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Journal articles on the topic 'Waiting time distributions'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Hwang, Gang Uk, Bong Dae Choi, and Jae-Kyoon Kim. "The waiting time analysis of a discrete-time queue with arrivals as a discrete autoregressive process of order 1." Journal of Applied Probability 39, no. 3 (2002): 619–29. http://dx.doi.org/10.1239/jap/1034082132.

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We consider a discrete-time queueing system with the discrete autoregressive process of order 1 (DAR(1)) as an input process and obtain the actual waiting time distribution and the virtual waiting time distribution. As shown in the analysis, our approach provides a natural numerical algorithm to compute the waiting time distributions, based on the theory of the GI/G/1 queue, and consequently we can easily investigate the effect of the parameters of the DAR(1) on the waiting time distributions. We also derive a simple approximation of the asymptotic decay rate of the tail probabilities for the

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2

Hwang, Gang Uk, Bong Dae Choi, and Jae-Kyoon Kim. "The waiting time analysis of a discrete-time queue with arrivals as a discrete autoregressive process of order 1." Journal of Applied Probability 39, no. 03 (2002): 619–29. http://dx.doi.org/10.1017/s0021900200021847.

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We consider a discrete-time queueing system with the discrete autoregressive process of order 1 (DAR(1)) as an input process and obtain the actual waiting time distribution and the virtual waiting time distribution. As shown in the analysis, our approach provides a natural numerical algorithm to compute the waiting time distributions, based on the theory of the GI/G/1 queue, and consequently we can easily investigate the effect of the parameters of the DAR(1) on the waiting time distributions. We also derive a simple approximation of the asymptotic decay rate of the tail probabilities for the

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3

Hou, Yusong, Jianguo Jiang, and J. Wu. "The Form of Waiting Time Distributions of Continuous Time Random Walk in Dead-End Pores." Geofluids 2018 (2018): 1–6. http://dx.doi.org/10.1155/2018/8329406.

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Anomalous dispersion of solute in porous media can be explained by the power-law distribution of waiting time of solute particles. In this paper, we simulate the diffusion of nonreactive tracer in dead-end pores to explore the waiting time distributions. The distributions of waiting time in different dead-end pores show similar power-law decline at early time and transit to an exponential decline in the end. The transition time between these two decline modes increases with the lengths of dead-end pores. It is well known that power-law distributions of waiting time may lead to anomalous (non-F

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4

Sabatelli, L., S. Keating, J. Dudley, and P. Richmond. "Waiting time distributions in financial markets." European Physical Journal B - Condensed Matter 27, no. 2 (2002): 273–75. http://dx.doi.org/10.1140/epjb/e20020151.

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5

Davidsen, Jörn, and Christian Goltz. "Are seismic waiting time distributions universal?" Geophysical Research Letters 31, no. 21 (2004): n/a. http://dx.doi.org/10.1029/2004gl020892.

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6

Norton, Robert M. "A relationship between a family of waiting time distributions and the asymptotic residual waiting time distribution." Communications in Statistics - Simulation and Computation 14, no. 3 (1985): 709–17. http://dx.doi.org/10.1080/03610918508812466.

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7

Fu, James C., and Y. M. Chang. "On probability generating functions for waiting time distributions of compound patterns in a sequence of multistate trials." Journal of Applied Probability 39, no. 1 (2002): 70–80. http://dx.doi.org/10.1239/jap/1019737988.

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Probability generation functions of waiting time distributions of runs and patterns have been used successfully in various areas of statistics and applied probability. In this paper, we provide a simple way to obtain the probability generating functions for waiting time distributions of compound patterns by using the finite Markov chain imbedding method. We also study the characters of waiting time distributions for compound patterns. A computer algorithm based on Markov chain imbedding technique has been developed for automatically computing the distribution, probability generating function,

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8

Fu, James C., and Y. M. Chang. "On probability generating functions for waiting time distributions of compound patterns in a sequence of multistate trials." Journal of Applied Probability 39, no. 01 (2002): 70–80. http://dx.doi.org/10.1017/s0021900200021513.

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Probability generation functions of waiting time distributions of runs and patterns have been used successfully in various areas of statistics and applied probability. In this paper, we provide a simple way to obtain the probability generating functions for waiting time distributions of compound patterns by using the finite Markov chain imbedding method. We also study the characters of waiting time distributions for compound patterns. A computer algorithm based on Markov chain imbedding technique has been developed for automatically computing the distribution, probability generating function,

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9

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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10

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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11

Slaven, J. E., A. Mnatsakanova, S. Li, et al. "Waiting Time Distributions of Actigraphy Measured Sleep." Open Sleep Journal 1, no. 1 (2008): 1–5. http://dx.doi.org/10.2174/1874620900801010001.

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12

Higgins, Erin R., Heiko Schmidle, and Martin Falcke. "Waiting time distributions for clusters of receptors." Journal of Theoretical Biology 259, no. 2 (2009): 338–49. http://dx.doi.org/10.1016/j.jtbi.2009.03.018.

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13

Eryilmaz, Serkan. "Generalized waiting time distributions associated with runs." Metrika 79, no. 3 (2015): 357–68. http://dx.doi.org/10.1007/s00184-015-0558-4.

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14

Tarasov, V. N. "Queuing Systems with a Time Lag." INFORMACIONNYE TEHNOLOGII 27, no. 6 (2021): 291–98. http://dx.doi.org/10.17587/it.27.291-298.

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The article discusses various queuing systems (QS) formed by four laws of probability distributions: exponential, hyperexponential, Erlang and hyper-Erlang of the second order. These four laws form sixteen different QS. In contrast to the classical theory, this article considers QS with distribution laws shifted to the right from the zero point. Such QS are of type G/G/1 with arbitrary laws of the distribution of intervals between the requirements of the input flow and the service time. As you know, for such systems it is impossible to obtain solutions for the main characteristic of QS the ave

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15

Vis, P., R. Bekker, and R. D. van der Mei. "Heavy-traffic limits for polling models with exhaustive service and non-FCFS service order policies." Advances in Applied Probability 47, no. 4 (2015): 989–1014. http://dx.doi.org/10.1239/aap/1449859797.

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We study cyclic polling models with exhaustive service at each queue under a variety of non-FCFS (first-come-first-served) local service orders, namely last-come-first-served with and without preemption, random-order-of-service, processor sharing, the multi-class priority scheduling with and without preemption, shortest-job-first, and the shortest remaining processing time policy. For each of these policies, we first express the waiting-time distributions in terms of intervisit-time distributions. Next, we use these expressions to derive the asymptotic waiting-time distributions under heavy-tr

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16

Vis, P., R. Bekker, and R. D. van der Mei. "Heavy-traffic limits for polling models with exhaustive service and non-FCFS service order policies." Advances in Applied Probability 47, no. 04 (2015): 989–1014. http://dx.doi.org/10.1017/s0001867800048989.

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We study cyclic polling models with exhaustive service at each queue under a variety of non-FCFS (first-come-first-served) local service orders, namely last-come-first-served with and without preemption, random-order-of-service, processor sharing, the multi-class priority scheduling with and without preemption, shortest-job-first, and the shortest remaining processing time policy. For each of these policies, we first express the waiting-time distributions in terms of intervisit-time distributions. Next, we use these expressions to derive the asymptotic waiting-time distributions under heavy-tr

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17

Chao, Wen, and Liu Fusui. "Continuous time random walks with momentless waiting time distributions." Chinese Physics Letters 3, no. 9 (1986): 429–31. http://dx.doi.org/10.1088/0256-307x/3/9/012.

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18

Tarasov, V. N., and N. F. Bakhareva. "QUEUEING SYSTEMS WITH TIME LAG." Radio Electronics, Computer Science, Control, no. 4 (January 10, 2022): 49–57. http://dx.doi.org/10.15588/1607-3274-2021-4-5.

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Context. In the queuing theory of a research of the G/G/1 systems are relevant because it is impossible to receive decisions for the average waiting time in queue in a final form in case of arbitrary laws of distributions of an input flow and service time. Therefore, the study of such systems for particular cases of input distributions is important. The problem of deriving solutions for the average waiting time in a queue in closed form for systems with distributions shifted to the right from the zero point is considered. Objective. Getting solutions for the main characteristics of the s

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19

Inoue, Kiyoshi, and Sigeo Aki. "On Generating Functions of Waiting Times and Numbers of Occurrences of Compound Patterns in a Sequence of Multistate Trials." Journal of Applied Probability 44, no. 1 (2007): 71–81. http://dx.doi.org/10.1239/jap/1175267164.

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In this paper we study two distributions, namely the distribution of the waiting times until given numbers of occurrences of compound patterns and the distribution of the numbers of occurrences of compound patterns in a fixed number of trials. We elucidate the interrelation between these two distributions in terms of the generating functions. We provide perspectives on the problems related to compound patterns in statistics and probability. As an application, the waiting time problem of counting runs of specified lengths is considered in order to illustrate how the distributions of waiting tim

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20

Inoue, Kiyoshi, and Sigeo Aki. "On Generating Functions of Waiting Times and Numbers of Occurrences of Compound Patterns in a Sequence of Multistate Trials." Journal of Applied Probability 44, no. 01 (2007): 71–81. http://dx.doi.org/10.1017/s0021900200002722.

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In this paper we study two distributions, namely the distribution of the waiting times until given numbers of occurrences of compound patterns and the distribution of the numbers of occurrences of compound patterns in a fixed number of trials. We elucidate the interrelation between these two distributions in terms of the generating functions. We provide perspectives on the problems related to compound patterns in statistics and probability. As an application, the waiting time problem of counting runs of specified lengths is considered in order to illustrate how the distributions of waiting tim

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21

Stefanov, Valeri T. "On some waiting time problems." Journal of Applied Probability 37, no. 3 (2000): 756–64. http://dx.doi.org/10.1239/jap/1014842834.

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A unifying technology is introduced for finding explicit closed form expressions for joint moment generating functions of various random quantities associated with some waiting time problems. Sooner and later waiting times are covered for general discrete- and continuous-time models. The models are either Markov chains or semi-Markov processes with a finite number of states. Waiting times associated with generalized phase-type distributions, that are of interest in survival analysis and other areas, are also covered.

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22

Stefanov, Valeri T. "On some waiting time problems." Journal of Applied Probability 37, no. 03 (2000): 756–64. http://dx.doi.org/10.1017/s0021900200015977.

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A unifying technology is introduced for finding explicit closed form expressions for joint moment generating functions of various random quantities associated with some waiting time problems. Sooner and later waiting times are covered for general discrete- and continuous-time models. The models are either Markov chains or semi-Markov processes with a finite number of states. Waiting times associated with generalized phase-type distributions, that are of interest in survival analysis and other areas, are also covered.

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23

Ryden, T. "Waiting time distributions in buffers with batch service." IEEE Transactions on Communications 41, no. 7 (1993): 1027–30. http://dx.doi.org/10.1109/26.231931.

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24

Thul, R., and M. Falcke. "Waiting time distributions for clusters of complex molecules." Europhysics Letters (EPL) 79, no. 3 (2007): 38003. http://dx.doi.org/10.1209/0295-5075/79/38003.

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25

Jonsdottir, Kristin, Mattias Lindman, Roland Roberts, Björn Lund, and Reynir Bödvarsson. "Modelling fundamental waiting time distributions for earthquake sequences." Tectonophysics 424, no. 3-4 (2006): 195–208. http://dx.doi.org/10.1016/j.tecto.2006.03.036.

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26

Stanford, David A., Peter Taylor, and Ilze Ziedins. "Waiting time distributions in the accumulating priority queue." Queueing Systems 77, no. 3 (2013): 297–330. http://dx.doi.org/10.1007/s11134-013-9382-6.

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27

Murphree, Emily S. "Transient renewal processes in the subexponential case." Journal of Applied Probability 24, no. 1 (1987): 88–96. http://dx.doi.org/10.2307/3214061.

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A transient renewal process based on a sequence of possibly infinite waiting times is defined. The process is studied when the (rescaled) distribution of the waiting times belongs to the subexponential class of distributions. In this case, even conditional on all waiting times observed by time t being finite, the distributions of the forward and backward delays at t are asymptotically degenerate. Also, the conditional moments of the number of events by time t converge to the same finite limits as the unconditional moments.

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28

Murphree, Emily S. "Transient renewal processes in the subexponential case." Journal of Applied Probability 24, no. 01 (1987): 88–96. http://dx.doi.org/10.1017/s0021900200030631.

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A transient renewal process based on a sequence of possibly infinite waiting times is defined. The process is studied when the (rescaled) distribution of the waiting times belongs to the subexponential class of distributions. In this case, even conditional on all waiting times observed by time t being finite, the distributions of the forward and backward delays at t are asymptotically degenerate. Also, the conditional moments of the number of events by time t converge to the same finite limits as the unconditional moments.

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29

Kushvaha, Bhaskar, Dhruba Das, and Asmita Tamuli. "Single server queueing model with Poisson arrival and gamma service time distribution." Global Journal of Computer Sciences: Theory and Research 14, no. 1 (2024): 15–27. http://dx.doi.org/10.18844/gjcs.v14i1.9324.

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Queueing theory is pivotal in understanding waiting lines and their pervasive role in everyday life. Its profound application spans across diverse sectors, including computer programming networks, healthcare, transportation, and so on. Researchers have applied many statistical distributions in analyzing queueing data. This article focuses on the analysis of a single server queueing system with Poisson input and service times distributed according to a two-parameter gamma distribution. The study elaborates on the construction and estimation of key queueing properties such as steady state equati

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30

Kim, Woo Sung, and Kyungsu Park. "Waiting time distribution in single-channel deterministic flow lines with discrete interarrival time distributions." European J. of Industrial Engineering 16, no. 2 (2022): 1. http://dx.doi.org/10.1504/ejie.2022.10039905.

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31

Chaudhry, Mohan L., Dae W. Choi, and Kyung C. Chae. "COMPUTATIONAL ANALYSIS OF STATIONARY WAITING-TIME DISTRIBUTIONS OF GIX/R/1 AND GIX/D/1 QUEUES." Probability in the Engineering and Informational Sciences 19, no. 1 (2005): 121–40. http://dx.doi.org/10.1017/s0269964805050084.

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In this article, we obtain, in a unified way, a closed-form analytic expression, in terms of roots of the so-called characteristic equation of the stationary waiting-time distribution for the GIX/R/1 queue, where R denotes the class of distributions whose Laplace–Stieltjes transforms are rational functions (ratios of a polynomial of degree at most n to a polynomial of degree n). The analysis is not restricted to generalized distributions with phases such as Coxian-n (Cn) but also covers nonphase-type distributions such as deterministic (D). In the latter case, we get approximate results. Numer

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32

Minami, Mihoko. "Multivariate inverse Gaussian distribution as a limit of multivariate waiting time distributions." Journal of Statistical Planning and Inference 137, no. 11 (2007): 3626–33. http://dx.doi.org/10.1016/j.jspi.2007.03.038.

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33

Yamazaki, Genji, and Masakiyo Miyazawa. "The equality of the workload and total attained waiting time in average." Journal of Applied Probability 28, no. 1 (1991): 238–44. http://dx.doi.org/10.2307/3214755.

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It has recently been shown that, for the FCFS G/G/1 queue, the workload and attained waiting time of a customer in service have the same stationary distribution. We show that, for a general queueing system setting, the workload and total attained waiting time of customers in service are identical in average but the equality of the distributions is not true in general except for the FCFS G/G/1 queue.

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34

Yamazaki, Genji, and Masakiyo Miyazawa. "The equality of the workload and total attained waiting time in average." Journal of Applied Probability 28, no. 01 (1991): 238–44. http://dx.doi.org/10.1017/s0021900200039577.

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It has recently been shown that, for the FCFS G/G/1 queue, the workload and attained waiting time of a customer in service have the same stationary distribution. We show that, for a general queueing system setting, the workload and total attained waiting time of customers in service are identical in average but the equality of the distributions is not true in general except for the FCFS G/G/1 queue.

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35

Deng, Kai Ying, and Jing Wei Deng. "Properties and Moving Time Average for Lévy Walks with Power-Law Waiting-Time Distributions." Applied Mechanics and Materials 580-583 (July 2014): 3079–82. http://dx.doi.org/10.4028/www.scientific.net/amm.580-583.3079.

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Lévy walks are a natural model for the description of sub-ballistic, superdiffusive motion. The waiting times and jump lengths of Lévy walks are coupled in the form . The-coupling introduces a time cost for each jump in the form of the generalized velocity , such that long jumps get penalized by a higher time cost. In this paper, we firstly investigate the properties of Lévy walks with power-law waiting-time distributions; then discuss its moving time average.

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36

Aki, Sigeo, and Katuomi Hirano. "Joint Distributions of Waiting Time Random Variables for Patterns." JOURNAL OF THE JAPAN STATISTICAL SOCIETY 38, no. 1 (2008): 97–105. http://dx.doi.org/10.14490/jjss.38.97.

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37

Metzler, Ralf, and Theo F. Nonnenmacher. "Fractional diffusion, waiting-time distributions, and Cattaneo-type equations." Physical Review E 57, no. 6 (1998): 6409–14. http://dx.doi.org/10.1103/physreve.57.6409.

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38

Norman, James P., Paul Charbonneau, Scott W. McIntosh, and Han‐Li Liu. "Waiting‐Time Distributions in Lattice Models of Solar Flares." Astrophysical Journal 557, no. 2 (2001): 891–96. http://dx.doi.org/10.1086/321678.

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39

Vyas, Reeta, and Surendra Singh. "Waiting-time distributions in the photodetection of squeezed light." Physical Review A 38, no. 5 (1988): 2423–30. http://dx.doi.org/10.1103/physreva.38.2423.

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40

Aki, Sigeo, and Katuomi Hirano. "Waiting time distributions for a run with additional constraints." Journal of Statistical Planning and Inference 138, no. 11 (2008): 3492–501. http://dx.doi.org/10.1016/j.jspi.2005.09.011.

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41

Kolomeisky, Anatoly B., and Michael E. Fisher. "Extended kinetic models with waiting-time distributions: Exact results." Journal of Chemical Physics 113, no. 24 (2000): 10867–77. http://dx.doi.org/10.1063/1.1326912.

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42

Fajardo, Val Andrei, and Steve Drekic. "Waiting Time Distributions in the Preemptive Accumulating Priority Queue." Methodology and Computing in Applied Probability 19, no. 1 (2015): 255–84. http://dx.doi.org/10.1007/s11009-015-9476-1.

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43

Heidemann, Dirk. "Queue length and waiting-time distributions at priority intersections." Transportation Research Part B: Methodological 25, no. 4 (1991): 163–74. http://dx.doi.org/10.1016/0191-2615(91)90001-y.

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44

Zhang, Chen. "A Bayesian-based study on the average waiting time of airport taxis." Highlights in Science, Engineering and Technology 12 (August 26, 2022): 5–12. http://dx.doi.org/10.54097/hset.v12i.1357.

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In recent years, the incompatibility of airport taxis with passenger time, scale and other factors has led to the problem that airport taxi traffic is difficult to control. This topic starts from the perspective of the number of taxis in Zhengzhou Airport, uses Bayesian statistics and R implementation, applies Bayesian calculation to the analysis of the average waiting time of airport taxis, and establishes the Poisson distribution model of the actual airport taxi traffic flow and Exponential distribution model for waiting time. This topic clearly presents the influence of factors such as the

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45

Bertsimas, Dimitris J., Julian Keilson, Daisuke Nakazato, and Hongtao Zhang. "Transient and busy period analysis of the GIG/1 Queue as a Hilbert factorization problem." Journal of Applied Probability 28, no. 4 (1991): 873–85. http://dx.doi.org/10.2307/3214690.

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In this paper we find the waiting time distribution in the transient domain and the busy period distribution of the GI G/1 queue. We formulate the problem as a two-dimensional Lindley process and then transform it to a Hilbert factorization problem. We achieve the solution of the factorization problem for the GI/R/1, R/G/1 queues, where R is the class of distributions with rational Laplace transforms. We obtain simple closed-form expressions for the Laplace transforms of the waiting time distribution and the busy period distribution. Furthermore, we find closed-form formulae for the first two

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46

Bertsimas, Dimitris J., Julian Keilson, Daisuke Nakazato, and Hongtao Zhang. "Transient and busy period analysis of the GI G/1 Queue as a Hilbert factorization problem." Journal of Applied Probability 28, no. 04 (1991): 873–85. http://dx.doi.org/10.1017/s0021900200042789.

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In this paper we find the waiting time distribution in the transient domain and the busy period distribution of the GI G/1 queue. We formulate the problem as a two-dimensional Lindley process and then transform it to a Hilbert factorization problem. We achieve the solution of the factorization problem for the GI/R/1, R/G/1 queues, where R is the class of distributions with rational Laplace transforms. We obtain simple closed-form expressions for the Laplace transforms of the waiting time distribution and the busy period distribution. Furthermore, we find closed-form formulae for the first two

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47

Tarasov, V. N. "COMPARISON OF TWO FORMS OF ERLANGIAN DISTRIBUTION LAW IN QUEUING THEORY." Radio Electronics, Computer Science, Control, no. 3 (October 6, 2021): 48–56. http://dx.doi.org/10.15588/1607-3274-2021-3-5.

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Context. For modeling various data transmission systems, queuing systems G/G/1 are in demand, this is especially important because there is no final solution for them in the general case. The problem of the derivation in closed form of the solution for the average waiting time in the queue for ordinary system with erlangian input distributions of the second order and for the same system with shifted to the right distributions is considered. Objective. Obtaining a solution for the main system characteristic – the average waiting time for queue requirements for three types of queuing syste

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48

Kim, Woo sung, and Kyungsu Park. "Waiting time distribution in single-channel deterministic flow lines with discrete inter-arrival time distributions." European J. of Industrial Engineering 16, no. 2 (2022): 117. http://dx.doi.org/10.1504/ejie.2022.121185.

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49

AKHTAR, NAZIMA, and AJAZ AHMAD BHAT. "PRANAV-POWER SERIES DISTRIBUTION: PROPERTIES AND APPLICATIONS TO SURVIVAL AND WAITING TIME DATA." Journal of Science and Arts 23, no. 1 (2023): 107–20. http://dx.doi.org/10.46939/j.sci.arts-23.1-a08.

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This research article presents a new Pranav power series class of distributions which is obtained by compounding one parameter Pranav and power series distributions. Various special cases of the new model have been unfolded. Numerous statistical properties of the proposed model are investigated including closed-form expressions for the density function, cumulative distribution function, survival function, hazard rate function, the moments of order statistics and MLEs. Finally, the flexibility and potentiality of the PPS distribution has been demonstrated by means of two real life data sets.

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50

Becker-Kern, Peter, Mark M. Meerschaert, and Hans-Peter Scheffler. "Limit theorem for continuous-time random walks with two time scales." Journal of Applied Probability 41, no. 2 (2004): 455–66. http://dx.doi.org/10.1239/jap/1082999078.

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Continuous-time random walks incorporate a random waiting time between random jumps. They are used in physics to model particle motion. A physically realistic rescaling uses two different time scales for the mean waiting time and the deviation from the mean. This paper derives the scaling limits for such processes. These limit processes are governed by fractional partial differential equations that may be useful in physics. A transfer theorem for weak convergence of finite-dimensional distributions of stochastic processes is also obtained.

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