Artalejo, Jesús R. and Gómez Corral, Antonio
(1997)
*Steady state solution of a single-server queue with linear repeated requests.*
Journal of Applied Probability , 34
(1).
pp. 223-233.
ISSN 0021-9002

PDF
Restringido a Repository staff only hasta 2020. 826kB |

Official URL: http://www.jstor.org/stable/3215189 .

## Abstract

Queueing systems with repeated requests have many useful applications in communications and computer systems modeling. In the majority of previous work the repeat requests are made individually by each unsatisfied customer. However, there is in the literature another type of queueing situation, in which the time between two successive repeated attempts is independent of the number of customers applying for service. This paper deals with the M/G/1 queue with repeated orders in its most general setting, allowing the simultaneous presence of both types of repeat requests. We first study the steady state distribution and the partial generating functions. When the service time distribution is exponential we show that the performance characteristics can be expressed in terms of hypergeometric functions.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Queues with repeated requests; hypergeometric functions |

Subjects: | Sciences > Mathematics > Stochastic processes |

ID Code: | 15889 |

References: | ABRAMOWITZ, M. AND STEGUN, I.A. (1972) Handbook of Mathematical Functions. Dover, New York. ARTALEJO, J.R. (1993) Explicit formulae for the characteristics of the M/H2/1 retrial queue. J Operat. Res. Soc. 44, 309-313. ARTALEJO, J.R. AND FALIN,G.I. (1994) Stochastic decomposition for retrial queues. Top 2, 329-342. BAILEYW, N. (1972) Generalized Hypergeometric Series. Hafner, New York. COOPER, R.B. (1981) Introduction to Queueing Theory. Elsevier, Amsterdam. FALIN, G.I. (1980) An M/M/1 queue with repeated calls in the presence of persistence function. Paper #1606-80. All-Union Institute for Scientific and Technical Information, Moscow. FALIN, G.I. (1984) Double-channel queueing system with repeated calls. Paper #4221-84. All-Union Institute for Scientific and Technical Information, Moscow. FALIN, G.I. (1990) A survey of retrial queues. QUESTA 7, 127-168. FARAHMAND, K. (1990) Single line queue with repeated demands. QUESTA 6, 223-228. FAYOLLE, G. (1986) A simple telephone exchange with delayed feedbacks. In Teletraffic Analysis and Computer Performance Evaluation. ed. O.J. Boxma, J. W. Cohen and H. C. Tijms. Elsevier, Amsterdam. FUHRMANNS, W. AND COOPER, R.B. (1985) Stochastic decomposition in the M/G/1 queue with generalized vacations. Operat. Res. 33, 1117-1129. HANSCHKE, T. (1987) Explicit formulas for the characteristics of the M/M/2/2 queue with repeated attempts. J Appl. Prob. 24, 486-494. JONIN, G.L. AND SEDOLJ, J. (1970) Telephone systems with repeated calls. Proc. 6th Int. Teletraffic Congress 435/1-435/5. MARTIN, M. AND ARTALEJO, J. R. (1995) Analysis of an M/G/1 queue with two types of impatient units. Adv. Appl. Prob. 27, 840-861. PEARCE, C. (1989) Extended continued fractions, recurrence relations and two-dimensional Markov processes. Adv. Appl. Prob. 21, 357-375. SENNOTT L.I., HUMBLET, P.A. AND TWEEDIE, R.L. (1983) Mean drifts and the non-ergodicity of Markov chains. Operat. Res. 31, 783-789. YANG,T. AND TEMPLETON, J.G.C. (1987) A survey on retrial queues. QUESTA 2, 201-233. |

Deposited On: | 10 Jul 2012 11:43 |

Last Modified: | 10 Jul 2012 11:43 |

Repository Staff Only: item control page