A single-server queueing system with an infinite buffer is considered. The service of a customer is possible only in the presence of at least one unit of energy, and during the service the number of available units decreases by one. New units of energy arrive in the system at random instants of time if the finite buffer for maintenance of energy is not full. Customers are impatient and leave the system without service after a random amount of waiting time. Such a queueing system describes, e.g., the operation of a sensor node which harvests energy necessary for information transmission from the environment. Aiming to minimize the loss of customers due to their impatience (and maximize the throughput of the system), a new strategy of control by providing service is proposed. This strategy suggests that service temporarily stops if the number of customers or units of energy in the system becomes zero. The server is switched off (is in sleep mode) for some time. This time finishes (the server wakes up) if both the number of customers in the buffer and the number of energy units reach some fixed threshold values or when the number of energy units reaches some threshold value and there are customers in the buffer. Arrival flows of customers and energy units are assumed to be described by an independent Markovian arrival process. The service time has a phase-type distribution. The system behavior is described by a multi-dimensional Markov chain. The generator of this Markov chain is derived. The ergodicity condition is presented. Expressions for key performance measures are given. Numerical results illustrating the dependence of a customer's loss probability on the thresholds defining the discipline of waking up the server are provided. The importance of the account of correlation in arrival processes is numerically illustrated.
@article{bwmeta1.element.bwnjournal-article-amcv26i2p367bwm,
author = {Alexander Dudin and Moon Ho Lee and Sergey Dudin},
title = {Optimization of the service strategy in a queueing system with energy harvesting and customers' impatience},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {26},
year = {2016},
pages = {367-378},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv26i2p367bwm}
}
Alexander Dudin; Moon Ho Lee; Sergey Dudin. Optimization of the service strategy in a queueing system with energy harvesting and customers' impatience. International Journal of Applied Mathematics and Computer Science, Tome 26 (2016) pp. 367-378. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv26i2p367bwm/
[000] Akyildiz, I., Su, W., Sankarasubramaniam, Y. and Cayirci, E. (2002). Wireless sensor networks: A survey, Computer Networks 38(4): 393-422.
[001] Atencia, I. (2014). A discrete-time system with service control and repairs, International Journal of Applied Mathematics and Computer Science 24(3): 471-484, DOI: 10.2478/amcs-2014-0035. | Zbl 1322.90019
[002] Doshi, B. (1986). Queueing systems with vacations-a survey, Queueing Systems 1(1): 29-66. | Zbl 0655.60089
[003] Dudin, A. and Klimenok, V. (1996). Queueing systems with passive servers, Journal of Applied Mathematics and Stochastic Analysis 9(2): 185-204. | Zbl 0858.60084
[004] Dudina, O., Kim, C. and Dudin, S. (2013). Retrial queuing system with Markovian arrival flow and phase-type service time distribution, Computers & Industrial Engineering 66(2): 360-373.
[005] Gelenbe, E. (2015). Synchronising energy harvesting and data packets in a wireless sensor, Energies 8(1): 356-369.
[006] Kim, C., Dudin, A., Dudin, S. and Dudina, O. (2014). Analysis of an M M AP/PH₁ , PH₂/N/∞ queueing system operating in a random environment, International Journal of Applied Mathematics and Computer Science 24(3): 485-501, DOI: 10.2478/amcs-2014-0036. | Zbl 1322.60195
[007] Kim, C., Dudin, S. and Klimenok, V. (2009). The M AP/P H/1/N queue with flows of customers as model for traffic control in telecommunication networks, Performance Evaluation 66(9-10): 564-579.
[008] Klimenok, V. and Dudin, A. (2006). Multi-dimensional asymptotically quasi-Toeplitz Markov chains and their application in queueing theory, Queueing Systems 54(4): 245-259. | Zbl 1107.60060
[009] Mészáros, A., Papp, J. and Telek, M. (2014). Fitting traffic with discrete canonical phase type distribution and Markov arrival processes, International Journal of Applied Mathematics and Computer Science 24(3): 453-470, DOI: 10.2478/amcs-2014-0034. | Zbl 1322.93092
[010] Neuts, M. (1981). Matrix-geometric Solutions in Stochastic Models-An Algorithmic Approach, Johns Hopkins University Press, Baltimore, MD. | Zbl 0469.60002
[011] Sharma, V., Mukherji, U., Joseph, V. and Gupta, S. (2010). Optimal energy management policies for energy harvesting sensor nodes, IEEE Transactions on Wireless Communications 9(4): 1326-1336.
[012] Takagi, H. (1991). Queueing Analysis: A Foundation of Performance Evaluation, North-Holland, Amsterdam. | Zbl 0744.60114
[013] Tian, N. and Zhang, Z. (2006). Vacation Queueing Models- Theory and Applications, Springer, Heidelberg. | Zbl 1104.60004
[014] Tutuncuoglu, K. and Yener, A. (2012). Optimum transmission policies for battery limited energy harvesting nodes, IEEE Transactions on Wireless Communications 11(3): 1180-1189.
[015] Yang, J. and Ulukus, S. (2012a). Optimal packet scheduling in a multiple access channel with energy harvesting transmitters, Journal of Communications and Networks 14(2): 140-150.
[016] Yang, J. and Ulukus, S. (2012b). Optimal packet scheduling in an energy harvesting communication system, IEEE Transactions on Communications 60(1): 220-230.