Abstract
The aim of this paper is to improve the machine interference model with vacation to deal with more recent problems of the communication area. To this scope the model is extended to include parallelism in the vacation station. The underlying Markov process is analyzed and a state arrangement is found that yields an efficient matrix-analytic technique that substantially lowers down the time- and space-complexity of standard methods. A numerical example of the method effectiveness is presented, and an example of resource allocation is introduced that finds applications in the QoS management of wireless networks.
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References
Chao, X., & Zhao, Y. Q. (1998). Analysis of multi-server queues with station and server vacations. European Journal of Operational Research, 110, 392–406.
de Nitto Personè, V., & Grassi, V. (1996). Solution of finite QBD processes. Journal of Applied Probability, 33(4), 1003–1010.
de Nitto Personè, V., & Iazeolla, G. (2006). QoS Management in Wireless Networks. In SPECTS’06, international symposium on performance evaluation of computer and telecommunication systems, Calgary, Canada.
Fiems, D., Steyaert, B., & Bruneel, H. (2001). Performance evaluation of CAI and RAI transmission modes in a GI-G-1 queue. Computers & Operations Research, 28, 1299–1313.
Frigui, I., & Alfa, A. S. (1998). Analysis of a time-limited polling system. Computer Communications, 21, 558–571.
Grassman, W. K., & Heyman, D. P. (1990). Equilibrium distribution of block-structured Markov chains with repeating rows. Journal of Applied Probability, 27, 557–576.
Gupta, S. M. (1997). Machine interference problem with spares, server vacations and exhaustive service. Performance Evaluation, 29, 195–211.
Gupta, U. C., & Sikdar, K. (2004). The finite-buffer M/G/1 queue with general bulk-service rule and single vacation. Performance Evaluation, 57, 199–219.
Iazeolla, G., & Marinuzzi, F. (1989). A few remarks on cost/performance relationships in parallel computer architectures. In ESM 89, European simulation multiconference, Rome, Italy.
Le Boudec, J. Y. (1989). A generalization of matrix geometric solutions for Markov models. IBM Research Division Zurich, Res. Rep. RZ 1903 (#67353).
Lee, Y., & Choi, B. D. (2001). Queueing system with multiple delay and loss priorities for ATM networks. Information Sciences, 138, 7–29.
Mehmet-Ali, M., Zhang, X., & Hayes, J. F. (2003). A performance analysis of a discrete-time queueing system with server interruption for modeling wireless ATM multiplexer. Performance Evaluation, 51, 1–31.
Servi, L. D., & Finn, S. G. (2002). M/M/1 queues with working vacations (M/M/1/WV). Performance Evaluation, 50, 41–52.
Sevcik, K. (2005). The origin of queueing network models. Ubiquity, 6(3).
Stallings, W. (2005). Wireless communications & networks. Upper Saddle River, NJ: Prentice Hall.
Takagi, H. (1991). Queueing analysis—a foundation of performance evaluation. Vacation and Priority Systems (Part I, Vol. I). Amsterdam: Elsevier.
Xu, E., & Alfa, A. S. (2002). A vacation model for the non-satured Readers and Writers system with a threshold policy. Performance Evaluation, 50, 233–244.
Ye, J., & Li, S. Q. (1994). Folding algorithm: a computational method for finite QBD processes with level-dependent transitions. IEEE Transactions on Communications, 42(2/3/4), 625–639.
Zhang, Z. G., & Tian, N. (2003). Analysis on queueing systems with synchronous vacations of partial servers. Performance Evaluation, 52, 269–282.
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The author is thankful to the anonymous referees for the improvements their comments have earned to the quality of the presentation and to the completeness of the paper. The author is thankful to Giuseppe Iazeolla, whose careful reading of the original draft of this paper led to significant improvements in its overall quality. This work was partially supported by funds from the FIRB project “Performance Evaluation of Complex Systems: Techniques Methodologies and Tools” and by the University of Roma TorVergata project on High Performance ICT Platforms.
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de Nitto Personè, V. Analysis of cyclic queueing networks with parallelism and vacation. Ann Oper Res 170, 95–112 (2009). https://doi.org/10.1007/s10479-008-0433-z
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DOI: https://doi.org/10.1007/s10479-008-0433-z