A discussion on the optimality of bulk entry queue with differentiated hiatuses

• Authors: VADIVUKARASI Manickam , KALIDASS Kaliappan
• Languages of publication: EN

Abstracts

EN

We consider Markovian differentiated hiatuses queues with bulk entries. With the help of the matrix geometric method, we discuss the stability condition for the existence of the steady-state solution of our model and we obtain the stationary system size by using a probability generating function. The stochastic decomposition form of stationary system size and the waiting time distribution of an arbitrary beneficiary are also analysed. Furthermore, we perform the expense analysis using the particle swarm optimization technique and we obtain the optimality of service rate and hiatus rate. Finally, we study the effects of changes in the parameters on some important performance measures of the system through numerical observations.

Keywords

EN

differentiated hiatus times; steady state probabilities; waiting time distribution; optimization of expenses

• Publisher: Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
• Journal: Operations Research and Decisions
• Year: 2022
• Volume: 32
• Issue: 2
• Pages: 137-150

Contributors

author

VADIVUKARASI Manickam

• Department of Mathematics, Karpagam Academy of Higher Education, Coimbatore - 641 020, Tamil Nadu, India

author

KALIDASS Kaliappan

• Department of Mathematics, Karpagam Academy of Higher Education, Coimbatore - 641 020, Tamil Nadu, India

References

• Baba, Y. On the M X /G/1 queue with vacation time. Operations Research Letters 5, 2 (1986), 93–98.
• Baba, Y. The M X /M/1 queue with multiple working vacations. American Journal of Operations Research 2, 2 (2012), 217–224.
• Bouchentouf, A. A., and Guendouzi, A. Sensitivity analysis of feedback multiple vacation queuing system with differentiated vacations, vacation interruptions and impatient customers. International Journal of Applied Mathematics and Statistics 57, 6 (2018), 104–121.
• Bouchentouf, A. A., and Guendouzi, A. Single server batch arrival Bernoulli feedback queueing system with waiting server, K-variant vacations and impatient customers. SN Operations Research Forum 2 (2021), 1–23.
• Bouchentouf, A. A., Guendouzi, A., and Majid, S. On impatience in Markovian M/M/1/N/DW V queue with vacation interruption. Croatian Operational Research Review 11 (2020), 21–37.
• Bouchentouf, A. A., and Medjahri, L. Performance and economic evaluation of differentiated multiple vacation queuing system with feedback and balked customers. Applications and Applied Mathematics: an International Journal (AAM) 14, 1 (2019), 46–62.
• Burke, P. J. Delay in single-server queues with batch arrivals. Operations Research 23, 4 (1975), 830–833.
• Doshi, B. T. Queueing systems with vacations - a survey. Queueing Systems 1, 1 (1986), 29–66.
• Gao, S., and Yin, C. Discrete-time GeoX /G/1 queue with geometrically working vacations and vacation interruption. Quality Technology & Quantitative Management 10, 4 (2013), 423–442.
• Gupta, P., and Kumar, N. Analysis of classical retrial queue with differentiated vacation and state dependent arrival rate. Ratio Mathematica 40 (2021), 47–66.
• Ibe, O. C., and Isijola, O. A. M/M/1 multiple vacation queueing systems with differentiated vacations. Modelling and Simulation in Engineering (2014), 1–6.
• Ke, J.-C. Operating characteristic analysis on the M X /G/1 system with a variant vacation policy and balking. Applied Mathematical Modelling 31, 7 (2007), 1321–1337.
• Ke, J.-C., and Chu, Y.-K. A modified vacation model M X /G/1 system. Applied Stochastic Models in Business and Industry 22, 1 (2006), 1–16.
• Ke, J.-C., Huang, K.-B., and Pearn, W. L. The performance measures and randomized optimization for an unreliable server M [X]/G/1 vacation system. Applied Mathematics and Computation 217, 21 (2011), 8277–8290.
• Lee, H. W., Lee, S. S., Park, J. O., and Chae, K. C. Analysis of the M X /G/1 queue with N-policy and multiple vacations. Journal of Applied Probability 31, 2 (1994), 476–496.
• Li, J., Liu, W., and Tian, N. Steady-state analysis of a discrete-time batch arrival queue with working vacations. Performance Evaluation 67, 10 (2010), 897–912.
• Luo, C., Li, W., Yu, K., and Ding, C. The matrix-form solution for GeoX /G/1/N working vacation queue and its application to state-dependent cost control. Computers & Operations Research 67 (2016), 63–74.
• Medhi, J. Stochastic Models in Queueing Theory. Academic Press, USA, 2003.
• Neuts, M. F. Matrix-Geometric Solution in Stochasic Models - an Algorithmic Approach. The Johns Hopkins University Press, Baltimore, 1981.
• Rao, S. S. Engineering Optimization: Theory and Practice. John Wiley & Sons Ltd, University of Miami, Coral Gables, Florida, 2009.
• Suranga Sampath, M. I. G., Kalidass, K., and Liu, J. Transient analysis of an M/M/1 queueing system subjected to multiple differentiated vacations, impatient customers and a waiting server with application to IEEE 802.16E power saving mechanism. Indian Journal of Pure and Applied Mathematics 51, 1 (2020), 297–320.
• Suranga Sampath, M. I. G., and Liu, J. Impact of customers impatience on an M/M/1 queueing system subject to differentiated vacations with a waiting server. Quality Technology & Quantitative Management 17, 2 (2018), 125–148.
• Takagi, H. Queueing Analysis: A Foundation of Performance Evaluation, vol. 1. Elsevier, 2009.
• Teghem, J. Control of the service process in a queueing system. European Journal of Operational Research 23, 2 (1986), 141–158.
• Tian, N., and Zhang, Z. G. Vacation Queueing Models: Theory and Applications. Springer Science & Business Media, 2006.
• Vadivukarasi, M., Kalidass, K., and Jayaraman, R. Discussion on the optimization of finite buffer markovian queue with differentiated vacations. In Soft Computing: Theories and Applications (Singapore, 2022), T. K. Sharma, C. W. Ahn, O. P. Verma, and B. K. Panigrahi, Eds., Springer Singapore, pp. 523–534.
• Vijayashree, K. V., and Janani, B. Transient analysis of an M/M/1 queueing system subject to differentiated vacations. Quality Technology & Quantitative Management 15, 6 (2018), 730–748.
• Xu, X.-L., Zhang, Z.-J., China, P.-R., and Tian, N.-S. Analysis for the M X /M/1 working vacation queue. International Journal of Information and Management Science 20, 3 (2009), 379–394.
• Ye, Q. The analysis of M X /M/1 queue with two-stage vacations policy. Communications and Statistics - Theory and Methods 48, 18 (2019), 4492–4510.
• Yu, M. M., Tang, Y. H., and Fu, Y. H. Steady state analysis and computation of the GIx/M b/1/L queue with multiple working vacations and partial batch rejection. Computers & Industrial Engineering 56, 4 (2009), 1243–1253.

Identifiers

DOI

10.37190/ord220209