This paper proposes a discrete-time multi-server queue with multiple synchronous vacations under balking and reneging. Arriving customers decide whether to join the system or balk on the basis of some state-dependent joining/balking probabilities, and renege according to a geometric distribution when servers are busy. The servers take a vacation together if there are no customers in the system at a service completion instant. When the servers are on vacation, an arriving customer activates an impatience timer which is geometrically distributed. The inter-arrival times, service times and vacation times are assumed to be independent and geometrically distributed. We obtain closed-form expressions and develop a computational algorithm for calculating the steady-state probabilities. Specifically, we establish the application of the proposed framework in analyzing a multi-server queueing system with synchronous vacation under balking and reneging. Applications of such models can be found in a wide variety of real-time systems including call centers, computer and communication systems, cloud computing, quality control and maintenance in industrial establishments. We develop a cost model to determine the optimal service rate. Various performance measures and numerical examples are sketched out to demonstrate the impact of the proposed method. Some special cases of the model have also been discussed. Finally, we show that in the limiting case the results converge to the corresponding continuous-time counterparts.
Accepté le :
DOI : 10.1051/ro/2016025
Mots-clés : Discrete-time, multi-server, balking, reneging, synchronous vacations, queueing, finite-buffer
@article{RO_2017__51_2_343_0, author = {Goswami, V. and Mund, G. B.}, title = {Computational analysis of multi-server discrete-time queueing system with balking, reneging and synchronous vacations}, journal = {RAIRO - Operations Research - Recherche Op\'erationnelle}, pages = {343--358}, publisher = {EDP-Sciences}, volume = {51}, number = {2}, year = {2017}, doi = {10.1051/ro/2016025}, mrnumber = {3619708}, zbl = {1367.60111}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ro/2016025/} }
TY - JOUR AU - Goswami, V. AU - Mund, G. B. TI - Computational analysis of multi-server discrete-time queueing system with balking, reneging and synchronous vacations JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2017 SP - 343 EP - 358 VL - 51 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2016025/ DO - 10.1051/ro/2016025 LA - en ID - RO_2017__51_2_343_0 ER -
%0 Journal Article %A Goswami, V. %A Mund, G. B. %T Computational analysis of multi-server discrete-time queueing system with balking, reneging and synchronous vacations %J RAIRO - Operations Research - Recherche Opérationnelle %D 2017 %P 343-358 %V 51 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2016025/ %R 10.1051/ro/2016025 %G en %F RO_2017__51_2_343_0
Goswami, V.; Mund, G. B. Computational analysis of multi-server discrete-time queueing system with balking, reneging and synchronous vacations. RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 2, pp. 343-358. doi : 10.1051/ro/2016025. http://www.numdam.org/articles/10.1051/ro/2016025/
The queue with balking and reneging. Comput. Oper. Res. 19 (1992) 713–716. | DOI | Zbl
and ,Transient solution of the queue with balking and reneging. Comput. Math. Appl. 57 (2009) 1280–1285. | DOI | MR | Zbl
, , and ,Analysis of customers impatience in queues with server vacations. Queueing Systems 52 (2006) 261–279. | DOI | MR | Zbl
and ,Infinite-server queues with system’s additional tasks and impatient customers. Probab. Eng. Inform. Sci. 22 (2008) 477–493. | DOI | MR | Zbl
and ,Performance analysis and optimal control of the queue. Perform. Eval. 52 (2003) 15–39. | DOI
and ,A discrete-time queue with customers with geometric deadlines. Perform. Eval. 85 (2015) 52–70. | DOI
and ,Analysis of a multi-server queue with markovian arrivals and synchronous phase type vacations. Asia-Pacific J. Oper. Res. 26 (2009) 85–113. | DOI | MR | Zbl
,queue in discrete-time. INFOR 16 (1978) 232–252. | MR | Zbl
and ,M. Chaudhry and U. Gupta, Numerical evaluation of state probabilities at different epochs in multiserver queue. Proc. of Advances on Methodological and Applied Aspects of Probability and Statistics (2001) 31–46. | MR | Zbl
On discrete-time multiserver queues with finite buffer: . Comput. Oper. Res. 31 (2004) 2137–2150. | DOI | MR | Zbl
, and ,Balking and reneging in multiserver markovian queuing system. Int. J. Math. Oper. Res. 3 (2011) 377–394. | DOI | MR | Zbl
and ,Optimal balking strategies in single-server queues with general service and vacation times. Perform. Eval. 68 (2011) 967–982. | DOI
, and ,Discrete-time multiserver queues with geometric service times. Comput. Oper. Res. 31 (2004) 81–99. | DOI | Zbl
, and ,Analysis of discrete-time multi-server queue with balking. Int. J. Manage. Sci. Eng. Manage. 9 (2014) 21–32.
,A discrete-time queue with balking, reneging, and working vacations. Int. J. Stochastic Anal. 2014 (2014). | MR | Zbl
,Study of customers’ impatience in a queue with working vacations. Int. J. Manage. Sci. Eng. Manage. 10 (2015) 144–154.
,D. Guha, A.D. Banik, V. Goswami and S. Ghosh, Equilibrium balking strategy in an unobservable queue with customers’ impatience. In Distributed Computing and Internet Technology. Springer (2014) 188–199.
Multi-server machine repair model with standbys and synchronous multiple vacation. Comput. Ind. Eng. 62 (2012) 296–305. | DOI
and ,Queueing models of call centers: An introduction. Ann. Oper. Res. 113 (2002) 41–59. | DOI | MR | Zbl
and ,Economic analysis of an queuing model with balking, reneging and retention of reneged customers. OPSEARCH 50 (2013) 383–403. | DOI | MR | Zbl
,A discrete time single-server queue with balking: economic applications. Appl. Econ. 40 (2008) 735–748. | DOI
and ,R.L Rardin, Optimization in operations research. Vol. 166. Prentice Hall Upper Saddle River, NJ (1998).
Impatient customers in an queue with single and multiple working vacations. Comput. Ind. Eng. 65 (2013) 207–215. | DOI
and ,The interarrival hyperexponential queues: with balking and reneging. Stochastics: Int. J. Probab. Stochastic Processs 69 (2000) 67–76. | MR | Zbl
and ,Discrete-time renewal input queue with balking and multiple working vacations. Int. J. Manage. Sci. Eng. Manage. 10 (2015) 224–236.
, and ,Optimal management of the machine repair problem with working vacation: Newtons method. J. Comput. Appl. Math. 233 (2009) 449–458. | DOI | MR | Zbl
, and ,Computational algorithm and parameter optimization for a multi-server system with unreliable servers and impatient customers. J. Comput. Appl. Math. 235 (2010) 547–562. | DOI | MR | Zbl
and ,Waiting time of queuing system with balking, reneging, and multiple synchronous vacations of partial servers. Systems Engineering-Theory Practice 28 (2008) 89–97. | DOI
and ,D. Yue and W. Yue, Analysis of an queueing system with balking, reneging, and synchronous vacations. In Advances in Queueing Theory and Network Applications. Springer (2009) 165–180. | MR
Optimal performance analysis of an queue system with balking, reneging and server vacation. Int. J. Pure Appl. Math. 28 (2006) 101–115. | MR | Zbl
, and ,Analysis of customers’impatience in an queue with working vacations. J. Ind. Manage. Optim. 8 (2012) 895–908. | DOI | MR | Zbl
, and ,Z. Zhang, Call centres with balking and abandonment: from queueing to queueing network models. Ph.D. thesis, University of Saskatchewan Saskatoon (2010). | MR
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