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Journal articles on the topic 'M/G/1'

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Published: 10 December 2022

Last updated: 28 January 2023

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1

Aalto, Samuli, Urtzi Ayesta, and Eeva Nyberg-Oksanen. "M/G/1/MLPS compared to M/G/1/PS." Operations Research Letters 33, no. 5 (September 2005): 519–24. http://dx.doi.org/10.1016/j.orl.2004.09.009.

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2

J., Joseline Manora, and Vignesh S. "Results on $\gamma_{M}^{-1}(G)$ and $\gamma_{M}^{-1}(\bar{G})$." Malaya Journal of Matematik S, no. 1 (2020): 358–62. http://dx.doi.org/10.26637/mjm0s20/0067.

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3

Nakatsuka, Toshinao. "QUEUE LENGTH DISTRIBUTION IN M/G/1, M^x/G/1 AND THEIR VARIANTS WITH COMPLETION TIME." Journal of the Operations Research Society of Japan 52, no. 1 (2009): 11–34. http://dx.doi.org/10.15807/jorsj.52.11.

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4

Ali, Hydar. "Expected number of departures in M/M/1 and G/G/1 queues." Advances in Applied Probability 22, no. 3 (September 1990): 770–72. http://dx.doi.org/10.2307/1427474.

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For an initially empty M/M/1 queue, it is shown that the transform of the expectation of the number of departures in the interval (0, t] is invariant under an interchange of arrival and service rates. However, in the GI/G/1 queue with an initial single customer, the corresponding transform does not have this symmetric property.

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5

Gail, H. R., S. L. Hantler, and B. A. Taylor. "Spectral analysis of M/G/1 and G/M/1 type Markov chains." Advances in Applied Probability 28, no. 1 (March 1996): 114–65. http://dx.doi.org/10.2307/1427915.

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When analyzing the equilibrium behavior of M/G/1 type Markov chains by transform methods, restrictive hypotheses are often made to avoid technical problems that arise in applying results from complex analysis and linear algebra. It is shown that such restrictive assumptions are unnecessary, and an analysis of these chains using generating functions is given under only the natural hypotheses that first moments (or second moments in the null recurrent case) exist. The key to the analysis is the identification of an important subspace of the space of bounded solutions of the system of homogeneous vector-valued Wiener–Hopf equations associated with the chain. In particular, the linear equations in the boundary probabilities obtained from the transform method are shown to correspond to a spectral basis of the shift operator on this subspace. Necessary and sufficient conditions under which the chain is ergodic, null recurrent or transient are derived in terms of properties of the matrix-valued generating functions determined by transitions of the Markov chain. In the transient case, the Martin exit boundary is identified and shown to be associated with certain eigenvalues and vectors of one of these generating functions. An equilibrium analysis of the class of G/M/1 type Markov chains by similar methods is also presented.

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6

Gail, H. R., S. L. Hantler, and B. A. Taylor. "Non-Skip-Free M/G/1 and G/M/1 Type Markov Chains." Advances in Applied Probability 29, no. 3 (September 1997): 733–58. http://dx.doi.org/10.2307/1428084.

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For Markov chains of M/G/1 type that are not skip-free to the left, the corresponding G matrix is shown to have special structure and be determined by its first block row. An algorithm that takes advantage of this structure is developed for computing G. For non-skip-free M/G/1 type Markov chains, the algorithm significantly reduces the computational complexity of calculating the G matrix, when compared with reblocking to a system that is skip-free to the left and then applying usual iteration schemes to find G. A similar algorithm to calculate the R matrix for G/M/1 type Markov chains that are not skip-free to the right is also described.

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7

Ali, Hydar. "Expected number of departures in M/M/1 and G/G/1 queues." Advances in Applied Probability 22, no. 03 (September 1990): 770–72. http://dx.doi.org/10.1017/s0001867800020048.

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For an initially empty M/M/1 queue, it is shown that the transform of the expectation of the number of departures in the interval (0, t] is invariant under an interchange of arrival and service rates. However, in the GI/G/1 queue with an initial single customer, the corresponding transform does not have this symmetric property.

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8

Gail, H. R., S. L. Hantler, and B. A. Taylor. "Spectral analysis of M/G/1 and G/M/1 type Markov chains." Advances in Applied Probability 28, no. 01 (March 1996): 114–65. http://dx.doi.org/10.1017/s0001867800027300.

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Abstract:

When analyzing the equilibrium behavior of M/G/1 type Markov chains by transform methods, restrictive hypotheses are often made to avoid technical problems that arise in applying results from complex analysis and linear algebra. It is shown that such restrictive assumptions are unnecessary, and an analysis of these chains using generating functions is given under only the natural hypotheses that first moments (or second moments in the null recurrent case) exist. The key to the analysis is the identification of an important subspace of the space of bounded solutions of the system of homogeneous vector-valued Wiener–Hopf equations associated with the chain. In particular, the linear equations in the boundary probabilities obtained from the transform method are shown to correspond to a spectral basis of the shift operator on this subspace. Necessary and sufficient conditions under which the chain is ergodic, null recurrent or transient are derived in terms of properties of the matrix-valued generating functions determined by transitions of the Markov chain. In the transient case, the Martin exit boundary is identified and shown to be associated with certain eigenvalues and vectors of one of these generating functions. An equilibrium analysis of the class of G/M/1 type Markov chains by similar methods is also presented.

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9

Gail, H. R., S. L. Hantler, and B. A. Taylor. "Non-Skip-Free M/G/1 and G/M/1 Type Markov Chains." Advances in Applied Probability 29, no. 03 (September 1997): 733–58. http://dx.doi.org/10.1017/s0001867800028329.

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Abstract:

For Markov chains of M/G/1 type that are not skip-free to the left, the corresponding G matrix is shown to have special structure and be determined by its first block row. An algorithm that takes advantage of this structure is developed for computing G. For non-skip-free M/G/1 type Markov chains, the algorithm significantly reduces the computational complexity of calculating the G matrix, when compared with reblocking to a system that is skip-free to the left and then applying usual iteration schemes to find G. A similar algorithm to calculate the R matrix for G/M/1 type Markov chains that are not skip-free to the right is also described.

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10

Kim, Bara, and Jeongsim Kim. "Analysis of the $$M^X/G/1$$ M X / G / 1 retrial queue." Annals of Operations Research 247, no. 1 (June 13, 2015): 193–210. http://dx.doi.org/10.1007/s10479-015-1921-6.

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11

Boxma, Onno, David Perry, and Wolfgang Stadje. "The M/G/1+G queue revisited." Queueing Systems 67, no. 3 (January 26, 2011): 207–20. http://dx.doi.org/10.1007/s11134-010-9205-y.

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12

Takagi, Hideaki, and Tsuyoshi Nishi. "CORRELATION OF INTERDEPARTURE TIMES IN M/G/1 AND M/G/1/K QUEUES." Journal of the Operations Research Society of Japan 41, no. 1 (1998): 142–51. http://dx.doi.org/10.15807/jorsj.41.142.

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13

Jeeva, M., and E. Rathnakumari. "Fuzzy Cost Computations of M/M/1 and M/G/1 Queueing Models." British Journal of Mathematics & Computer Science 4, no. 1 (January 10, 2014): 120–32. http://dx.doi.org/10.9734/bjmcs/2014/4353.

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14

Pourbabai, B. "Tandem behavior of an M/M/1/N → G/M/1 queuing system." Computers & Mathematics with Applications 16, no. 3 (1988): 215–20. http://dx.doi.org/10.1016/0898-1221(88)90181-2.

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15

Das, Sudipta, Lawrence Jenkins, and Debasis Sengupta. "Analysis of an $$M/M/1+G$$ M / M / 1 + G queue operated under the FCFS policy with exact admission control." Queueing Systems 75, no. 2-4 (June 14, 2013): 169–88. http://dx.doi.org/10.1007/s11134-013-9366-6.

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16

Yeo, Wee Meng, Xue-Ming Yuan, and Joyce Mei Wan Low. "On $$M^{X}/G(M/H)/1$$ M X / G ( M / H ) / 1 retrial system with vacation: service helpline performance measurement." Annals of Operations Research 248, no. 1-2 (May 5, 2016): 553–78. http://dx.doi.org/10.1007/s10479-016-2207-3.

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17

Adan, Ivo, Onno Boxma, and David Perry. "The G/M/1 queue revisited." Mathematical Methods of Operations Research 62, no. 3 (November 19, 2005): 437–52. http://dx.doi.org/10.1007/s00186-005-0032-6.

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18

Schormans, J. A., and J. M. Pitts. "Solution for M/G/1 queues." Electronics Letters 33, no. 25 (1997): 2109. http://dx.doi.org/10.1049/el:19971459.

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19

Perry, D., W. Stadje, and S. Zacks. "Busy period analysis for M/G/1 and G/M/1 type queues with restricted accessibility." Operations Research Letters 27, no. 4 (November 2000): 163–74. http://dx.doi.org/10.1016/s0167-6377(00)00043-2.

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20

Aalto, Samuli. "M/G/1/MLPS compared with M/G/1/PS within service time distribution class IMRL." Mathematical Methods of Operations Research 64, no. 2 (August 15, 2006): 309–25. http://dx.doi.org/10.1007/s00186-006-0080-6.

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21

Haviv, Moshe, and Yoav Kerner. "The age of the arrival process in the G/M/1 and M/G/1 queues." Mathematical Methods of Operations Research 73, no. 1 (December 14, 2010): 139–52. http://dx.doi.org/10.1007/s00186-010-0337-y.

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22

Ziya, Serhan. "On the Relationships Among Traffic Load, Capacity, and Throughput for the M/M/1/m, M/G/1/m-PS, and M/G/c/c Queues." IEEE Transactions on Automatic Control 53, no. 11 (December 2008): 2696–701. http://dx.doi.org/10.1109/tac.2008.2007173.

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23

Zhernovyi, K. Yu, and Yu V. Zhernovyi. "M θ/G/1/m and M θ/G/1 systems with the service time dependent on the queue length." Journal of Communications Technology and Electronics 58, no. 12 (December 2013): 1267–75. http://dx.doi.org/10.1134/s1064226913120206.

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24

Kim, Sunggon. "Conditional sojourn time distributions in M/G/1 and G/M/1 queues under PλM-service policy." Communications for Statistical Applications and Methods 25, no. 4 (July 31, 2018): 443–51. http://dx.doi.org/10.29220/csam.2018.25.4.443.

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25

Inoue, Yoshiaki, and Tetsuya Takine. "The M/D/1+D queue has the minimum loss probability among M/G/1+G queues." Operations Research Letters 43, no. 6 (November 2015): 629–32. http://dx.doi.org/10.1016/j.orl.2015.10.003.

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26

POURBABAI, BEHNAM. "Approximation of the departure processes from G/M/1/K and M/G/1/K queueing systems." International Journal of Systems Science 24, no. 4 (April 1993): 627–40. http://dx.doi.org/10.1080/00207729308949511.

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27

WANG, Hao, Ming-He HUANG, and Hao LONG. "The Performance Analysis of Web Services Composition Based on Queueing Network with G/G/1-FCFS、M/G/1-PS and M/G/∞ Nodes." Chinese Journal of Computers 36, no. 1 (March 7, 2014): 22–38. http://dx.doi.org/10.3724/sp.j.1016.2013.00022.

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28

Lee, Chihoon, and Jianqiang C. Wang. "Waiting time probabilities in the M/G/1 + M queue." Statistica Neerlandica 65, no. 1 (January 25, 2011): 72–83. http://dx.doi.org/10.1111/j.1467-9574.2010.00476.x.

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29

Sudhesh, R., and K. V. Vijayashree. "Stationary and transient analysis of M/M/1 G-queues." International Journal of Mathematics in Operational Research 5, no. 2 (2013): 282. http://dx.doi.org/10.1504/ijmor.2013.052457.

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30

Blanc, Hans (J P. C. ). "M/G/1 Queues with Postponed Interruptions." ISRN Probability and Statistics 2012 (September 19, 2012): 1–12. http://dx.doi.org/10.5402/2012/653167.

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This paper studies the effect of postponing interruptions of the service in M/G/1 queueing systems until the end of the service in progress. The waiting and sojourn times in systems with postponement are compared with those in comparable systems without post-ponement, both for the case that interruptions can only occur during busy times of the server and for the case that interruptions are also possible during idle times of the server.

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31

Chol, Bong Dae, and Dong Hwan Han. "G/M^/1 QUEUES WITH SERVER VACATIONS." Journal of the Operations Research Society of Japan 37, no. 3 (1994): 171–81. http://dx.doi.org/10.15807/jorsj.37.171.

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32

Abouee-Mehrizi, Hossein, and Opher Baron. "State-dependent M/G/1 queueing systems." Queueing Systems 82, no. 1-2 (October 15, 2015): 121–48. http://dx.doi.org/10.1007/s11134-015-9461-y.

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33

Dorfmeister, Josef, and Erhard Neher. "Isoparametric hypersurfaces, case g=6, m=1." Communications in Algebra 13, no. 11 (January 1985): 2299–368. http://dx.doi.org/10.1080/00927878508823278.

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34

Han, Dong Hwan, and Doo Il Choi. "G/M/1 queues with delayed vacations." Korean Journal of Computational & Applied Mathematics 5, no. 1 (January 1998): 1–11. http://dx.doi.org/10.1007/bf03008931.

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35

Bhagat, Amita, and Madhu Jain. "N-policy for $${M}^{{x}}/\hbox {G}/1$$ M x / G / 1 Unreliable Retrial G-Queue with Preemptive Resume and Multi-services." Journal of the Operations Research Society of China 4, no. 4 (June 18, 2016): 437–59. http://dx.doi.org/10.1007/s40305-016-0128-0.

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36

Arcara, D., and F. Sato. "Recursive formula for $\psi ^g-\lambda _1\psi ^{g-1}+\cdots +(-1)^g\lambda _g$ in $\overline {\mathcal {M}}_{g,1}$." Proceedings of the American Mathematical Society 137, no. 12 (July 14, 2009): 4077–81. http://dx.doi.org/10.1090/s0002-9939-09-10018-7.

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37

Kijima, Masaaki. "DISTRIBUTION PROPERTIES OF DISCRETE CHARACTERISTICS IN M/G/1 AND GI/M/1 QUEUES." Journal of the Operations Research Society of Japan 31, no. 2 (1988): 172–89. http://dx.doi.org/10.15807/jorsj.31.172.

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38

Shi, Jian-Yi. "Congruence classes of presentations for the complex reflection groups G(m, 1, n) and G(m, m, n)." Indagationes Mathematicae 16, no. 2 (June 2005): 267–88. http://dx.doi.org/10.1016/s0019-3577(05)80028-x.

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39

Kempa, Wojciech M. "Transient workload distribution in the $$M/G/1$$ M / G / 1 finite-buffer queue with single and multiple vacations." Annals of Operations Research 239, no. 2 (February 4, 2015): 381–400. http://dx.doi.org/10.1007/s10479-015-1804-x.

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40

Lee, Doo Ho. "A Note on the Inter-Loss Time Distribution of an M/G/1/1 Queuing System." Journal of the Korean Operations Research and Management Science Society 41, no. 3 (August 31, 2016): 37–43. http://dx.doi.org/10.7737/jkorms.2016.41.3.037.

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41

daya Chandrika, A. Divya, Dr K. U. "An M[X]/G/1 Retrial G-Queue with Server Breakdown." International Journal of Innovative Research in Science, Engineering and Technology 04, no. 04 (April 15, 2015): 1906–17. http://dx.doi.org/10.15680/ijirset.2015.0404014.

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42

Wu, Yuqiang, and Lijun Gao. "On the finite queuing model M/G/m/1/h system." International Journal of Modelling, Identification and Control 10, no. 1/2 (2010): 19. http://dx.doi.org/10.1504/ijmic.2010.033840.

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43

Zhang, Y., and H. Tam. "(1+1)-dimensional m-cKdV, g-cKdV integrable systems, and (2+1)-dimensional m-cKdV hierarchy." Canadian Journal of Physics 86, no. 12 (December 1, 2008): 1367–80. http://dx.doi.org/10.1139/p08-098.

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A few isospectral problems are introduced by referring to that of the cKdV equation hierarchy, for which two types of integrable systems called the (1 + 1)-dimensional m-cKdV hierarchy and the g-cKdV hierarchy are generated, respectively, whose Hamiltonian structures are also discussed by employing a linear functional and the quadratic-form identity. The corresponding expanding integrable models of the (1 + 1)-dimensional m-cKdV hierarchy and g-cKdV hierarchy are obtained. The Hamiltonian structure of the latter one is given by the variational identity, proposed by Ma Wen-Xiu as well. Finally, we use a Lax pair from the self-dual Yang–Mills equations to deduce a higher dimensional m-cKdV hierarchy of evolution equations and its Hamiltonian structure. Furthermore, its expanding integrable model is produced by the use of a enlarged Lie algebra.PACS Nos.: 02.30, 03.40.K

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44

Chao, Xiuli. "On the departure processes of M/M/1/N and GI/G/1/N queues." Advances in Applied Probability 24, no. 3 (September 1992): 751–54. http://dx.doi.org/10.2307/1427488.

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The purpose of this note is to point out the connection between the invariance property of M/M/1 and GI/G/1 queues (which has been reported in several papers) and the interchangeability and reversibility properties of tandem queues. This enables us to gain new insights for both problems and obtain stronger invariance results for M/M/1, GI/G/1, as well as loss systems M/M/1/N, GI/G/1/N and tandem systems.

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45

Chao, Xiuli. "On the departure processes of M/M/1/N and GI/G/1/N queues." Advances in Applied Probability 24, no. 03 (September 1992): 751–54. http://dx.doi.org/10.1017/s0001867800024496.

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The purpose of this note is to point out the connection between the invariance property of M/M/1 and GI/G/1 queues (which has been reported in several papers) and the interchangeability and reversibility properties of tandem queues. This enables us to gain new insights for both problems and obtain stronger invariance results for M/M/1, GI/G/1, as well as loss systems M/M/1/N, GI/G/1/N and tandem systems.

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46

Greenberg, Betsy S. "M/G/1 queueing systems with returning customers." Journal of Applied Probability 26, no. 1 (March 1989): 152–63. http://dx.doi.org/10.2307/3214325.

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Single-channel queues with Poisson arrivals, general service distributions, and no queue capacity are studied. A customer who finds the server busy either leaves the system for ever or may return to try again after an exponentially distributed time. Steady-state probabilities are approximated and bounded in two different ways. We characterize the service distribution by its Laplace transform, and use this characterization to determine the better method of approximation.

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47

Hansen, Martin B., and Susan M. Pitts. "Nonparametric inference from the M/G/1 workload." Bernoulli 12, no. 4 (August 2006): 737–59. http://dx.doi.org/10.3150/bj/1155735934.

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48

Harrison, Peter G., and Edwige Pitel. "The M/G/1 queue with negative customers." Advances in Applied Probability 28, no. 2 (June 1996): 540–66. http://dx.doi.org/10.2307/1428071.

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We derive expressions for the generating function of the equilibrium queue length probability distribution in a single server queue with general service times and independent Poisson arrival streams of both ordinary, positive customers and negative customers which eliminate a positive customer if present. For the case of first come first served queueing discipline for the positive customers, we compare the killing strategies in which either the last customer in the queue or the one in service is removed by a negative customer. We then consider preemptive-restart with resampling last come first served queueing discipline for the positive customers, combined with the elimination of the customer in service by a negative customer—the case of elimination of the last customer yields an analysis similar to first come first served discipline for positive customers. The results show different generating functions in contrast to the case where service times are exponentially distributed. This is also reflected in the stability conditions. Incidently, this leads to a full study of the preemptive-restart with resampling last come first served case without negative customers. Finally, approaches to solving the Fredholm integral equation of the first kind which arises, for instance, in the first case are considered as well as an alternative iterative solution method.

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49

Johansen, Søren Glud. "Optimal Prices of an M/G/1 Jobshop." Operations Research 42, no. 4 (August 1994): 765–74. http://dx.doi.org/10.1287/opre.42.4.765.

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50

Perry, D., W. Stadje, and S. Zacks. "Hysteretic Capacity Switching for M/G/1 Queues." Stochastic Models 23, no. 2 (May 8, 2007): 277–305. http://dx.doi.org/10.1080/15326340701300811.

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