Geo/Geo/1 retrial queue with non-persistent customers and working vacations

In this paper, we consider a Geo/Geo/1 retrial queue with non-persistent customers and working vacations. The server works at a lower service rate in a working vacation period. Assume that the customers waiting in the orbit request for service with a constant retrial rate, if the arriving retrial customer finds the server busy, the customer will go back to the orbit with probability q (0≤q≤1), or depart from the system immediately with probability $\bar{q}=1-q$. Based on the necessary and sufficient condition for the system to be stable, we develop the recursive formulae for the stationary distribution by using matrix-geometric solution method. Furthermore, some performance measures of the system are calculated and an average cost function is also given. We finally illustrate the effect of the parameters on the performance measures by some numerical examples.

[1]  Naishuo Tian,et al.  Discrete-time GI/Geo/1 queue with multiple working vacations , 2007, Queueing Syst. Theory Appl..

[2]  Yutaka Baba,et al.  Analysis of a GI/M/1 queue with multiple working vacations , 2005, Oper. Res. Lett..

[3]  B. Krishna Kumar,et al.  On multiserver feedback retrial queue with finite buffer , 2009 .

[4]  Antonio Gómez-Corral,et al.  A bibliographical guide to the analysis of retrial queues through matrix analytic techniques , 2006, Ann. Oper. Res..

[5]  Bin Liu,et al.  Tail asymptotics for M/M/c retrial queues with non-persistent customers , 2012, Oper. Res..

[6]  Leslie D. Servi,et al.  M/M/1 queues with working vacations (M/M/1/WV) , 2002, Perform. Evaluation.

[7]  Naishuo Tian,et al.  The discrete time Geom/Geom/1 queue with multiple working vacations , 2008 .

[8]  Vaidyanathan Ramaswami,et al.  Introduction to Matrix Analytic Methods in Stochastic Modeling , 1999, ASA-SIAM Series on Statistics and Applied Mathematics.

[9]  Naishuo Tian,et al.  Vacation Queueing Models Theory and Applications , 2006 .

[10]  Bong D. Choi,et al.  The M/G/1 retrial queue with bernoulli schedule , 1990, Queueing Syst. Theory Appl..

[11]  Sherif I. Rabia,et al.  A discrete time Geo/G/1 retrial queue with general retrial times and balking customers , 2008 .

[12]  Attahiru Sule Alfa,et al.  Queueing Theory for Telecommunications - Discrete Time Modelling of a Single Node System , 2010 .

[13]  A. Krishnamoorthy,et al.  A single server feedback retrial queue with collisions , 2010, Comput. Oper. Res..

[14]  Tien Van Do.  M/M/1 retrial queue with working vacations , 2009, Acta Informatica.

[15]  Tien Van Do,et al.  An efficient computation algorithm for a multiserver feedback retrial queue with a large queueing capacity , 2010 .

[16]  Zaiming Liu,et al.  Geo/Geo/1 retrial queue with working vacations and vacation interruption , 2012 .

[17]  Bin Liu,et al.  Analyzing retrial queues by censoring , 2010, Queueing Syst. Theory Appl..

[18]  Jesus R. Artalejo,et al.  Analysis of multiserver queues with constant retrial rate , 2001, Eur. J. Oper. Res..

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

[20]  Gopal Sekar,et al.  Retrial Queueing System with Single Working Vacation Under Pre-Emptive Priority Service , 2010 .

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

[22]  Hui Li,et al.  A Retrial Queue with a Constant Retrial Rate, Server Downs and Impatient Customers , 2005 .