##
**Single line queue with repeated demands.**
*(English)*
Zbl 0712.60100

The authors deal with a single server system with Poisson demand and general service time in which, if the server is free at the instant of an arrival, service commences immediately. Otherwise, the unsatisfied customer enters the orbit and can seek service at subsequent epochs, until he finds the server free and then enters service.

Three types of orbit discipline are considered, in each of which the times between arrival of repeat requests turns out to be exponentially distributed. Steady state operating characteristics such as average orbit size and average waiting time are calculated.

Three types of orbit discipline are considered, in each of which the times between arrival of repeat requests turns out to be exponentially distributed. Steady state operating characteristics such as average orbit size and average waiting time are calculated.

Reviewer: S.Kalpakam

### MSC:

60K25 | Queueing theory (aspects of probability theory) |

90B22 | Queues and service in operations research |

### Keywords:

generating function; orbit discipline; Steady state operating characteristics; average waiting time
Full Text:
DOI

### References:

[1] | C. Clos, An aspect of the dialing behaviour of subscribers and its effect on the trunk plant, Bell Syst. Tech. J. 27 (1948) 424–445. |

[2] | J.W. Cohen, On the fundamental problems of telephone traffic theory and the influence of repeated calls, Philips Telecomm. Rep. 18 (1957) 49–100. |

[3] | B.W. Conolly, Generalized state-dependent Erlangian queues: Speculations about calculating measures of effectiveness, J. Appl. Prob. 12 (1975) 358–363. · Zbl 0304.60051 |

[4] | G.I. Falin, On the waiting-time process in a single line queue with repeated calls, J. Appl. Prob. 23 (1986) 185–192. · Zbl 0589.60077 |

[5] | J. Keilson, J. Cozzolino and H. Young, A service system with unfilled requests repeated, Oper. Res. 16 (1968) 1126–1132. · Zbl 0165.52703 |

[6] | J. Keilson and A. Kooharian, On time dependent queueing processes, Ann. Math. Stat. 31 (1960) 104–112. · Zbl 0091.30302 |

[7] | J.D.C. Little, A proof for the queueing formulaL={\(\lambda\)}W, Oper. Res. 9 (1961) 383–387. · Zbl 0108.14803 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.