Tool supported performance modelling of finite-source retrial queues with breakdowns

In this paper the tool supported performance modelling of a single server homogeneous finite-source retrial queueing system is presented. The server is assumed to be 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 investigations is the different type of non-reliability of the server. The mosel (Modeling, Specification and Evaluation Language) tool, developed at the University of Erlangen, Germany, 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, the overall utilization of the system, and the mean number of calls staying at the server or in the orbit. Mathematics Subject Classification: 60K25, 68M20, 60J27.

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

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

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

[4]  Boudewijn R. Haverkort,et al.  Performance of computer communication systems - a model-based approach , 1998 .

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

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

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

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

[9]  Ignas G. Niemegeers,et al.  Performability Modelling Tools and Techniques , 1996, Perform. Evaluation.

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

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

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

[13]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[14]  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..

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