The Discrete-Time Bulk-Service Geo/Geo/1 Queue with Multiple Working Vacations

This paper deals with a discrete-time bulk-service queueing system with infinite buffer space and multiple working vacations. Considering an early arrival system, as soon as the server empties the system in a regular busy period, he leaves the system and takes a working vacation for a random duration at time . The service times both in a working vacation and in a busy period and the vacation times are assumed to be geometrically distributed. By using embedded Markov chain approach and difference operator method, queue length of the whole system at random slots and the waiting time for an arriving customer are obtained. The queue length distributions of the outside observer’s observation epoch are investigated. Numerical experiment is performed to validate the analytical results.

[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]  Naishuo Tian,et al.  The discrete-time GI/Geo/1 queue with working vacations and vacation interruption , 2007, Appl. Math. Comput..

[4]  K. Sikdar,et al.  GI/M/1 Queues with Server Vacations and Dependent Interarrival and Service Times , 2008 .

[5]  Mohan L. Chaudhry,et al.  Analysis of the discrete-time bulk-service queue Geo/GY/1/N+B , 2004, Oper. Res. Lett..

[6]  U. C. Gupta,et al.  Performance analysis of finite buffer discrete-time queue with bulk service , 2002, Comput. Oper. Res..

[7]  Zhang Li-hui.  M/G/1 Queue with Multiple Working Vacations , 2013 .

[8]  N. Tian,et al.  Analysis of the Discrete Time Geo/Geo/1 Queue with Single Working Vacation , 2008 .

[9]  U. C. Gupta,et al.  Computing system length distribution of a finite-buffer bulk-arrival bulk-service queue with variable server capacity , 2011 .

[10]  Qi-Ming He,et al.  Algorithmic analysis of the discrete time GIX/GY/1 queueing system , 2008 .

[11]  Yinghui Tang,et al.  Steady state analysis and computation of the GI[x]/Mb/1/L queue with multiple working vacations and partial batch rejection , 2009, Comput. Ind. Eng..

[12]  Herwig Bruneel,et al.  Analysis of threshold-based batch-service queueing systems with batch arrivals and general service times , 2011, Perform. Evaluation.

[13]  Veena Goswami,et al.  Analysis of discrete-time batch service renewal input queue with multiple working vacations , 2011, Comput. Ind. Eng..

[14]  P. Vijaya Laxmi,et al.  Renewal input infinite buffer batch service queue with single exponential working vacation and accessibility to batches , 2011, Int. J. Math. Oper. Res..

[15]  Murray R. Spiegel,et al.  Schaum's outline of theory and problems of calculus of finite differences and difference equations , 1971 .

[16]  Tetsuya Takine,et al.  Factorization and Stochastic Decomposition Properties in Bulk Queues with Generalized Vacations , 2005, Queueing Syst. Theory Appl..

[17]  U. C. Gupta,et al.  Analytic and numerical aspects of batch service queues with single vacation , 2005, Comput. Oper. Res..

[18]  Kyung C. Chae,et al.  Analysis of the queue-length distribution for the discrete-time batch-service Geo , 2007, Eur. J. Oper. Res..

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

[20]  Veena Goswami,et al.  Analysis of a discrete-time GI/Geo/1/N queue with multiple working vacations , 2010 .

[21]  Herwig Bruneel,et al.  Tail distribution of the delay in a general batch-service queueing model , 2012, Computers & Operations Research.

[22]  Kyung C. Chae,et al.  The GI/M/1 queue and the GI/Geo/1 queue both with single working vacation , 2009, Perform. Evaluation.

[23]  U. C. Gupta,et al.  Reducing congestion in bulk-service finite-buffer queueing system using batch-size-dependent service , 2012, Perform. Evaluation.

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

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

[26]  M. R. Spiegel.  Schaum's outline series theory and problems of calculus of finite differences and difference equations : including 420 solved problems / Murray R. Spiegel , 1971 .