Complutense University Library

On the busy period of the M/G/1 retrial queue

Artalejo, Jesús R. and Lopez-Herrero, M. J. (2000) On the busy period of the M/G/1 retrial queue. Naval Research Logistics (NRL), 47 (2). pp. 115-127. ISSN 0894-069X

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

153kB

Official URL: http://onlinelibrary.wiley.com/doi/10.1002/%28SICI%291520-6750%28200003%2947:2%3C115::AID-NAV3%3E3.0.CO;2-C/abstract

View download statistics for this eprint

==>>> Export to other formats

Abstract

The M/G/1 queue with repeated attempts is considered. A customer who finds the server busy, leaves the service area and joins a pool of unsatisfied customers. Each customer in the pool repeats his demand after a random amount of time until he finds the server free. We focus on the busy period L of the M/G/1$ retrial queue. The structure of the busy period and its analysis in terms of Laplace transforms have been discussed by several authors. However, this solution has serious limitations in practice. For instance, we cannot compute the first moments of L by direct differentiation. This paper complements the existing work and provides a direct method of calculation for the second moment of L.


Item Type:Article
Additional Information:

This research was supported by the European Commission under INTAS Grant no. 96-0828, the Complutense University under Grant no. PR64/99-8501 and the DGICYT under Grant no.
PB98-0837. The authors thank the referee for his/her helpful comments on an earlier version of this paper.

Subjects:Sciences > Mathematics > Operations research
ID Code:15866
References:

J.R. Artalejo and G.I. Falin, On the orbit characteristics of the M/G/1 retrial queue, Nav Res Logistics 43 (1996), 1147–1161.

J.R. Artalejo, Accessible bibliography on retrial queues, Math Comput Model 30 (1999), 1–6.

Q.H. Choo and B. Conolly, New results in the theory of repeated orders queueing systems, J Appl Probab 16 (1979), 631–640.

G.I. Falin, A single-line system with secondary orders, Eng Cybernet Rev 17 (1979), 76–83.

G.I. Falin, A survey of retrial queues, Queue Syst 7 (1990), 127–167.

G.I. Falin, M. Martin, and J.R. Artalejo, Information theoretic approximations for the M/G/1 retrial queue, Acta Inf 31 (1994), 559–571.

G.I. Falin and J.G.C. Templeton, Retrial queues, Chapman and Hall, London, 1997.

D.D. Kouvatsos, Entropy maximization and queueing network models, Ann Oper Res 48 (1994), 63–126.

W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical recipes in Fortran. The art of scientific computing, Cambridge University Press, Cambridge, 1992.

Deposited On:09 Jul 2012 09:25
Last Modified:06 Feb 2014 10:33

Repository Staff Only: item control page