Heterogeneous Finite-Source Retrial Queues with Server Subject to Breakdowns and Repairs

This paper deals with a retrial queueing system with a finite number of heterogeneous sources of calls and a single non-reliable server, which means that the server is subject to random breakdowns depending on whether it is busy or idle. The failure of the server may block or unblock the system’s operations and the service of the interrupted request may be resumed or the call can be transmitted to the orbit. All random variables involved in the model constructions are supposed to be exponentially distributed and independent of each other. The novelty of the investigation is the heterogeneous sources and the variability of this non-reliablility of the server which makes the system rather complicated. The MOSEL tool was used to formulate and solve the problem and the main performance and reliability measures were derived and graphically displayed. Several numerical calculations were performed to show the effect of the non-reliability of the server on the mean response times of the calls and the mean number of requests staying at the service facility.

[1]  Quanlin Li,et al.  Reliability Analysis of the Retrial Queue with Server Breakdowns and Repairs , 2001, Queueing Syst. Theory Appl..

[2]  Terry Williams,et al.  Probability and Statistics with Reliability, Queueing and Computer Science Applications , 1983 .

[3]  J. Templeton.  Retrial queues , 1999 .

[4]  János Sztrik,et al.  Homogeneous finite-source retrial queues with server subject to breakdowns and repairs , 2005, Math. Comput. Model..

[5]  Hideaki Takagi,et al.  Queueing analysis: a foundation of performance evaluation , 1993 .

[6]  Ahmed K. Elhakeem,et al.  Traffic analysis of a local area network with a star topology , 1988, IEEE Trans. Commun..

[7]  Gennadi Falin,et al.  A multiserver retrial queue with a finite number of sources of primary calls , 1999 .

[8]  János Sztrik,et al.  On the heterogeneous machine interference with limited server's availability , 1987 .

[9]  Vidyadhar G. Kulkarni,et al.  Retrial queues with server subject to breakdowns and repairs , 1990, Queueing Syst. Theory Appl..

[10]  Jesús R. Artalejo,et al.  Information theoretic analysis for queueing systems with quasi-random input , 1995 .

[11]  Bela Almasi,et al.  Comparing two queueing models for nonhomogeneous nonreliable terminal systems , 1995 .

[12]  Jesus R. Artalejo,et al.  A finite source retrial queue , 1998, Eur. J. Oper. Res..

[13]  Gennadi Falin,et al.  A survey of retrial queues , 1990, Queueing Syst. Theory Appl..

[14]  Jesús R. Artalejo,et al.  New results in retrial queueing systems with breakdown of the servers , 1994 .

[15]  Antonio Gómez-Corral,et al.  On a bivariate Markov process arising in the theory of single‐server retrial queues , 2000 .

[16]  Jesus R. Artalejo,et al.  On the single server retrial queue subject to breakdowns , 1998, Queueing Syst. Theory Appl..

[17]  Wai Sum Lai,et al.  Traffic Modeling and Analysis of Hybrid Fiber-Coax Systems , 1998, Comput. Networks.

[18]  Gunter Bolch,et al.  Practical Performance Modeling , 2001 .

[19]  Jesús R. Artalejo,et al.  RETRIAL QUEUES WITH A FINITE NUMBER OF SOURCES , 1998 .

[20]  Yoshitaka Takahashi,et al.  An analysis of repeated call model with a finite number of sources , 1985 .

[21]  Antonio Gómez-Corral.  Analysis of a single-server retrial queue with quasi-random input and nonpreemptive priority☆ , 2002 .

[22]  A. I. Kalmychkov,et al.  Probability characteristics of Markov local-area networks with random-access protocols , 1991 .

[23]  Jesús R. Artalejo,et al.  Accessible bibliography on retrial queues , 1999 .

[24]  Tao Yang,et al.  A single-server retrial queue with server vacations and a finite number of input sources , 1995 .

[25]  Gunter Bolch,et al.  Heterogeneous Finite-Source Retrial Queues , 2004 .

[26]  Phuoc Tran-Gia,et al.  Modeling of Customer Retrial Phenomenon in Cellular Mobile Networks , 1997, IEEE J. Sel. Areas Commun..

[27]  Hideaki Takagi.  Queueing analysis A foundation of Performance Evaluation Volume 1: Vacation and priority systems , 1991 .

[28]  Gerrit K. Janssens.  The quasi-random input queueing system with repeated attempts as a model for a collision-avoidance star local area network , 1997, IEEE Trans. Commun..

[29]  William S. Griffith,et al.  athematical Theory of Reliability of Time Dependent Systems With Practical Applications , 1999, Technometrics.

[30]  de Ag Ton Kok,et al.  ALGORITHMIC METHODS FOR SINGLE SERVER SYSTEMS WITH REPEATED ATTEMPTS , 1984 .

[31]  Bela Almasi,et al.  Response time for finite heterogeneous nonreliable queueing systems , 1996 .