American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Stability of a retrial queueing network with different classes of customers and restricted resource pooling
  • JIMO Home
  • This Issue
  • Next Article
    Performance evaluation of a power saving mechanism in IEEE 802.16 wireless MANs with bi-directional traffic
July  2011, 7(3): 735-751. doi: 10.3934/jimo.2011.7.735

Partially shared buffers with full or mixed priority

Thomas Demoor 1, , Dieter Fiems 1, , Joris Walraevens 1, and  Herwig Bruneel 1,

1. 

Department of Telecommunications and Information Processing, Ghent University, St-Pietersnieuwstraat 41, 9000 Gent

Received  September 2010 Revised  January 2011 Published  June 2011

This paper studies a finite-sized discrete-time two-class priority queue. Packets of both classes arrive according to a two-class discrete batch Markovian arrival process (2-DBMAP), taking into account the correlated nature of arrivals in heterogeneous telecommunication networks. The model incorporates time and space priority to provide different types of service to each class. One of both classes receives absolute time priority in order to minimize its delay. Space priority is implemented by the partial buffer sharing acceptance policy and can be provided to the class receiving time priority or to the other class. This choice gives rise to two different queueing models and this paper analyses both these models in a unified manner. Furthermore, the buffer finiteness and the use of space priority raise some issues on the order of arrivals in a slot. This paper does not assume that all arrivals from one class enter the queue before those of the other class. Instead, a string representation for sequences of arriving packets and a probability measure on the set of such strings are introduced. This naturally gives rise to the notion of intra-slot space priority. Performance of these queueing systems is then determined using matrix-analytic techniques. The numerical examples explore the range of service differentiation covered by both models.
Keywords: Queueing theory, space priority, partial buffer sharing, time priority, matrix analytic method..
Mathematics Subject Classification: Primary: 60J10, 60K25; Secondary: 68M1.
Citation: Thomas Demoor, Dieter Fiems, Joris Walraevens, Herwig Bruneel. Partially shared buffers with full or mixed priority. Journal of Industrial & Management Optimization, 2011, 7 (3) : 735-751. doi: 10.3934/jimo.2011.7.735
References:
[1]

C. Blondia and O. Casals, Statistical multiplexing of VBR sources: A matrix-analytic approach,, Performance Evaluation, 16 (1992), 5.  doi: 10.1016/0166-5316(92)90064-N.  Google Scholar

[2]

T. Demoor, J. Walraevens, D. Fiems, S. De Vuyst and H. Bruneel, Influence of real-time queue capacity on system contents in DiffServ's expedited forwarding per-hop-behavior,, Journal of Industrial and Management Optimization, 6 (2010), 587.  doi: 10.3934/jimo.2010.6.587.  Google Scholar

[3]

T. Demoor, D. Fiems, J. Walraevens and H. Bruneel, Time and space priority in a partially shared priority queue,, in, (2010).   Google Scholar

[4]

D. Fiems and H. Bruneel, A note on the discretization of Little's result,, Operations Research Letters, 30 (2002), 17.  doi: 10.1016/S0167-6377(01)00112-2.  Google Scholar

[5]

D. Fiems, J. Walraevens and H. Bruneel, Performance of a partially shared priority buffer with correlated arrivals,, Lecture Notes in Computer Science, 4516 (2007), 582.  doi: 10.1007/978-3-540-72990-7_52.  Google Scholar

[6]

G. Hwang and B. Choi, Performance analysis of the $DAR(1)$/$D$/$c$ priority queue under partial buffer sharing policy,, Computers & Operations Research, 31 (2004), 2231.  doi: 10.1016/S0305-0548(03)00175-8.  Google Scholar

[7]

H. Kröner, G. Hébuterne, P. Boyer and A. Gravey, Priority management in ATM switching nodes,, IEEE Journal on Selected Areas in Communications, 9 (1991), 418.  doi: 10.1109/49.76641.  Google Scholar

[8]

K. Laevens and H. Bruneel, Discrete-time multiserver queues with priorities,, Performance Evaluation, 33 (1998), 249.  doi: 10.1016/S0166-5316(98)00024-8.  Google Scholar

[9]

G. Latouche and V. Ramaswami, "Introduction to Matrix Analytic Methods in Stochastic Modeling,", Series on Statistics and Applied Probability. ASA-SIAM, (1999).   Google Scholar

[10]

M. Mehmet Ali and X. Song, A performance analysis of a discrete-time priority queueing system with correlated arrivals,, Performance Evaluation, 57 (2004), 307.  doi: 10.1016/j.peva.2004.01.001.  Google Scholar

[11]

H. Radha, Y.Chen, K. Parthasarathy and R. Cohen, Scalable internet video using MPEG-4,, Signal Processing: Image Communication, 15 (1999), 95.  doi: 10.1016/S0923-5965(99)00026-0.  Google Scholar

[12]

K. Spaey, "Superposition of Markovian Traffic Sources and Frame Aware Buffer Acceptance,", Ph.D. thesis, (2002).   Google Scholar

[13]

T. Takine, B. Sengupta and T. Hasegawa, An analysis of a discrete-time queue for broadband ISDN with priorities among traffic classes,, IEEE Transactions on Communications, 42 (1994), 1837.  doi: 10.1109/TCOMM.1994.582893.  Google Scholar

[14]

J. Van Velthoven, B. Van Houdt and C. Blondia, The impact of buffer finiteness on the loss rate in a priority queueing system,, Lecture Notes in Computer Science, 4054 (2006), 211.  doi: 10.1007/11777830_15.  Google Scholar

[15]

J. Walraevens, B. Steyaert and H. Bruneel, Performance analysis of a single-server ATM queue with a priority scheduling,, Computers & Operations Research, 30 (2003), 1807.  doi: 10.1016/S0305-0548(02)00108-9.  Google Scholar

[16]

J. Walraevens, S. Wittevrongel and H. Bruneel, A discrete-time priority queue with train arrivals,, Stochastic Models, 23 (2007), 489.  doi: 10.1080/15326340701471158.  Google Scholar

[17]

Y. Wang, C. Liu and C. Lu, Loss behavior in space priority queue with batch Markovian arrival process - discrete-time case,, Performance Evaluation, 41 (2000), 269.  doi: 10.1016/S0166-5316(99)00079-6.  Google Scholar

[18]

Y. C. Wang, J. S. Wang and F. H. Tsai, Analysis of Discrete-Time Space Priority Queue with Fuzzy Threshold,, Journal of Industrial and Management Optimization, 5 (2009), 467.  doi: 10.3934/jimo.2009.5.467.  Google Scholar

[19]

J. Zhao, B. Li, X. Cao and I. Ahmad, A matrix-analytic solution for the $DBMAP$/$PH$/$1$ priority queue,, Queueing Systems, 53 (2006), 127.  doi: 10.1007/s11134-006-8306-0.  Google Scholar

show all references

References:
[1]

C. Blondia and O. Casals, Statistical multiplexing of VBR sources: A matrix-analytic approach,, Performance Evaluation, 16 (1992), 5.  doi: 10.1016/0166-5316(92)90064-N.  Google Scholar

[2]

T. Demoor, J. Walraevens, D. Fiems, S. De Vuyst and H. Bruneel, Influence of real-time queue capacity on system contents in DiffServ's expedited forwarding per-hop-behavior,, Journal of Industrial and Management Optimization, 6 (2010), 587.  doi: 10.3934/jimo.2010.6.587.  Google Scholar

[3]

T. Demoor, D. Fiems, J. Walraevens and H. Bruneel, Time and space priority in a partially shared priority queue,, in, (2010).   Google Scholar

[4]

D. Fiems and H. Bruneel, A note on the discretization of Little's result,, Operations Research Letters, 30 (2002), 17.  doi: 10.1016/S0167-6377(01)00112-2.  Google Scholar

[5]

D. Fiems, J. Walraevens and H. Bruneel, Performance of a partially shared priority buffer with correlated arrivals,, Lecture Notes in Computer Science, 4516 (2007), 582.  doi: 10.1007/978-3-540-72990-7_52.  Google Scholar

[6]

G. Hwang and B. Choi, Performance analysis of the $DAR(1)$/$D$/$c$ priority queue under partial buffer sharing policy,, Computers & Operations Research, 31 (2004), 2231.  doi: 10.1016/S0305-0548(03)00175-8.  Google Scholar

[7]

H. Kröner, G. Hébuterne, P. Boyer and A. Gravey, Priority management in ATM switching nodes,, IEEE Journal on Selected Areas in Communications, 9 (1991), 418.  doi: 10.1109/49.76641.  Google Scholar

[8]

K. Laevens and H. Bruneel, Discrete-time multiserver queues with priorities,, Performance Evaluation, 33 (1998), 249.  doi: 10.1016/S0166-5316(98)00024-8.  Google Scholar

[9]

G. Latouche and V. Ramaswami, "Introduction to Matrix Analytic Methods in Stochastic Modeling,", Series on Statistics and Applied Probability. ASA-SIAM, (1999).   Google Scholar

[10]

M. Mehmet Ali and X. Song, A performance analysis of a discrete-time priority queueing system with correlated arrivals,, Performance Evaluation, 57 (2004), 307.  doi: 10.1016/j.peva.2004.01.001.  Google Scholar

[11]

H. Radha, Y.Chen, K. Parthasarathy and R. Cohen, Scalable internet video using MPEG-4,, Signal Processing: Image Communication, 15 (1999), 95.  doi: 10.1016/S0923-5965(99)00026-0.  Google Scholar

[12]

K. Spaey, "Superposition of Markovian Traffic Sources and Frame Aware Buffer Acceptance,", Ph.D. thesis, (2002).   Google Scholar

[13]

T. Takine, B. Sengupta and T. Hasegawa, An analysis of a discrete-time queue for broadband ISDN with priorities among traffic classes,, IEEE Transactions on Communications, 42 (1994), 1837.  doi: 10.1109/TCOMM.1994.582893.  Google Scholar

[14]

J. Van Velthoven, B. Van Houdt and C. Blondia, The impact of buffer finiteness on the loss rate in a priority queueing system,, Lecture Notes in Computer Science, 4054 (2006), 211.  doi: 10.1007/11777830_15.  Google Scholar

[15]

J. Walraevens, B. Steyaert and H. Bruneel, Performance analysis of a single-server ATM queue with a priority scheduling,, Computers & Operations Research, 30 (2003), 1807.  doi: 10.1016/S0305-0548(02)00108-9.  Google Scholar

[16]

J. Walraevens, S. Wittevrongel and H. Bruneel, A discrete-time priority queue with train arrivals,, Stochastic Models, 23 (2007), 489.  doi: 10.1080/15326340701471158.  Google Scholar

[17]

Y. Wang, C. Liu and C. Lu, Loss behavior in space priority queue with batch Markovian arrival process - discrete-time case,, Performance Evaluation, 41 (2000), 269.  doi: 10.1016/S0166-5316(99)00079-6.  Google Scholar

[18]

Y. C. Wang, J. S. Wang and F. H. Tsai, Analysis of Discrete-Time Space Priority Queue with Fuzzy Threshold,, Journal of Industrial and Management Optimization, 5 (2009), 467.  doi: 10.3934/jimo.2009.5.467.  Google Scholar

[19]

J. Zhao, B. Li, X. Cao and I. Ahmad, A matrix-analytic solution for the $DBMAP$/$PH$/$1$ priority queue,, Queueing Systems, 53 (2006), 127.  doi: 10.1007/s11134-006-8306-0.  Google Scholar

[1]

Xiaomao Deng, Xiao-Chuan Cai, Jun Zou. A parallel space-time domain decomposition method for unsteady source inversion problems. Inverse Problems & Imaging, 2015, 9 (4) : 1069-1091. doi: 10.3934/ipi.2015.9.1069
[2]

Tao Wu, Yu Lei, Jiao Shi, Maoguo Gong. An evolutionary multiobjective method for low-rank and sparse matrix decomposition. Big Data & Information Analytics, 2017, 2 (1) : 23-37. doi: 10.3934/bdia.2017006
[3]

Juliang Zhang, Jian Chen. Information sharing in a make-to-stock supply chain. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1169-1189. doi: 10.3934/jimo.2014.10.1169
[4]

Guillaume Bal, Wenjia Jing. Homogenization and corrector theory for linear transport in random media. Discrete & Continuous Dynamical Systems - A, 2010, 28 (4) : 1311-1343. doi: 10.3934/dcds.2010.28.1311
[5]

W. Cary Huffman. On the theory of $\mathbb{F}_q$-linear $\mathbb{F}_{q^t}$-codes. Advances in Mathematics of Communications, 2013, 7 (3) : 349-378. doi: 10.3934/amc.2013.7.349
[6]

Valery Y. Glizer. Novel Conditions of Euclidean space controllability for singularly perturbed systems with input delay. Numerical Algebra, Control & Optimization, 2020  doi: 10.3934/naco.2020027
[7]

Alina Chertock, Alexander Kurganov, Mária Lukáčová-Medvi${\rm{\check{d}}}$ová, Șeyma Nur Özcan. An asymptotic preserving scheme for kinetic chemotaxis models in two space dimensions. Kinetic & Related Models, 2019, 12 (1) : 195-216. doi: 10.3934/krm.2019009
[8]

Wei Liu, Pavel Krejčí, Guoju Ye. Continuity properties of Prandtl-Ishlinskii operators in the space of regulated functions. Discrete & Continuous Dynamical Systems - B, 2017, 22 (10) : 3783-3795. doi: 10.3934/dcdsb.2017190
[9]

Charles Fulton, David Pearson, Steven Pruess. Characterization of the spectral density function for a one-sided tridiagonal Jacobi matrix operator. Conference Publications, 2013, 2013 (special) : 247-257. doi: 10.3934/proc.2013.2013.247
[10]

Nhu N. Nguyen, George Yin. Stochastic partial differential equation models for spatially dependent predator-prey equations. Discrete & Continuous Dynamical Systems - B, 2020, 25 (1) : 117-139. doi: 10.3934/dcdsb.2019175
[11]

Bin Pei, Yong Xu, Yuzhen Bai. Convergence of p-th mean in an averaging principle for stochastic partial differential equations driven by fractional Brownian motion. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 1141-1158. doi: 10.3934/dcdsb.2019213
[12]

Armin Lechleiter, Tobias Rienmüller. Factorization method for the inverse Stokes problem. Inverse Problems & Imaging, 2013, 7 (4) : 1271-1293. doi: 10.3934/ipi.2013.7.1271
[13]

Cécile Carrère, Grégoire Nadin. Influence of mutations in phenotypically-structured populations in time periodic environment. Discrete & Continuous Dynamical Systems - B, 2020, 25 (9) : 3609-3630. doi: 10.3934/dcdsb.2020075
[14]

Paula A. González-Parra, Sunmi Lee, Leticia Velázquez, Carlos Castillo-Chavez. A note on the use of optimal control on a discrete time model of influenza dynamics. Mathematical Biosciences & Engineering, 2011, 8 (1) : 183-197. doi: 10.3934/mbe.2011.8.183
[15]

Guillermo Reyes, Juan-Luis Vázquez. Long time behavior for the inhomogeneous PME in a medium with slowly decaying density. Communications on Pure & Applied Analysis, 2009, 8 (2) : 493-508. doi: 10.3934/cpaa.2009.8.493
[16]

Wei-Jian Bo, Guo Lin, Shigui Ruan. Traveling wave solutions for time periodic reaction-diffusion systems. Discrete & Continuous Dynamical Systems - A, 2018, 38 (9) : 4329-4351. doi: 10.3934/dcds.2018189
[17]

Kin Ming Hui, Soojung Kim. Asymptotic large time behavior of singular solutions of the fast diffusion equation. Discrete & Continuous Dynamical Systems - A, 2017, 37 (11) : 5943-5977. doi: 10.3934/dcds.2017258
[18]

Qiang Guo, Dong Liang. An adaptive wavelet method and its analysis for parabolic equations. Numerical Algebra, Control & Optimization, 2013, 3 (2) : 327-345. doi: 10.3934/naco.2013.3.327
[19]

Deren Han, Zehui Jia, Yongzhong Song, David Z. W. Wang. An efficient projection method for nonlinear inverse problems with sparsity constraints. Inverse Problems & Imaging, 2016, 10 (3) : 689-709. doi: 10.3934/ipi.2016017
[20]

Boris Kramer, John R. Singler. A POD projection method for large-scale algebraic Riccati equations. Numerical Algebra, Control & Optimization, 2016, 6 (4) : 413-435. doi: 10.3934/naco.2016018

2019 Impact Factor: 1.366

Tools

Metrics

  • PDF downloads (138)
  • HTML views (0)
  • Cited by (6)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences