A retrial queue with redundancy and unreliable server

Retrial queues are useful in the stochastic modelling of computer and telecommunication systems amongst others. In this paper we study a version of the retrial queue with variable service. Such a point of view gives another look at the unreliable retrial queueing problem which includes the redundancy model.By using the theory of piecewise Markovian processes, we obtain the analogue of the Pollaczek-Khintchine formula for such retrial queues, which is useful for operations researchers to obtain performance measures of interest.

[1]  Betsy S. Greenberg.  M/G/1 queueing systems with returning customers , 1989 .

[2]  Awtonín Lešanovský,et al.  Stochastical ordering in a two-unit standby redundant system with three states of units , 1984 .

[3]  Marvin Zelen,et al.  Mathematical Theory of Reliability , 1965 .

[4]  Kailash C. Madan,et al.  A single channel queue with bulk service subject to interruptions , 1989 .

[5]  R. Subramanian,et al.  Probabilistic analysis of redundant systems , 1980 .

[6]  Gennadi Falin.  Aggregate arrival of customers in a one-line system with repeated calls , 1976 .

[7]  James G. C. Templeton.  Editorial Introduction: Special Issue on Retrial Queues. , 1990 .

[8]  Thomas E. Phipps.  Machine Repair as a Priority Waiting-Line Problem , 1956 .

[9]  K. Murari,et al.  Cost analysis of a two-unit warm standby reliability system with two types of repair facilities , 1985 .

[10]  Peter Franken,et al.  Reliability Analysis of Complex Systems with Repair , 1984, J. Inf. Process. Cybern..

[11]  V. S. Srinivasan.  A Standby Redundant Model with Noninstantaneous Switchover , 1968 .

[12]  C Brindle,et al.  RELIABILITY AND MAINTENANCE OF SHIP MACHINERY , 1983 .

[13]  R. Natarajan,et al.  A two-unit redundant system with different types of failure and “imperfect” repair , 1990 .

[14]  Julian Keilson,et al.  A Service System with Unfilled Requests Repeated , 1968, Oper. Res..

[15]  Ashok Kumar,et al.  A Review of Standby Redundant Systems , 1980, IEEE Transactions on Reliability.

[16]  I. S. Mikadze.  A queueing system with an unreliable server and periodic checking , 1988 .

[17]  Amar Aissani,et al.  Unreliable queuing with repeated orders , 1993 .

[18]  Frank Kelly,et al.  On Auto-repeat Facilities and Telephone Network Performance , 1986 .

[19]  Brian Conolly,et al.  New results in the theory of repeated orders queueing systems , 1979 .

[20]  S. N. Rayapati,et al.  Human error modelling of parallel and standby redundant systems , 1988 .

[21]  Ludo Gelders,et al.  Reliability and maintenance , 1988 .

[22]  L. R. Goel,et al.  Stochastic analysis of a two unit warm standby system with fault detection and inspection , 1990 .

[23]  Tao Yang,et al.  A survey on retrial queues , 1987, Queueing Syst. Theory Appl..

[24]  G. S. Mokaddis,et al.  Two models for two unit warm standby redundant system with two different kinds of repair and tolerable time , 1990 .

[25]  Henry C. Co,et al.  Age-maintenance of an M/G/l production system , 1991 .

[26]  Maxim Finkelstein.  Some notes on wear-dependent systems , 1993 .

[27]  Charles S. Tapiero,et al.  Maintenance of an unreliable M/G/1 queue-like job shop , 1987, Queueing Syst. Theory Appl..

[28]  Boris Gnedenko,et al.  Introduction to queueing theory , 1968 .