped Markovian bulk-arriving queues." Advances in Applied Probability 40, no. 1 (2008): 95–121. http://dx.doi.org/10.1239/aap/1208358888.

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We consider decay properties including the decay parameter, invariant measures, invariant vectors, and quasistationary distributions of a Markovian bulk-arriving queue that stops immediately after hitting the zero state. Investigating such behavior is crucial in realizing the busy period and some other related properties of Markovian bulk-arriving queues. The exact value of the decay parameter λC is obtained and expressed explicitly. The invariant measures, invariant vectors, and quasistationary distributions are then presented. We show that there exists a family of invariant measures indexed

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22

Li, Junping, and Anyue Chen. "Decay property of stopped Markovian bulk-arriving queues." Advances in Applied Probability 40, no. 01 (2008): 95–121. http://dx.doi.org/10.1017/s0001867800002391.

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We consider decay properties including the decay parameter, invariant measures, invariant vectors, and quasistationary distributions of a Markovian bulk-arriving queue that stops immediately after hitting the zero state. Investigating such behavior is crucial in realizing the busy period and some other related properties of Markovian bulk-arriving queues. The exact value of the decay parameter λCis obtained and expressed explicitly. The invariant measures, invariant vectors, and quasistationary distributions are then presented. We show that there exists a family of invariant measures indexed b

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23

Lee, Ho Woo, Se Won Lee, and Jongwoo Jeon. "Using factorization in analyzing D-BMAP/G/1 queues." Journal of Applied Mathematics and Stochastic Analysis 2005, no. 2 (2005): 119–32. http://dx.doi.org/10.1155/jamsa.2005.119.

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We demonstrate how one can use the factorization property to derive the queue-length distributions of the discrete-time BMAP/G/1 queues with complex operational behavior during the idle period. The procedure demonstrated in this paper can be applied to the analysis of many other discrete-time BMAP/G/1 queues with more behavioral complexities.

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24

Shanthikumar, J. George, and Ushio Sumita. "On the busy-period distributions of M/G/1/K queues by state-dependent arrivals and FCFS/LCFS-P service disciplines." Journal of Applied Probability 22, no. 4 (1985): 912–19. http://dx.doi.org/10.2307/3213958.

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The busy-period distributions of M/G/1/K queues with state-dependent arrival rates are considered. Two recursion formulas for the Laplace–Stieltjes transforms of the busy periods under the FCFS and preempt resume LCFS service disciplines are obtained. It is shown that the busy-period distributions for the two service disciplines are, in general, different, in contrast to the fact that they coincide for ordinary M/G/1 queues. For deterministic service times and arrival rates non-increasing in the number of customers in the system, stochastic ordering between these two busy periods is also estab

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25

Shanthikumar, J. George, and Ushio Sumita. "On the busy-period distributions of M/G/1/K queues by state-dependent arrivals and FCFS/LCFS-P service disciplines." Journal of Applied Probability 22, no. 04 (1985): 912–19. http://dx.doi.org/10.1017/s0021900200108149.

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The busy-period distributions of M/G/1/K queues with state-dependent arrival rates are considered. Two recursion formulas for the Laplace–Stieltjes transforms of the busy periods under the FCFS and preempt resume LCFS service disciplines are obtained. It is shown that the busy-period distributions for the two service disciplines are, in general, different, in contrast to the fact that they coincide for ordinary M/G/1 queues. For deterministic service times and arrival rates non-increasing in the number of customers in the system, stochastic ordering between these two busy periods is also estab

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26

Glynn, Peter W., and Ward Whitt. "A new view of the heavy-traffic limit theorem for infinite-server queues." Advances in Applied Probability 23, no. 1 (1991): 188–209. http://dx.doi.org/10.2307/1427517.

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This paper presents a new approach for obtaining heavy-traffic limits for infinite-server queues and open networks of infinite-server queues. The key observation is that infinite-server queues having deterministic service times can easily be analyzed in terms of the arrival counting process. A variant of the same idea applies when the service times take values in a finite set, so this is the key assumption. In addition to new proofs of established results, the paper contains several new results, including limits for the work-in-system process, limits for steady-state distributions, limits for

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27

Glynn, Peter W., and Ward Whitt. "A new view of the heavy-traffic limit theorem for infinite-server queues." Advances in Applied Probability 23, no. 01 (1991): 188–209. http://dx.doi.org/10.1017/s0001867800023399.

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This paper presents a new approach for obtaining heavy-traffic limits for infinite-server queues and open networks of infinite-server queues. The key observation is that infinite-server queues having deterministic service times can easily be analyzed in terms of the arrival counting process. A variant of the same idea applies when the service times take values in a finite set, so this is the key assumption. In addition to new proofs of established results, the paper contains several new results, including limits for the work-in-system process, limits for steady-state distributions, limits for

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28

Boxma, O. J., and V. Dumas. "Fluid queues with long-tailed activity period distributions." Computer Communications 21, no. 17 (1998): 1509–29. http://dx.doi.org/10.1016/s0140-3664(98)00219-9.

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29

Fakinos, D. "Equilibrium queue size distributions for semi-reversible queues." Stochastic Processes and their Applications 36, no. 2 (1990): 331–37. http://dx.doi.org/10.1016/0304-4149(90)90099-e.

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30

Ciucu, Florin, Felix Poloczek, and Amr Rizk. "Queue and Loss Distributions in Finite-Buffer Queues." ACM SIGMETRICS Performance Evaluation Review 47, no. 1 (2019): 65–66. http://dx.doi.org/10.1145/3376930.3376972.

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31

Takács, Lajos. "Limit distributions for queues and random rooted trees." Journal of Applied Mathematics and Stochastic Analysis 6, no. 3 (1993): 189–216. http://dx.doi.org/10.1155/s1048953393000176.

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In this paper several limit theorems are proved for the fluctuations of the queue size during the initial busy period of a queuing process with one server. These theorems are used to find the solutions of various problems connected with the heights and widths of random rooted trees.

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32

Ciucu, Florin, Felix Poloczek, and Amr Rizk. "Queue and Loss Distributions in Finite-Buffer Queues." Proceedings of the ACM on Measurement and Analysis of Computing Systems 3, no. 2 (2019): 1–29. http://dx.doi.org/10.1145/3341617.3326146.

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33

Kijima, Masaaki, and Naoki Makimoto. "Computation of quasi-stationary distributions in Markovian queues." Computers & Industrial Engineering 27, no. 1-4 (1994): 429–32. http://dx.doi.org/10.1016/0360-8352(94)90326-3.

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34

Pollett, P. K., and P. G. Taylor. "On the Problem of Establishing the Existence of Stationary Distributions for Continuous-Time Markov Chains." Probability in the Engineering and Informational Sciences 7, no. 4 (1993): 529–43. http://dx.doi.org/10.1017/s0269964800003119.

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We consider the problem of establishing the existence of stationary distributions for continuous-time Markov chains directly from the transition rates Q. Given an invariant probability distribution m for Q, we show that a necessary and sufficient condition for m to be a stationary distribution for the minimal process is that Q be regular. We provide sufficient conditions for the regularity of Q that are simple to verify in practice, thus allowing one to easily identify stationary distributions for a variety of models. To illustrate our results, we shall consider three classes of multidimension

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35

Schassberger, R., and H. Daduna. "Sojourn times in queuing networks with multiserver modes." Journal of Applied Probability 24, no. 2 (1987): 511–21. http://dx.doi.org/10.2307/3214274.

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36

Schassberger, R., and H. Daduna. "Sojourn times in queuing networks with multiserver modes." Journal of Applied Probability 24, no. 02 (1987): 511–21. http://dx.doi.org/10.1017/s0021900200031144.

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37

Neuts, Marcel F. "Generalizations of the Pollaczek-Khinchin integral equation in the theory of queues." Advances in Applied Probability 18, no. 4 (1986): 952–90. http://dx.doi.org/10.2307/1427258.

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A classical result in queueing theory states that in the stable M/G/1 queue, the stationary distribution W(x) of the waiting time of an arriving customer or of the virtual waiting time satisfies a linear Volterra integral equation of the second kind, of convolution type. For many variants of the M/G/1 queue, there are corresponding integral equations, which in most cases differ from the Pollaczek–Khinchin equation only in the form of the inhomogeneous term. This leads to interesting factorizations of the waiting-time distribution and to substantial algorithmic simplifications. In a number of p

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38

Miyoshi, Naoto, and Toshiharu Hasegawa. "Smoothed Perturbation Analysis for Single-Server Queues by Some General Service Disciplines." Advances in Applied Probability 29, no. 2 (1997): 545–66. http://dx.doi.org/10.2307/1428016.

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We consider some single-server queues with general service disciplines, where the family of the queueing processes are parameterized by the service time distributions. Through the smoothed perturbation analysis (SPA) technique, we present under some mild conditions a unified approach to give the strongly consistent estimator for the gradient of the steady-state mean sojourn time with respect to the parameter of service time distributions, provided that it exists. Although the implementation of the SPA requires the additional sub-paths in general, the derived estimator is given as suitable for

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39

Miyoshi, Naoto, and Toshiharu Hasegawa. "Smoothed Perturbation Analysis for Single-Server Queues by Some General Service Disciplines." Advances in Applied Probability 29, no. 02 (1997): 545–66. http://dx.doi.org/10.1017/s0001867800028123.

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We consider some single-server queues with general service disciplines, where the family of the queueing processes are parameterized by the service time distributions. Through the smoothed perturbation analysis (SPA) technique, we present under some mild conditions a unified approach to give the strongly consistent estimator for the gradient of the steady-state mean sojourn time with respect to the parameter of service time distributions, provided that it exists. Although the implementation of the SPA requires the additional sub-paths in general, the derived estimator is given as suitable for

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40

Chao, Xiuli, Qi-Ming He, and Sheldon Ross. "Tollbooth tandem queues with infinite homogeneous servers." Journal of Applied Probability 52, no. 4 (2015): 941–61. http://dx.doi.org/10.1239/jap/1450802745.

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In this paper we analyze a tollbooth tandem queueing problem with an infinite number of servers. A customer starts service immediately upon arrival but cannot leave the system before all customers who arrived before him/her have left, i.e. customers depart the system in the same order as they arrive. Distributions of the total number of customers in the system, the number of departure-delayed customers in the system, and the number of customers in service at time t are obtained in closed form. Distributions of the sojourn times and departure delays of customers are also obtained explicitly. Bo

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41

Chao, Xiuli, Qi-Ming He, and Sheldon Ross. "Tollbooth tandem queues with infinite homogeneous servers." Journal of Applied Probability 52, no. 04 (2015): 941–61. http://dx.doi.org/10.1017/s0021900200113002.

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In this paper we analyze a tollbooth tandem queueing problem with an infinite number of servers. A customer starts service immediately upon arrival but cannot leave the system before all customers who arrived before him/her have left, i.e. customers depart the system in the same order as they arrive. Distributions of the total number of customers in the system, the number of departure-delayed customers in the system, and the number of customers in service at time t are obtained in closed form. Distributions of the sojourn times and departure delays of customers are also obtained explicitly. Bo

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42

König, Dieter, and Volker Schmidt. "Stationary queue-length characteristics in queues with delayed feedback." Journal of Applied Probability 22, no. 2 (1985): 394–407. http://dx.doi.org/10.2307/3213782.

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A class of two-node queueing networks with general stationary ergodic governing sequence is considered. This means that, in particular, a non-Poissonian arrival process and dependent service times, as well as a non-Bernoulli feedback mechanism are admitted. A mixing condition ensures that the limiting distributions of the number of customers in the nodes observed in continuous time as well as at certain embedded epochs can be expressed by the Palm distributions of appropriately chosen marked point processes. This gives the possibility of connecting the classical concept of embedding with a gen

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43

König, Dieter, and Volker Schmidt. "Stationary queue-length characteristics in queues with delayed feedback." Journal of Applied Probability 22, no. 02 (1985): 394–407. http://dx.doi.org/10.1017/s0021900200037852.

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A class of two-node queueing networks with general stationary ergodic governing sequence is considered. This means that, in particular, a non-Poissonian arrival process and dependent service times, as well as a non-Bernoulli feedback mechanism are admitted. A mixing condition ensures that the limiting distributions of the number of customers in the nodes observed in continuous time as well as at certain embedded epochs can be expressed by the Palm distributions of appropriately chosen marked point processes. This gives the possibility of connecting the classical concept of embedding with a gen

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44

Macêdo, Rafael Lacerda, Francisco Diogo R. Sousa, Sheila Bonfim de Jesus, Bárbara Janaina Bezerra Nunesmaia, Christina Wyss Castelo Branco, and Lourdes M. A. Elmoor-Loureiro. "Cladocera (Crustacea, Branchiopoda) species of Bahia State, Brazil: a critical update on species descriptions, distributions, and new records." Nauplius 29 (March 22, 2021): 1–26. https://doi.org/10.1590/2358-2936e2021011.

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Macêdo, Rafael Lacerda, Sousa, Francisco Diogo R., Jesus, Sheila Bonfim de, Nunesmaia, Bárbara Janaina Bezerra, Branco, Christina Wyss Castelo, Elmoor-Loureiro, Lourdes M. A. (2021): Cladocera (Crustacea, Branchiopoda) species of Bahia State, Brazil: a critical update on species descriptions, distributions, and new records. Nauplius (e2021011) 29: 1-26, DOI: 10.1590/2358-2936e2021011, URL: http://dx.doi.org/10.1590/2358-2936e2021011

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Whitt, Ward. "LIMITS FOR CUMULATIVE INPUT PROCESSES TO QUEUES." Probability in the Engineering and Informational Sciences 14, no. 2 (2000): 123–50. http://dx.doi.org/10.1017/s0269964800142019.

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We establish functional central limit theorems (FCLTs) for a cumulative input process to a fluid queue from the superposition of independent on–off sources, where the on periods and off periods may have heavy-tailed probability distributions. Variants of these FCLTs hold for cumulative busy-time and idle-time processes associated with standard queueing models. The heavy-tailed on-period and off-period distributions can cause the limit process to have discontinuous sample paths (e.g., to be a non-Brownian stable process or more general Lévy process) even though the converging processes have con

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Blanc, J. P. C. "A note on waiting times in systems with queues in parallel." Journal of Applied Probability 24, no. 2 (1987): 540–46. http://dx.doi.org/10.2307/3214278.

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Numerical data are presented concerning the mean and the standard deviation of the waiting-time distribution for multiserver systems with queues in parallel, in which customers choose one of the shortest queues upon arrival. Moreover, a new numerical method is outlined for calculating state probabilities and moments of queue-length distributions. This method is based on power series expansions and recursion. It is applicable to many systems with more than one waiting line.

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Blanc, J. P. C. "A note on waiting times in systems with queues in parallel." Journal of Applied Probability 24, no. 02 (1987): 540–46. http://dx.doi.org/10.1017/s0021900200031181.

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Numerical data are presented concerning the mean and the standard deviation of the waiting-time distribution for multiserver systems with queues in parallel, in which customers choose one of the shortest queues upon arrival. Moreover, a new numerical method is outlined for calculating state probabilities and moments of queue-length distributions. This method is based on power series expansions and recursion. It is applicable to many systems with more than one waiting line.

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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 (20

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D. Gangadhar, Nandyala, and Govind R. Kadambi. "Delay Distributions in Discrete Time Multiclass Tandem Communication Network Models." International journal of electrical and computer engineering systems 13, no. 6 (2022): 417–25. http://dx.doi.org/10.32985/ijeces.13.6.1.

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An exact computational algorithm for the solution of a discrete time multiclass tandem network with a primary class and cross-traffic at each queue is developed. A sequence of truncated Lindley recursions is defined at each queue relating the delays experienced by the first packet from consecutive batches of a class at that queue. Using this sequence of recursions, a convolve-and-sweep algorithm is developed to compute the stationary distributions of the delay and inter-departure processes of each class at a queue, delays experienced by a typical packet from the primary class along its path as

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Neuts, Marcel F. "Generalizations of the Pollaczek-Khinchin integral equation in the theory of queues." Advances in Applied Probability 18, no. 04 (1986): 952–90. http://dx.doi.org/10.1017/s0001867800016232.

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A classical result in queueing theory states that in the stable M/G/1 queue, the stationary distribution W(x) of the waiting time of an arriving customer or of the virtual waiting time satisfies a linear Volterra integral equation of the second kind, of convolution type. For many variants of the M/G/1 queue, there are corresponding integral equations, which in most cases differ from the Pollaczek–Khinchin equation only in the form of the inhomogeneous term. This leads to interesting factorizations of the waiting-time distribution and to substantial algorithmic simplifications. In a number of p

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