RT Journal Article
T1 Algorithmic approximations for the busy period distribution of the M/M/c retrial queue
A1 Artalejo Rodríguez, Jesús Manuel
A1 Economou, A.
A1 López Herrero, María Jesús
AB In this paper we deal with the main multiserver retrialqueue of M/M/c type with exponential repeated attempts. This model is known to be analytically intractable due to the spatial heterogeneity of the underlying Markov chain, caused by the retrial feature. For this reason several models have been proposed for approximating its stationary distribution, that lead to satisfactory numerical implementations. This paper extends these studies by developing efficient algorithmic procedures for calculating the busyperioddistribution of the main approximation models of Wilkinson [Wilkinson, R.I., 1956. Theories for toll traffic engineering in the USA, The Bell System Technical Journal 35, 421–514], Falin [Falin, G.I., 1983. Calculations of probability characteristics of a multiline system with repeated calls, Moscow University Computational Mathematics and Cybernetics 1, 43–49] and Neuts and Rao [Neuts, M.F., Rao, B.M., 1990. Numerical investigation of a multiserver retrial model, Queueing Systems 7, 169–190]. Moreover, we develop stable recursive schemes for the computation of the busyperiod moments. The corresponding distributions for the total number of customers served during a busyperiod are also studied. Several numerical results illustrate the efficiency of the methods and reveal interesting facts concerning the behavior of the M/M/cretrialqueue.
PB Elsevier Science
SN 0377-2217
YR 2007
FD 2007-02-01
LK https://hdl.handle.net/20.500.14352/49973
UL https://hdl.handle.net/20.500.14352/49973
LA eng
NO The authors thank the support received from the research project MTM2005-01248. A. Economou was supported by the University of Athens grant ELKE/70/4/6415 and by the Greek Ministry of Education and European Union program PYTHAGORAS/2004.
NO University of Athens
NO Greek Ministry of Education
NO European Union program PYTHAGORAS/2004
DS Docta Complutense
RD 9 abr 2025