Abstract
The paper analyzes a queuing system where customers are accepted for service either at the time of arrival (if the server if idle) or at the times that differ from it by intervals multiple of cycle time T. Formulas are derived to find the number of customers in the system, waiting time, and the existence condition for ergodic distribution.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
L. Lakatos, “On a simple continuous cyclic-waiting problem,” Annales Univ. Sci. Budapest. Sect. Comp., 14, 105–113 (1994).
L. Lakatos, “On a cyclic-waiting queueing system,” Theory of Stochastic Processes, 2 (18), 176–180 (1996).
L. Lakatos, “On a simple discrete cyclic-waiting queueing problem,” J. Math. Sci. (New York), 92 (4), 4031–4034 (1998).
L. Lakatos, “A retrial system with time-limited tasks,” Theory of Stochastic Processes, 8 (24), 250–256 (2002).
L. Lakatos, “A retrial queueing system with urgent customers,” J. Math. Sci., 138 (1), 5405–5409 (2006).
E. V. Koba, “On a GI/G/1 retrial queue with FCFS service discipline,” Dop. NANU, 6, 101–103 (2000).
E. V. Koba and K. V. Mikhalevich, “Comparing M/G/1 retrial queues with fast return from the orbit,” in: Queues: Flows, Systems, Networks, Proc. Int. Conf. “Modern Math. Methods of Telecommunication Networks,” [in Russian], Gomel, BGU, Minsk, 23–25 September (2003), pp. 136–138.
K. V. Mykhalevych, “A comparison of a classical retrial M/G/1 queueing system and a Lakatos-type M/G/1 cyclic-waiting time queueing system,” Annales Univ. Sci. Budapest. Sect. Comp., 23, 229–238 (2004).
P. Kárász, “Special retrial systems with requests of two types,” Theory of Stochastic Processes, 10 (26), 51–56 (2004).
P. Kárász, “A special discrete cyclic-waiting queuing system,” Central European J. Oper. Res., 16 (4), 391–406 (2008).
I. N. Kovalenko, “Loss probability in a T-retrial queue M/G/m under light traffic,” Dop. NANU, 5, 77–80 (2002).
I. N. Kovalenko and E. V. Koba, “Three retrial queuing systems representing some special features of aircraft landing,” J. Autom. Inform. Sci., 34, Issue 4 (2002).
K. Laevens, B. Van Houdt, C. Blondia, and H. Bruneel, “On the sustainable load of fiber delay line buffers,” Electronic Letters, 40, 137–138 (2004).
W. Rogiest, K. Laevens, D. Fiems, and H. Bruneel, “Analysis of a Lakatos-type queueing system with general service times,” in: Proc. ORBEL 20, Quantitative Methods for Decision Making, Ghent, January 19–20 (2006), pp. 95–97.
W. Rogiest, K. Laevens, J. Walraevens, and H. Bruneel, “Analyzing a degenerate buffer with general inter-arrival and service times in discrete time,” Queueing Systems, 56, 203–212 (2007).
Author information
Authors and Affiliations
Corresponding author
Additional information
The study was supported by the Hungarian Scientific Research Fund (OTKA Grant K60698/2005) and the Hungarian-Ukrainian intergovernmental cooperation in science and technology (Grant UA-28/2008).
Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 144–151, May–June 2010.
Rights and permissions
About this article
Cite this article
Lakatos, L. Cyclic-waiting systems. Cybern Syst Anal 46, 477–484 (2010). https://doi.org/10.1007/s10559-010-9222-1
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10559-010-9222-1