Skip to main content

Advertisement

SpringerLink
Log in

Analysis of MAP/G/1 queue with inventory as the model of the node of wireless sensor network with energy harvesting

  • Original Research
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

Queueing systems where certain inventory items are required to provide service to a customer have become popular in the literature from early 1990th. Such systems are similar to those models analysed in the literature models with paired customers, assembly-like queues, passenger–taxi models, etc. During the last few years they are considered in the context of modelling operation of the nodes of a wireless sensor network with energy harvesting. Distinguishing feature of the model considered in this paper, besides the suggestion that arrival flow of customers is described by the Markovian arrival process, is the assumption about a general distribution of the service time while only exponential or phase-type distribution was previously assumed in the existing literature. We apply the well-known technique of M/G/1 type Markov chains and semi-regenerative processes to obtain the ergodicity criterion in a transparent form, stationary distribution of the system under study and the Laplace–Stieltjes transform of the sojourn time distribution. This creates an opportunity to formulate and solve various optimization problems. A number of numerical examples illustrate the computational tractability of the theoretical results and illustrate the behavior of the system performance measures depending on its parameters.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  • Arafa, A., Tong, T., Fu, M., Ulukus, S., & Chen, W. (2018). Delay minimal policies in energy harvesting communication systems. IEEE Transactions on Communications, 66, 2918–2930. https://doi.org/10.1109/TCOMM.2018.2805357

    Article  Google Scholar 

  • Babayo, A. A., Anisi, M. H., & Ali, I. (2017). A Review on energy management schemes in energy harvesting wireless sensor networks. Renewable and Sustainable Energy Reviews, 76, 1176–1184.

    Article  Google Scholar 

  • Baek, J. H., Dudina, O., & Kim, C. S. (2017). Queueing system with heterogeneous impatient customers and consumable additional items. Applied Mathematics and Computer Science, 27, 367–384.

    Google Scholar 

  • Chai, X., Jiang, T., Li, L., Xu, W., & Liu, L. (2022). On a many-to-many matched queueing system with flexible matching mechanism and impatient customers. Journal of Computational and Applied Mathematics, 416, 114573.

    Article  Google Scholar 

  • Chakravarthy, S. R. (2001). The batch Markovian arrival process: A review and future work. In A. Krishnamoorthy, N. Raju, & V. Ramaswami (Eds.), Advances in probability theory and stochastic processes (pp. 21–29). New Jersey: Notable Publications Inc.

    Google Scholar 

  • Chakravarthy, S. R., & Rao, B. M. (2021). Queuing–inventory models with MAP demands and random replenishment opportunities. Mathematics, 9(10), 1092.

    Article  Google Scholar 

  • Cinlar, E. (2013). Introduction to stochastic processes. North Chelmsford: Courier Corporation.

    Google Scholar 

  • De Cuypere, E., De Turck, K., & Fiems, D. (2018). A queueing model of an energy harvesting sensor node with data buffering. Telecommunication Systems, 67, 281–295.

    Article  Google Scholar 

  • Dudin, A., Dudin, S., Dudina, O., & Kim, C. S. (2017). Analysis of a wireless sensor node with varying rates of energy harvesting and consumption. Lecture Notes in Computer Science, 10684, 172–182.

    Article  Google Scholar 

  • Dudin, A., & Dudina, O. (2015). Analysis of the \(MAP/PH/1\) service system with repeat calls and energy audit. Automatic Control and Computer Science, 45(5), 277–285.

    Article  Google Scholar 

  • Dudin, A. N., Lee, M. H., & Dudin, S. A. (2016). Optimization of service strategy in queueing system with energy harvesting and customers impatience. Applied Mathematics and Computer Science, 26(2), 367–378.

    Google Scholar 

  • Dudin, A. N., Klimenok, V. I., & Vishnevsky, V. M. (2020). The theory of queuing systems with correlated flows. Springer. ISBN 978-3-030-32072-0.

  • Dudin, S. A., & Lee, M. H. (2016). Analysis of single-server queue with phase-type service and energy harvesting. Mathematical Problems in Engineering, ID592794, 1–16.

  • Gelenbe, E. (2014). A sensor node with energy harvesting. ACM SIGMETRICS Performance Evaluation Review, 42(2), 37–39.

    Article  Google Scholar 

  • Gelenbe, E. (2015). Synchronising energy harvesting and data packets in a wireless sensor. Energies, 8(1), 356–369.

    Article  Google Scholar 

  • Graham, A. (2018). Kronecker products and matrix calculus with applications. North Chelmsford: Courier Dover Publications.

    Google Scholar 

  • Kim, C. S., Dudin, A., Dudin, S., & Dudina, O. (2017). Performance evaluation of a wireless sensor node with energy harvesting and varying conditions of operation. In Proceedings of IEEE international communication conference (pp. 1–6).

  • Kim, C. S., Dudin, S., Dudin, A., & Samouylov, K. (2018). Multi-threshold control by a single-server queuing model with a service rate depending on the amount of harvested energy. Performance Evaluation, 127–128, 1–20.

    Google Scholar 

  • Krishnamoorthy, A., Joshua, A. N., & Kozyrev, D. (2021a). Analysis of a batch arrival, batch service queuing–inventory system with processing of inventory while on vacation. Mathematics, 9(4), 419.

  • Krishnamoorthy, A., Lakshmy, B., & Manikandan, R. (2011). A survey on inventory models with positive service time. Opsearch, 48(2), 153–169.

    Article  Google Scholar 

  • Krishnamoorthy, A., Shajin, D., & Lakshmy, B. (2016). On a queueing–inventory with reservation, cancellation, common life time and retrial. Annals of Operations Research, 247(1), 365–389.

    Article  Google Scholar 

  • Krishnamoorthy, A., Shajin, D., & Viswanath, C. N. (2021b). Inventory with positive service time: A survey. In V. Anisimov & N. Limnios (Eds.), Queueing theory. 2—Advanced trends in queueing theory, mathematics and statistics series, sciences, chapter 6 (pp. 201–238). London: Wiley.

  • Lucantoni, D. M. (1991). New results on the single server queue with a batch Markovian arrival process. Communications in Statistics-Stochastic Models, 7, 1–46.

    Article  Google Scholar 

  • Melikov, A. Z., & Molchanov, A. A. (1992). Stock optimization in transportation/storage systems. Cybernetics and Systems Analysis, 28, 484–487.

    Article  Google Scholar 

  • Neuts, M. F. (1989). Structured stochastic matrices of M/G/1 type and their applications (p. 1989). New York: Marcel Dekker.

  • Patil, K., De Turck, K., & Fiems, D. (2018). A two-queue model for optimising the value of information in energy-harvesting sensor networks. Performance Evaluation, 119, 27–42.

    Article  Google Scholar 

  • Sharma, V., Mukherji, U., Joseph, V., & Gupta, S. (2010). Optimal energy management policies for energy harvesting sensor nodes. IEEE Transactions on Wireless Communications, 9(4), 1326–1336.

    Article  Google Scholar 

  • Sherazi, H. H. R., Grieco, L. A., & Boggia, G. (2018). A comprehensive review on energy harvesting MAC protocols in WSNs. Challenges and Tradeoffs, Ad Hoc Networks, 71, 117–134.

    Article  Google Scholar 

  • Tan, L., & Tang, S. (2017). Energy harvesting wireless sensor node with temporal death: Novel models and analyses. IEEE/ACM Transactions on Networking, 25(2), 896–909.

    Article  Google Scholar 

  • Tutuncuoglu, K., & Yener, A. (2012). Optimum transmission policies for battery limited energy harvesting nodes. IEEE Transactions on Wireless Communications, 11(3), 1180–1189.

    Article  Google Scholar 

  • Ulukus, S., Yener, A., Erkip, E., Simeone, O., Zorzi, M., Grover, P., & Huang, K. (2015). Energy harvesting wireless communications: A review of recent advances. IEEE Journal on Selected Areas in Communications, 33, 360–381.

    Article  Google Scholar 

  • Vishnevskii, V. M., & Dudin, A. N. (2017). Queueing systems with correlated arrival flows and their applications to modeling telecommunication networks. Automation and Remote Control, 78(8), 1361–1403.

    Article  Google Scholar 

  • Yang, J., & Ulukus, S. (2012a). Optimal packet scheduling in an energy harvesting communication system. IEEE Transactions on Communications, 60(1), 220–230.

  • Yang, J., & Ulukus, S. (2012b). Optimal packet scheduling in a multiple access channel with energy harvesting transmitters. Journal of Communications and Networks, 14, 140–150.

Download references

Funding

This paper has been supported by the RUDN University Strategic Academic Leadership Program.

Author information

Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Avenue, 220030, Minsk, Belarus

    Alexander Dudin & Valentina Klimenok

  2. Department of Applied Probability and Informatics, RUDN University, 6, Miklukho-Maklaya St., Moscow, Russia, 117198

    Alexander Dudin

Authors
  1. Alexander Dudin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Valentina Klimenok
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alexander Dudin.

Ethics declarations

Conflict of interest

Authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dudin, A., Klimenok, V. Analysis of MAP/G/1 queue with inventory as the model of the node of wireless sensor network with energy harvesting. Ann Oper Res 331, 839–866 (2023). https://doi.org/10.1007/s10479-022-05036-0

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-022-05036-0

Keywords

Search

Navigation