Artalejo, Jesús R. and Martín Apaolaza, Níriam (2005) On the time to reach a certain orbit level in multi-server retrial queues. Applied Mathematics and Computation, 168 (1). pp. 686-703. ISSN 0096-3003
Restricted to Repository staff only until 31 December 2020.
Multi-server retrial queues are widely used to model stochastically many telephone systems and computer networks. This paper studies the distribution of the time needed to reach a certain level of congestion, i.e., a given number of customers in the retrial group. We present a detailed algorithmic analysis which includes the computation of the time to reach a critical number of customers (continuous descriptor), the number of customers served during such a time (discrete descriptor) and the corresponding moments for both queueing performance measures
The authors thank the support received from the research project BFM2002-02189. N.M. Apaolaza was supported by a grant (‘Formación de Investigadores’) awarded by the Basque Government.
|Uncontrolled Keywords:||Multi-server retrial queue; First passage time; Number of customers served; Moments; Numerical inversion|
|Subjects:||Sciences > Mathematics > Operations research|
J.R. Artalejo, Accessible bibliography on retrial queues, Mathematical and Computer Modelling 30 (1999) 1–6.
J.R. Artalejo, A classified bibliography of research on retrial queues: progress in 1990–1999, Top 7 (1999) 187–211.
J.R. Artalejo, G.I. Falin, On the orbit characteristics of the M/G/1 retrial queue, Naval Research Logistics 43 (1996) 1147–1161.
J.R. Artalejo, M.J. Lopez-Herrero, On the busy period of the M/G/1 retrial queue, Naval Research Logistics 47 (2000) 115–127.
J.R. Artalejo, M. Pozo, Numerical calculation of the stationary distribution of the main multiserver retrial queue, Annals of Operations Research 116 (2002) 41–56.
G. Choudhury, K.C. Madan, A two phase batch arrival queueing system with a vacation time under Bernoulli schedule, Applied Mathematics and Computation 149 (2004) 337–349.
P.G. Ciarlet, Introduction to Numerical Linear Algebra and Optimization, Cambridge University Press, Cambridge, 1989.
G.I. Falin, J.G.C. Templeton, Retrial Queues, Chapman and Hall, London, 1997.
D.P. Gaver, P.A. Jacobs, G. Latouche, Finite birth-and-death models in randomly changing environments, Advances in Applied Probability 16 (1984) 715–731.
G. Latouche, V. Ramaswami, Introduction to Matrix Analytic Methods in Stochastic Modeling, ASA-SIAM Series on Statistics and Applied Probability, Philadelphia, 1999.
E.A. Lebedev, On the first passage time of removing level for retrial queues, Reports of the National Academy of Sciences of Ukraine No. 3, 2002, pp. 47–50.
M.S. Mostafa, K.M.F. El-Sayed, Matrix-geometric solution of a multiserver queue with Markovian group arrival and Coxian servers, Applied Mathematics and Computation 49 (1992) 177–196.
W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in Fortran. The Art of Scientific Computing, Cambridge University Press, Cambridge, 1992.
M.A. Remiche, Time to congestion in homogeneous quasi-birth-and-death processes, Opsearch 35 (1998) 169–192.
L. Tadj, A matrix analytic solution to a hysteretic queueing system with random server capacity, Applied Mathematics and Computation 119 (2001) 161–175.
|Deposited On:||15 Jun 2012 08:03|
|Last Modified:||06 Feb 2014 10:29|
Repository Staff Only: item control page