36e9b140-8d48-4238-a413-403da3532ba320231027064354448wseas:wseasmdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON SYSTEMS AND CONTROL2224-28561991-876310.37394/23203http://wseas.org/wseas/cms.action?id=40731220231220231810.37394/23203.2023.18https://wseas.com/journals/sac/2023.phpMarioLefebvreDepartment of Mathematics and Industrial Engineering Polytechnique Montréal 2500, chemin de Polytechnique, Montréal (Québec) H3T 1J4 CANADAThe problem of reducing the number of customers waiting for service in a modifiedM/G/k queueing model is considered. We assume that the optimizer can decide how many servers are working at any time instant. The optimization problem ends as soon as the objective has been achieved or a time limit has been reached. Cases when dynamic programming can be used to determine the optimal control even if the service time is not exponentially distributed are presented.102720231027202334234535https://wseas.com/journals/sac/2023/a705103-017(2023).pdf10.37394/23203.2023.18.35https://wseas.com/journals/sac/2023/a705103-017(2023).pdfM. Lefebvre and R. Yaghoubi. Optimal control of a queueing system. (Submitted for publication) P. Whittle. Optimization over Time, Vol. I, Wiley, Chichester, 1982. P. Whittle. Risk-sensitive Optimal Control, Wiley, Chichester, 1990. 10.1080/00207721.2022.2083258M. Lefebvre and P. Pazhoheshfar. An optimal control problem for the maintenance of a machine. International Journal of Systems Science, vol. 53, no. 15, 2022, pp. 3364–3373. https://doi.org/10.1080/00207721.2022.20832- 58 10.2307/3213947J. Kuhn. The risk-sensitive homing problem. Journal of Applied Probability, vol. 22, 1985, pp. 796–803. https://doi.org/10.2307/3213947 10.1016/j.automatica.2009.06.015C. Makasu. Risk-sensitive control for a class of homing problems. Automatica, vol. 45, no. 10, 2009, pp. 2454–2455. https://doi.org/10.1016/- j.automatica.2009.06.015 10.1007/s11009-020-09800-2M. Kounta and N.J. Dawson. Linear quadratic Gaussian homing for Markov processes with regime switching and applications to controlled population growth/decay. Methodology and Computing in Applied Probability, vol. 23, 2021, pp. 1155–1172. https://doi.org/10.1007/s11009-020-09800-2 M. Lefebvre. An optimal control problem for a modified M/G/k queueing system. Proceedings of the Workshop on Intelligent Information Systems (WIIS2023), October 2023, Chişinǎu, Republic of Moldova, 8 pages. 10.1007/s40305-022-00413-9L. Luo, Y.-H. Tang, M.-M. Yu and W.-Q. Wu. Optimal control policy of M/G/1 queueing system with delayed randomized multiple vacations under the modified min(N, D)-policy control. Journal of the Operations Research Society of China, 2022. https://doi.org/10.1007/s40305- 022-00413-9 10.1016/j.engappai.2022.105683A. Petrović, M. Nikolić, U. Bugarić, B. Delibašić and P. Lio. Controlling highway toll stations using deep learning, queuing theory, and differential evolution. Applications of Artificial Intelligence, vol. 119, 2023, 105683. https://doi.org/10.1016/j.engappai.2022.105683 10.1145/3570619F. Xinzhe and N. Modiano. Joint learning and control in stochastic queueing networks with unknown utilities. Proceedings of the ACM on Measurement and Analysis of Computing Systems, vol. 6, no. 3, 2022, Article 58, 32 pages. https://doi.org/10.1145/3570619