Geo/G/1 retrial queue with 2nd optional service

We consider a discrete-time Geo/G/1 retrial queue in which all the arriving customers demand a first essential service whereas only some of them ask for a second optional service. We study the Markov chain underlying the considered queueing system and derive a stochastic decomposition law. We also develop a recursive procedure for computing the distributions of the orbit and system size as well as the marginal distributions of the orbit size when the server is idle and busy with an essential or optional service. Finally, we prove the convergence to the continuous-time counterpart and show some numerical results.

[1]  Hui Li,et al.  An approximation method for the M/G/1 retrial queue with general retrial times , 1994 .

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

[3]  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..

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

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

[6]  Bharat T. Doshi,et al.  Analysis of a two phase queueing system with general service times , 1991, Oper. Res. Lett..

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

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

[9]  T. Meisling.  Discrete-Time Queuing Theory , 1958 .

[10]  Ivan Atencia,et al.  A Discrete-Time Geo/G/1 retrial queue with the server subject to starting failures , 2006, Ann. Oper. Res..

[11]  V. Sivasankaran,et al.  A two-phase queueing system with server vacations , 1994, Oper. Res. Lett..

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

[13]  Kailash C. Madan,et al.  An M/G/1 queue with second optional service with general service time distribution , 2003 .

[14]  Ivan Atencia,et al.  A Discrete-Time Geo/G/1 Retrial Queue with Server Breakdowns , 2006, Asia Pac. J. Oper. Res..

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

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

[17]  Gautam Choudhury,et al.  Some aspects of anM/G/1 queueing system with optional second service , 2003 .

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

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

[20]  G. Choudhury.  A batch arrival queueing system with an additional service channel , 2003 .

[21]  James G. C. Templeton,et al.  A survey on retrial queues , 1989 .

[22]  B. Krishna Kumar,et al.  An M/G/1 Retrial Queueing System with Two-Phase Service and Preemptive Resume , 2002, Ann. Oper. Res..

[23]  Kailash C. Madan,et al.  An M/G/1 queue with additional second stage service and optional re-service , 2002 .

[24]  Gautam Choudhury,et al.  A two phase queueing system with Bernoulli feedback , 2005 .

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

[26]  Robert B. Cooper,et al.  Stochastic Decompositions in the M/G/1 Queue with Generalized Vacations , 1985, Oper. Res..

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

[28]  B. Krishna Kumar,et al.  An M/G/1/1 queue with unreliable server and no waiting capacity , 2002 .

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

[30]  H. Tijms.  A First Course in Stochastic Models , 2003 .

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

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