Abstract
<p style='text-indent:20px;'>In this paper, a queuing system as multi server queue, in which customers have a deadline and they request service from a random number of identical severs, is considered. Indeed there are stochastic jumps, in which the time intervals between successive jumps are independent and exponentially distributed. These jumps will be occurred due to a new arrival or situation change of servers. Therefore the queuing system can be controlled by restricting arrivals as well as rate of service for obtaining optimal stochastic jumps. Our model consists of a single queue with infinity capacity and multi server for a Poisson arrival process. This processes contains deterministic rate <inline-formula><tex-math id="M1">\begin{document}$ \lambda(t) $\end{document}</tex-math></inline-formula> and exponential service processes with <inline-formula><tex-math id="M2">\begin{document}$ \mu $\end{document}</tex-math></inline-formula> rate. In this case relevant customers have exponential deadlines until beginning of their service. Our contribution is to extend the Ittimakin and Kao's results to queueing system with impatient customers. We also formulate the aforementioned problem with complete information as a stochastic optimal control. This optimal control law is found through dynamic programming.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Control and Optimization,Algebra and Number Theory,Applied Mathematics,Control and Optimization,Algebra and Number Theory
Reference15 articles.
1. J. Blazewics, M. Drozdowski, D. de Werra, J. Weglarz.Deadline scheduling of multiprocessor tasks, Discrete Applied Mathematics, 65 (1996), 81-95.
2. B. M. Boris.Optimization of queuing system via stochastic control, Automatica, 45 (2009), 1423-1430.
3. A. Delavarkhalafi, Randomized algorithm for arrival and departure of the ships in a simple port, in Proceedings of the 6th WSEAS International Conference on Simulation, Modelling and Optimization, Lisbon, Portugal, (2006), 44–48.
4. A. Delavarkhalafi, A. Poursherafatan.Filtering method for linear and non-linear stochastic optimal control of partially observable systems, Filomat, 31 (2017), 5979-5992.
5. Fabienne Gillent, Guy Latouche.Semi-explicit solutions for M/PH/1 -like queuing systems, European Journal of Operational Research, 13 (1983), 151-160.
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献