A discrete-time Geo/G/1 retrial queue with starting failures and second optional service

We consider a discrete-time Geo/G/1 retrial queue with starting failures in which all the arriving customers require a first essential service while only some of them ask for a second optional service. We study the Markov chain underlying the considered queueing system and its ergodicity condition. Explicit formulae for the stationary distribution and some performance measures of the system in steady state are obtained. We also obtain two stochastic decomposition laws regarding the probability generating function of the system size. Finally, some numerical examples are presented to illustrate the influence of the parameters on several performance characteristics.

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

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

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

[4]  J. Medhi,et al.  A Single Server Poisson Input Queue with a Second Optional Channel , 2002, Queueing Syst. Theory Appl..

[5]  Kailash C. Madan,et al.  An M/G/1 queue with second optional service , 1999, Queueing Syst. Theory Appl..

[6]  Ivan Atencia,et al.  A Discrete-Time Geo/G/1 Retrial Queue with General Retrial Times , 2004, Queueing Syst. Theory Appl..

[7]  M. L. Chaudhry,et al.  A first course in bulk queues , 1983 .

[8]  B. Krishna Kumar,et al.  The M/G/1 retrial queue with feedback and starting failures , 2002 .

[9]  Quan-Lin Li,et al.  A BMAP/G/1 Retrial Queue with a Server Subject to Breakdowns and Repairs , 2006, Ann. Oper. Res..

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

[11]  Bong Dae Choi,et al.  Discrete-time Geo1, Geo2/G/1 retrial queueing systems with two types of calls , 1997 .

[12]  Ivan Atencia,et al.  A discrete-time Geo[X]/G/1 retrial queue with control of admission , 2005 .

[13]  Hui Li,et al.  On the steady-state queue size distribution of the discrete-timeGeo/G/1 queue with repeated customers , 1995, Queueing Syst. Theory Appl..

[14]  I. Atencia,et al.  Discrete-time Geo[X]/GH/1 retrial queue with Bernoulli feedback , 2004 .

[15]  Herbert Freeman,et al.  Discrete-Time Systems , 1980 .

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

[17]  Jinting Wang,et al.  An M/G/1 queue with second optional service and server breakdowns , 2004 .

[18]  C. D. Litton,et al.  A First Course in Bulk Queues , 1983 .

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

[20]  Herwig Bruneel,et al.  Discrete-time models for communication systems including ATM , 1992 .

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

[22]  Jesús R. Artalejo,et al.  A classified bibliography of research on retrial queues: Progress in 1990–1999 , 1999 .

[23]  Jeffrey J. Hunter.  Discrete Time Models : Techniques and Applications , 1983 .

[24]  Thomas Yew Sing Lee.  The effect of workers with different capabilities on customer delay , 2004, Comput. Oper. Res..

[25]  H. Li,et al.  Steady-state queue size distribution of discrete-time PH/Geo/1 retrial queues , 1999 .

[26]  Hui Li,et al.  Geo/G/1 discrete time retrial queue with Bernoulli schedule , 1998, Eur. J. Oper. Res..

[27]  Jeffrey J. Hunter,et al.  Mathematical techniques of applied probability , 1985 .

[28]  M. E. Woodward,et al.  Communication and computer networks - modelling with discrete-time queues , 1993 .

[29]  Jeffrey J. Hunter,et al.  Mathematical Techniques of Applied Probability Volume 2 Discrete Time Models: Techniques and Applications , 2008 .

[30]  J. R. Artalejo,et al.  Stochastic decomposition for retrial queues , 1992 .

[31]  Hui Li,et al.  TheM/G/1 retrial queue with the server subject to starting failures , 1994, Queueing Syst. Theory Appl..

[32]  Pilar Moreno.  A Discrete-Time Retrial Queue with Unreliable Server and General Server Lifetime , 2006 .