zbMATH — the first resource for mathematics

Retrial queueing system of \(MMPP/M/2\) type with impatient calls in the orbit. (English) Zbl 1452.60077
Dudin, Alexander (ed.) et al., Information technologies and mathematical modelling. Queueing theory and applications. 17th international conference, ITMM 2018, named after A.F. Terpugov, and 12th workshop on retrial queues and related topics, WRQ 2018, Tomsk, Russia, September 10–15, 2018. Selected papers. Cham: Springer. Commun. Comput. Inf. Sci. 912, 387-399 (2018).
Summary: In the paper, the retrial queueing system of \(MMPP/M/2\) type with input MMPP-flow of events and impatient calls is considered. The delay time of calls in the orbit, the calls service time and the impatience time of calls in the orbit have exponential distribution. Asymptotic analysis method is proposed for the solving problem of finding distribution of the number of calls in the orbit under a system heavy load and long time patience of calls in the orbit condition. The theorem about the Gauss form of the asymptotic probability distribution of the number of calls in the orbit is formulated and proved. Numerical illustrations, results are also given.
For the entire collection see [Zbl 1403.60002].

60K25 Queueing theory (aspects of probability theory)
Full Text: DOI
[1] Wilkinson, R.I.: Theories for toll traffic engineering in the USA. Bell Syst. Tech. J. 35(2), 421-507 (1956)
[2] Cohen, J.W.: Basic problems of telephone traffic and the influence of repeated calls. Philips Telecommun. Rev. 18(2), 49-100 (1957)
[3] Gosztony, G.: Repeated call attempts and their effect on traffic engineering. Budavox Telecommun. Rev. 2, 16-26 (1976)
[4] Elldin, A., Lind, G.: Elementary Telephone Traffic Theory. Ericsson Public Telecommunications, Stockholm (1971)
[5] Artalejo, J.R., Gomez-Corral, A.: Retrial Queueing Systems. A Computational Approach. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78725-9 · Zbl 1161.60033
[6] Falin, G.I., Templeton, J.G.C.: Retrial Queues. Chapman & Hall, London (1997) · Zbl 0944.60005
[7] Artalejo, J.R., Falin, G.I.: Standard and retrial queueing systems: a comparative analysis. Rev. Mat. Complut. 15, 101-129 (2002) · Zbl 1009.60079
[8] Roszik, J., Sztrik, J., Kim, C.: Retrial queues in the performance modelling of cellular mobile networks using MOSEL. Int. J. Simul. 6, 38-47 (2005)
[9] Aguir, S., Karaesmen, F., Askin, O.Z., Chauvet, F.: The impact of retrials on call center performance. OR Spektrum 26, 353-376 (2004) · Zbl 1109.90019
[10] Nazarov, A., Sztrik, J., Kvach, A.: Comparative analysis of methods of residual and elapsed service time in the study of the closed retrial queuing system M/GI/1//N with collision of the customers and unreliable server. In: Dudin, A., Nazarov, A., Kirpichnikov, A. (eds.) ITMM 2017. CCIS, vol. 800, pp. 97-110. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-68069-9_8 · Zbl 1397.90128
[11] Dudin, A., Deepak, T.G., Joshua, V.C., Krishnamoorthy, A., Vishnevsky, V.: On a BMAP/G/1 retrial system with two types of search of customers from the orbit. In: Dudin, A., Nazarov, A., Kirpichnikov, A. (eds.) ITMM 2017. CCIS, vol. 800, pp. 1-12. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-68069-9_1 · Zbl 1397.90111
[12] Dudin, A.N., Klimenok, V.I.: Queueing system BMAP/G/1 with repeated calls. Math. Comput. Model. 30(3-4), 115-128 (1999) · Zbl 1042.60535
[13] Yang, T., Posner, M., Templeton, J.: The M/G/1 retrial queue with non-persistent customers. Queueing Syst. 7(2), 209-218 (1990) · Zbl 0745.60101
[14] Krishnamoorthy, A., Deepak, T.G., Joshua, V.C.: An M/G/1 retrial queue with non-persistent customers and orbital search. Stoch. Anal. Appl. 23, 975-997 (2005) · Zbl 1075.60577
[15] Kim, J.: Retrial queueing system with collision and impatience. Commun. Korean Math. Soc. 4, 647-653 (2010) · Zbl 1210.60102
[16] Martin, M., Artalejo, J.: Analysis of an M/G/1 queue with two types of impatient units. Adv. Appl. Probab. 27, 647-653 (1995) · Zbl 0829.60085
[17] Kumar, M., Arumuganathan, R.: Performance analysis of single server retrial queue with general retrial time, impatient subscribers, two phases of service and Bernoulli schedule. Tamkang J. Sci. Eng. 13(2), 135-143 (2010)
[18] Fedorova, E., Voytikov, K.: Retrial queue M/G/1 with impatient calls under heavy load condition. In: Dudin, A., Nazarov, A., Kirpichnikov, A. (eds.) ITMM 2017. CCIS, vol. 800, pp. 347-357. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-68069-9_28 · Zbl 1397.90113
[19] Bérczes, T., Sztrik, J., Tóth, Á., Nazarov, A.: Performance modeling of finite-source retrial queueing systems with collisions and non-reliable server using MOSEL. In: Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (eds.) DCCN 2017. CCIS, vol. 700, pp. 248-258. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66836-9_21 · Zbl 07229324
[20] Artalejo, J.R., Pozo, M.: Numerical calculation of the stationary distribution of the main multiserver retrial queue. Ann. Oper. Res. 116, 41-56 (2002) · Zbl 1013.90038
[21] Neuts, M.F., Rao, B.M.: Numerical investigation of a multiserver retrial model. Queueing Syst. 7(2), 169-189 (1990) · Zbl 0711.60094
[22] Klimenok, V.I., Orlovsky, D.S., Dudin, A.N.: BMAP/PH/N system with impatient repeated calls. Asia Pac. J. Oper. Res. 24(3), 293-312 (2007) · Zbl 1141.90360
[23] Kim, C.S., Klimenok, V., Dudin, A.: Retrial queueing system with correlated input, finite buffer, and impatient customers. In: Dudin, A., De Turck, K. (eds.) ASMTA 2013. LNCS, vol. 7984, pp. 262-276. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39408-9_19 · Zbl 1395.90116
[24] Dudin, A., Klimenok, V.: Retrial queue of BMAP/PH/N type with customers balking, impatience and non-persistence. In: 2013 Conference on Future Internet Communications (CFIC), pp. 1-6. IEEE (2013)
[25] Fedorova, E.: The second order asymptotic analysis under heavy load condition for retrial queueing system MMPP/M/1. In: Dudin, A., Nazarov, A., Yakupov, R. (eds.) ITMM 2015. CCIS, vol. 564, pp. 344-357. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-25861-4_29
[26] Borovkov, A.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.