Rare Events Queueing System - REQS

  • Ilija Tanackov Faculty of Technical Sciences, University of Novi Sad, Serbia
  • Žarko Jevtić Faculty of Technical Sciences, University of Novi Sad, Serbia
  • Gordan Stojić Faculty of Technical Sciences, University of Novi Sad, Serbia
  • Feta Sinani Faculty of Applied Sciences, State University of Tetovo, Republic of North Macedonia
  • Pamela Ercegovac Faculty of Technical Sciences, University of Novi Sad, Serbia
Keywords: collapse, special service, critical probability, stabilisation time


The paper deals with the queueing system for customers with Poisson’s input current intensity l and two service modes: in the regular service regime of intensity control m, customers are served with probability p»1 and in the special regime of servicing the special customers with intensity x. The special customers access the REQS with complementary probability (1-p)»0. The special customer service is analogous to a rare event. The standard methodology has developed analytical patterns for the stationary of REQS with one service channel and an infinite number of positions in the queue. The analysis of the work of REQS indicates that it is for favorable metering parameters r=l/m>2, queueing system is resistant to collapse when a occurrence occurs. However, the regular time losses of the regular customers in the REQS are extremely high. For this reason, it is the first time that the period of stabilization of the system is promoted which represents the time interval service the completion of the special customers until the REQS. The analytical apparatus of the queueing system has shown excellent adaptability to the heterogeneous demands of services m and special customers with low service intensity x, where m>x. The system can be applied to checkpoint calculations, the traffic cuts due to accidents, incidents to industrial systems, ie, the rare events due to anthropogenic and technical factors in intervals of 10-4 do 10-6. The model is not intended for natural hazards.


Agarwal, A., De Marco, S., Gobet, E., Liu, G. (2018). Study of new rare event simulation schemes and their application to extreme scenario generation. Mathematics and Computers in Simulation, 143, 89–98.
Bogdanović, V., Ruskić, N., Kuzović, M., Han, L. (2013). Toward a capacity analysis procedure for nonstandard two-way stop-controlled intersections, Transportation research record, 2395, 132138.
Cornell, C. A. (1968). Engineering seismic risk analysis. Bulletin of the Seismological Society of America, 58, 1583–1606.
Der Kiureghian, A, Liu, P. L. (1986). Structural reliability under incomplete probability information. Journal of Engineering Mechanics, 112, 85–104.
Garnier, J., Moral, P. D. (2006). Simulations of rare events in fiber optics by interacting particle systems, Optics Communinacions, 267, 205–214.
Jacquemart, D., Morio, J. (2016). Tuning of adaptive interacting particle system for rare event probability estimation. Simulation Modelling Practice and Theory, 66, 3649.
Morio, J., Balesdent, M., Jacquemart, D., Vergé, C. (2014). A survey of rare event simulation methods for static input–output models. Simulation Modelling Practice and Theory, 49, 287–304.
Paté-Cornell, M. E. (1994). Quantitative safety goals for risk management of industrial facilities. Structural Safety. 13, 145–157.
R. Zweimuller, Hitting-time limits for some exceptional rare events of ergodic maps, Stochastic Processes and their Applications (2018), https://doi.org/10.1016/j.spa.2018.05.011.
Ruijters, E., Reijsbergen, D., de Boer, P. T., Stoelinga, M. (2019). Rare event simulation for dynamic fault trees. Reliability Engineering and System Safety, 186, 220–231.
Siu-Kui Au, S. K., Patelli, E. (2016). Rare event simulation in finite-infinite dimensional space. Reliability Engineering and System Safety, 148, 67–77.
Tanackov, I., Dragić, D., Sremac, S., Bogdanović, V., Matić, B., Milojević, M. (2019). New analytic solutions of queueing system for shared-short lanes at unsignalized intersections, Symmetry, 11, 55.
Yang, M., Khana, F., Lye, L., Amyotte, P. (2015). Risk assessment of rare events. Process Safety and Environmental Protection 98, 102–108.
How to Cite
Tanackov, I., Jevtić, Žarko, Stojić, G., Sinani, F., & Ercegovac, P. (2019). Rare Events Queueing System - REQS. Operational Research in Engineering Sciences: Theory and Applications, 2(2), 1-11. Retrieved from http://www.oresta.org/index.php/oresta/article/view/20