A batch arrival retrial queue with two phases of service and Bernoulli vacation schedule

We consider an MX/G/1 queueing system with two phases of heterogeneous service and Bernoulli vacation schedule which operate under a linear retrial policy. In addition, each individual customer is subject to a control admission policy upon the arrival. This model generalizes both the classical M/G/1 retrial queue with arrivals in batches and a two phase batch arrival queue with a single vacation under Bernoulli vacation schedule. We will carry out an extensive stationary analysis of the system, including existence of the stationary regime, embedded Markov chain, steady state distribution of the server state and number of customer in the retrial group, stochastic decomposition and calculation of the first moment.

[1]  Kailash C. Madan,et al.  A two-stage batch arrival queueing system with a modified bernoulli schedule vacation under N-policy , 2005, Math. Comput. Model..

[2]  L. Breuer.  Introduction to Stochastic Processes , 2022, Statistical Methods for Climate Scientists.

[3]  Ronald W. Wolff,et al.  Poisson Arrivals See Time Averages , 1982, Oper. Res..

[4]  Jesús R. Artalejo,et al.  Standard and retrial queueing systems: a comparative analysis , 2002 .

[5]  Gautam Choudhury,et al.  Steady state analysis of an Mx/G/1 queue with two phase service and Bernoulli vacation schedule under multiple vacation policy , 2007 .

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

[7]  Ivan Atencia,et al.  On the single server retrial queue with batch arrivals , 2004 .

[8]  Julian Keilson,et al.  Oscillating random walk models for GI/G/1 vacation systems with Bernoulli schedules , 1986, Journal of Applied Probability.

[9]  G Fayolle.  A simple telephone exchange with delayed feedbacks , 1986 .

[10]  Yoshitaka Takahashi,et al.  ANALYSIS OF A TWO-CLASS PRIORITY QUEUE WITH BERNOULLI SCHEDULES , 1992 .

[11]  Linn I. Sennott,et al.  Technical Note - Mean Drifts and the Non-Ergodicity of Markov Chains , 1983, Oper. Res..

[12]  Oj Onno Boxma,et al.  Teletraffic Analysis and Computer Performance Evaluation , 1988 .

[13]  T. T. Soong,et al.  Book Reviews : INTRODUCTION TO STOCHASTIC PROCESSES E. Cinlar Prentice-Hall, 1975 , 1979 .

[14]  Amar Aissani.  An MX /G/1 retrial queue with exhaustive vacations , 2000 .

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

[16]  Kailash C. Madan,et al.  A two phase batch arrival queueing system with a vacation time under Bernoulli schedule , 2004, Appl. Math. Comput..

[17]  Ioannis Dimitriou,et al.  Analysis of a retrial queue with two-phase service and server vacations , 2008, Queueing Syst. Theory Appl..

[18]  Yann-Hang Lee,et al.  A study of two-phase service , 1990 .

[19]  Zhou Wenhui.  Analysis of a single-server retrial queue with FCFS orbit and Bernoulli vacation , 2005, Appl. Math. Comput..

[20]  Hanoch Levy.  Binomial-gated service: a method for effective operation and optimization of polling systems , 1991, IEEE Trans. Commun..

[21]  Kambiz Farahmand,et al.  Single line queue with repeated demands , 1990, Queueing Syst. Theory Appl..

[22]  Jesus R. Artalejo,et al.  On the time to reach a certain orbit level in multi-server retrial queues , 2005, Appl. Math. Comput..

[23]  V. G. Kulkarni.  Expected waiting times in a multiclass batch arrival retrial queue , 1986 .

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

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

[26]  H. M. Ghafir,et al.  Performance analysis of a multiple-access ring network , 1993, IEEE Trans. Commun..

[27]  Gautam Choudhury.  Steady state analysis of an M/G/1 queue with linear retrial policy and two phase service under Bernoulli vacation schedule , 2008 .

[28]  Yang Woo Shin,et al.  Retrial queues with collision arising from unslottedCSMA/CD protocol , 1992, Queueing Syst. Theory Appl..

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

[30]  Biswanath Mukherjee,et al.  The pi-persistent protocol for unidirectional broadcast bus networks , 1988, IEEE Trans. Commun..

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

[32]  Gennadi Falin.  Aggregate arrival of customers in a one-line system with repeated calls , 1976 .

[33]  Jianghua Li,et al.  A Repairable M/G/l Retrial Queue with Bernoulli Vacation and Two-Phase Service , 2008 .

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

[35]  Gautam Choudhury,et al.  A two phases queueing system with Bernoulli vacation schedule under multiple vacation policy , 2006 .

[36]  Chen-Khong Tham,et al.  Delay analysis of a probabilistic priority discipline , 2002, Eur. Trans. Telecommun..

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

[38]  C. Langaris.  Gated polling models with customers in orbit , 1999 .