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A dual tandem queueing system with GI service time at the first queue
A continuous-time queueing model with class clustering and global FCFS service discipline
1. | Department of Telecommunications and Information Processing, Ghent University - UGent, Sint-Pietersnieuwstraat 41, 9000 Ghent, Belgium, Belgium, Belgium |
2. | Department of Telecommunications and Information Processing, Ghent University, St-Pietersnieuwstraat 41, 9000 Gent |
References:
[1] |
I. Adan, T. de Kok and J. Resing, A multi-server queueing model with locking, EJOR, 116 (2000), 16-26. |
[2] |
I. J. B. F. Adan, J. Wessels and W. H. M. Zijm, A compensation approach for two-dimensional markov processes, Advances in Applied Probability, 25 (1993), 783-817.
doi: 10.2307/1427792. |
[3] |
P. Beekhuizen and J. Resing, Performance analysis of small non-uniform packet switches, Performance Evaluation, 66 (2009), 640-659. |
[4] |
Z. Berdowski, F. van den Broek-Serlé, J. Jetten, Y. Kawabata, J. Schoemaker and R. Versteegh, Survey on standard weights of passengers and baggage, Survey. EASA 2008.C.06/30800/R20090095/30800000/FBR/RLO, (2009). |
[5] |
D. Bertsimas, An exact fcfs waiting time analysis for a general class of G/G/s queueing systems, Queueing Systems Theory Appl., 3 (1988), 305-320.
doi: 10.1007/BF01157853. |
[6] |
D. Bertsimas, An analytic approach to a general class of G/G/s queueing systems, Operations Research, 38 (1990), 139-155.
doi: 10.1287/opre.38.1.139. |
[7] |
P. P. Bocharov and C. D'Apice, "Queueing Theory," Walter de Gruyter, 2004. |
[8] |
W. Grassmann, Real eigenvalues of certain tridiagonal matrix polynomials, with queueing applications, Linear Algebra and its Applications, 342 (2002), 93-106.
doi: 10.1016/S0024-3795(01)00462-1. |
[9] |
M. Karol, M. Hluchyj and S. Morgan, Input versus output queueing on a space-division packet switch, IEEE Transactions on Communications, 35 (1987), 1347-1356. |
[10] |
K. Laevens, A processor-sharing model for input-buffered ATM-switches in a correlated traffic environment, Microprocessors and Microsystems, 22 (1999), 589-596. |
[11] |
S. Liew, Performance of various input-buffered and output-buffered ATM switch design principles under bursty traffic: Simulation study, IEEE Transactions on Communications, 42 (1994), 1371-1379. |
[12] |
W. Mélange, H. Bruneel, B. Steyaert and J. Walraevens, A two-class continuous-time queueing model with dedicated servers and global fcfs service discipline, In "Analytical and Stochastic Modeling Techniques and Applications," Lecture Notes in Computer Science, Springer Berlin / Heidelberg, 6751 (2011), 14-27. |
[13] |
M. F. Neuts, "Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach," Corrected reprint of the 1981 original. Dover Publications, Inc., New York, 1994. |
[14] |
D. Ngoduy, Derivation of continuum traffic model for weaving sections on freeways, Transportmetrica, 2 (2006), 199-222. |
[15] |
R. Nishi, H. Miki, A. Tomoeda and K. Nishinari, Achievement of alternative configurations of vehicles on multiple lanes, Physical Review E, 79 (2009), 066119. |
[16] |
A. Stolyar, MaxWeight scheduling in a generalized switch: State space collapse and workload minimization in heavy traffic, Annals of Applied Probability, 14 (2004), 1-53.
doi: 10.1214/aoap/1075828046. |
[17] |
T. Van Woensel and N. Vandaele, Empirical validation of a queueing approach to uninterrupted traffic flows, 4OR, A Quarterly Journal of Operations Research, 4 (2006), 59-72. |
[18] |
T. Van Woensel and N. Vandaele, Modeling traffic flows with queueing models: A review, Asia-Pacific Journal of Operational Research, 24 (2007), 435-461. |
show all references
References:
[1] |
I. Adan, T. de Kok and J. Resing, A multi-server queueing model with locking, EJOR, 116 (2000), 16-26. |
[2] |
I. J. B. F. Adan, J. Wessels and W. H. M. Zijm, A compensation approach for two-dimensional markov processes, Advances in Applied Probability, 25 (1993), 783-817.
doi: 10.2307/1427792. |
[3] |
P. Beekhuizen and J. Resing, Performance analysis of small non-uniform packet switches, Performance Evaluation, 66 (2009), 640-659. |
[4] |
Z. Berdowski, F. van den Broek-Serlé, J. Jetten, Y. Kawabata, J. Schoemaker and R. Versteegh, Survey on standard weights of passengers and baggage, Survey. EASA 2008.C.06/30800/R20090095/30800000/FBR/RLO, (2009). |
[5] |
D. Bertsimas, An exact fcfs waiting time analysis for a general class of G/G/s queueing systems, Queueing Systems Theory Appl., 3 (1988), 305-320.
doi: 10.1007/BF01157853. |
[6] |
D. Bertsimas, An analytic approach to a general class of G/G/s queueing systems, Operations Research, 38 (1990), 139-155.
doi: 10.1287/opre.38.1.139. |
[7] |
P. P. Bocharov and C. D'Apice, "Queueing Theory," Walter de Gruyter, 2004. |
[8] |
W. Grassmann, Real eigenvalues of certain tridiagonal matrix polynomials, with queueing applications, Linear Algebra and its Applications, 342 (2002), 93-106.
doi: 10.1016/S0024-3795(01)00462-1. |
[9] |
M. Karol, M. Hluchyj and S. Morgan, Input versus output queueing on a space-division packet switch, IEEE Transactions on Communications, 35 (1987), 1347-1356. |
[10] |
K. Laevens, A processor-sharing model for input-buffered ATM-switches in a correlated traffic environment, Microprocessors and Microsystems, 22 (1999), 589-596. |
[11] |
S. Liew, Performance of various input-buffered and output-buffered ATM switch design principles under bursty traffic: Simulation study, IEEE Transactions on Communications, 42 (1994), 1371-1379. |
[12] |
W. Mélange, H. Bruneel, B. Steyaert and J. Walraevens, A two-class continuous-time queueing model with dedicated servers and global fcfs service discipline, In "Analytical and Stochastic Modeling Techniques and Applications," Lecture Notes in Computer Science, Springer Berlin / Heidelberg, 6751 (2011), 14-27. |
[13] |
M. F. Neuts, "Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach," Corrected reprint of the 1981 original. Dover Publications, Inc., New York, 1994. |
[14] |
D. Ngoduy, Derivation of continuum traffic model for weaving sections on freeways, Transportmetrica, 2 (2006), 199-222. |
[15] |
R. Nishi, H. Miki, A. Tomoeda and K. Nishinari, Achievement of alternative configurations of vehicles on multiple lanes, Physical Review E, 79 (2009), 066119. |
[16] |
A. Stolyar, MaxWeight scheduling in a generalized switch: State space collapse and workload minimization in heavy traffic, Annals of Applied Probability, 14 (2004), 1-53.
doi: 10.1214/aoap/1075828046. |
[17] |
T. Van Woensel and N. Vandaele, Empirical validation of a queueing approach to uninterrupted traffic flows, 4OR, A Quarterly Journal of Operations Research, 4 (2006), 59-72. |
[18] |
T. Van Woensel and N. Vandaele, Modeling traffic flows with queueing models: A review, Asia-Pacific Journal of Operational Research, 24 (2007), 435-461. |
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