Number of retrials in a Finite Source retrial Queue with Unreliable Server

The object of this paper is to continue investigation of a single server retrial queue with finite number of sources in which the server is subjected to breakdowns and repairs. The server life time as well as the intervals between repetitions are exponentially distributed, while the repair and the service times are generally distributed. Using the formulas for the stationary system state distributions, obtained by Wang et al. [in Wang, J, L Zhao and F Zhang (2011). Analysis of the finite source retrial queues with server breakdowns and repairs. Journal of Industrial and Management Optimization, 7, 655–676.] we investigate the distribution of the number of retrials, made by a customer before he reaches the server free. Recurrent schemes for computing this distribution in steady state as well as any arbitrary of its moments are established. Numerical results for five different distributions of the service and repair times are also presented.

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

[2]  J. Amador,et al.  The M/G/1 retrial queue: New descriptors of the customer's behavior , 2009 .

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

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

[5]  Gennadi Falin,et al.  ON THE VIRTUAL WAITING TIME IN AN M/G/1 RETRIAL QUEUE , 1991 .

[6]  Jesus R. Artalejo,et al.  On the distribution of the successful and blocked events in the M/M/c retrial queue: A computational approach , 2007, Appl. Math. Comput..

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

[8]  Velika Dragieva,et al.  A Finite Source Retrial Queue: Number of Retrials , 2013 .

[9]  G. I. Falin.  On the waiting-time process in a single-line queue with repeated calls , 1986 .

[10]  Jesús R. Artalejo,et al.  On the distribution of the number of retrials , 2007 .

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

[12]  Jesus R. Artalejo,et al.  Transient analysis of the successful and blocked events in retrial queues , 2009, Telecommun. Syst..

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

[14]  Jesús R. Artalejo,et al.  A second order analysis of the waiting time in the M/G/1 retrial queue , 2002 .

[15]  Jesús R. Artalejo,et al.  Retrial Queueing Systems: A Computational Approach , 2008 .

[16]  Feng Zhang,et al.  Analysis of the finite source retrial queues withserver breakdowns and repairs , 2011 .

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

[18]  Jesús R. Artalejo,et al.  Retrial Queueing Systems , 2008 .

[19]  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..