Analysis of Finite Buffer Markovian Queue with Balking, Reneging and Working Vacations

This article presents the analysis of a finite buffer M/M/1 queue with multiple and single working vacations. The arriving customers balk (that is do not join the queue) with a probability and renege (that is leave the queue after joining) according to exponential distribution. The inter-arrival times, service times during a regular service period, service times during a vacation period and vacation times are independent and exponentially distributed random variables. Steady-state behavior of the model is considered and various performance measures, some special cases of the model and cost analysis are discussed.

[1]  M. O. Abou-El-Ata,et al.  The single-server Markovian overflow queue with balking, reneging and an additional server for longer queues , 1992 .

[2]  A. M. A. Hariri,et al.  The M/M/c/N queue with balking and reneging , 1992, Comput. Oper. Res..

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

[4]  A. I. Shawky.  The single-server machine interference model with balking, reneging and an additional server for longer queues , 1997 .

[5]  Chafik Abid,et al.  Optimal management policy for a single and bulk service queue under Bernoulli vacation schedules , 2009, Int. J. Appl. Decis. Sci..

[6]  F. Baccelli,et al.  Single-server queues with impatient customers , 1984, Advances in Applied Probability.

[7]  Frank A. Haight,et al.  QUEUEING WITH BALKING , 1957 .

[8]  Hideaki Takagi,et al.  M/G/1 queue with multiple working vacations , 2006, Perform. Evaluation.

[9]  Kathryn E. Stecke,et al.  Meeting Correlated Spare Part Demands with Optimal Transshipments , 2010, Int. J. Strateg. Decis. Sci..

[10]  H. Tijms,et al.  A queueing system with impatient customers , 1985 .

[11]  M. O. Abou-El-Ata.  The state-dependent queue : M/M/1/N with reneging and general balk functions , 1991 .

[12]  Fu-wei Wang,et al.  Fluid Model Driven by an M/M/1/N Queue with Single Exponential Vacation , 2010 .

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

[14]  Payam Hanafizadeh,et al.  A Data Mining Model for Risk Assessment and Customer Segmentation in the Insurance Industry , 2013, Int. J. Strateg. Decis. Sci..

[15]  Frank A. Haight,et al.  Queueing with reneging , 1959 .

[16]  Eitan Altman,et al.  INFINITE-SERVER QUEUES WITH SYSTEM'S ADDITIONAL TASKS AND IMPATIENT CUSTOMERS , 2008, Probability in the Engineering and Informational Sciences.

[17]  C. J. Ancker,et al.  Some Queuing Problems with Balking and Reneging. I , 1963 .

[18]  Naishuo Tian,et al.  The M/M/1 Queue with Single Working Vacation , 2008 .

[19]  B. T. Doshi,et al.  Queueing systems with vacations — A survey , 1986, Queueing Syst. Theory Appl..

[20]  Douglas G. Woolford,et al.  A preemptive priority queue with balking , 2005, Eur. J. Oper. Res..

[21]  Chun-Hung Chen,et al.  A Regression Dependent Iterative Algorithm for Optimizing Top-K Selection in Simulation Query Language , 2012, Int. J. Decis. Support Syst. Technol..

[22]  Frada Burstein,et al.  Mobile Decision Support for Time-Critical Decision Making , 2008 .

[23]  Frédéric Adam,et al.  Encyclopedia of Decision Making and Decision Support Technologies , 2008 .