Complutense University Library

Analysis of Markov multiserver retrial queues with negative arrivals

Artalejo, Jesús R. and Anisimov , Vladimir V. (2001) Analysis of Markov multiserver retrial queues with negative arrivals. Queueing Systems, 39 (2-3). pp. 157-182. ISSN 0257-0130

[img] PDF
Restricted to Repository staff only until 31 December 2020.

191kB

Official URL: http://www.springerlink.com/content/m4250164066w9w25/

View download statistics for this eprint

==>>> Export to other formats

Abstract

Negative arrivals are used as a control mechanism in many telecommunication and computer networks. In the paper we analyze multiserver retrial queues; i.e., any customer finding all servers busy upon arrival must leave the service area and re-apply for service after some random time. The control mechanism is such that, whenever the service facility is full occupied, an exponential timer is activated. If the timer expires and the service facility remains full, then a random batch of customers, which are stored at the retrial pool, are automatically removed. This model extends the existing literature, which only deals
with a single server case and individual removals. Two different approaches are considered. For the stable case, the matrix–analytic formalism is used to study the joint distribution of the service facility and the retrial pool. The approximation by more simple infinite retrial model is also proved. In the overloading case we study the transient behaviour of the trajectory of the suitably normalized retrial queue and the long-run behaviour of the number of busy servers. The method of investigation in this case is based on the averaging principle for switching processes.

Item Type:Article
Additional Information:This research was supported in part by DGES98-0837 and the European Commission through INTAS Project 96-0828
Uncontrolled Keywords:Retrial queueing systems, Negative arrivals, Averaging principle, Matrix–analytic methods, Switching process
Subjects:Sciences > Mathematics > Operations research
ID Code:15838
References:

V.V. Anisimov, Switching processes, Cybernetics 13(4) (1977) 590–595.

V.V. Anisimov, Averaging principle for switching recurrent sequences, Theory Probab. Math. Statist. 45 (1992) 1–8.

V.V. Anisimov, Averaging principle for switching processes, Theory Probab. Math. Statist. 46 (1993) 1–10.

V.V. Anisimov, Switching processes: averaging principle, diffusion approximation and applications, Acta Appl. Math. 40 (1995) 95–141.

V.V. Anisimov, Diffusion approximation for processes with semi-Markov switches and applications in queueing models, in: Semi-Markov Models and Applications, eds. J. Janssen and N. Limnios (Kluwer, Dordrecht, 1999) pp. 77–101.

V.V. Anisimov, Averaging methods for transient regimes in overloading retrial queuing systems, Math. Comput. Modelling 30(3/4) (1999) 65–78.

V.V. Anisimov, Switching stochastic models and applications in retrial queues, Top 7(2) (1999) 169–186.

J.R. Artalejo, A classified bibliography of research on retrial queues: Progress in 1990–1999, Top 7(2) (1999) 187–211.

J.R. Artalejo, G-networks: a versatile approach for work removal in queueing networks, European J. Oper. Res. 126 (2000) 233–249.

J.R. Artalejo and A. Gomez-Corral, Stochastic analysis of the departure and quasi-input processes in a versatile single-server queue, J. Appl. Math. Stochastic Anal. 9 (1996) 171–183.

J.R. Artalejo and A. Gomez-Corral, Steady state solution of a single-server queue with linear repeated requests, J. Appl. Probab. 34 (1997) 223–233.

J.R. Artalejo and A. Gomez-Corral, Generalized birth and death processes with applications to queues with repeated attempts and negative arrivals, OR Spektrum 20 (1998) 5–14.

J.R. Artalejo and A. Gomez-Corral, On a single server queue with negative arrivals and request repeated, J. Appl. Probab. 36 (1999) 907–918.

X. Chao, M. Miyazawa and M. Pinedo, Queueing Networks: Customers, Signals and Product Form Solutions (Wiley, Chichester, 1999).

B.D. Choi, Y. Chang and B. Kim, MAP1/MAP2/M/c retrial queue with guard channels and its applications to cellular networks, Top 7 (1999) 231–248.

J.E. Diamond and A.S. Alfa, Matrix analytical methods for multi-server retrial queues with buffers, Top 7 (1999) 249–266.

A.N. Dudin and V.I. Klimenok, A retrial BMAP/SM/1 system with linear requests, Queueing Systems 34 (2000) 47–66.

S.N. Ethier and T.G. Kurtz, Markov Processes, Characterization and Convergence (Wiley, New York, 1986).

G.I. Falin and J.G.C. Templeton, Retrial Queues (Chapman and Hall, London, 1997).

E. Gelenbe and G. Pujolle, Introduction to Queueing Networks (Wiley, Chichester, 1998).

N. Grier,W.A. Massey, T. McKoy and W. Whitt, The time-dependent Erlang loss model with retrials, Telecommunication Systems 7 (1997) 253–265.

J. Jacod and A.N. Shiryaev, Limit Theorems for Stochastic Processes (Springer, Berlin, 1987).

G. Latouche and V. Ramaswani, Introduction to Matrix Analytic Methods in Stochastic Modeling (ASA–SIAM, Philadelphia, 1999).

M.F. Neuts, Matrix-Geometric Solutions in Stochastic Models – An Algorithmic Approach (Johns Hopkins Univ. Press, Baltimore, MD, 1981).

M.F. Neuts and B.M. Rao, Numerical investigation of a multiserver retrial model, Queueing Systems 7 (1990) 169–190.

R. Serfozo, Introduction to Stochastic Networks (Springer, New York, 1999).

Deposited On:05 Jul 2012 09:50
Last Modified:06 Feb 2014 10:32

Repository Staff Only: item control page