On a Discrete-Time GIX/Geo/1/N Queue with Single Working Vacation and Partial Batch Rejection
This paper treats a discrete-time finite buffer batch arrival queue with a single working vacation and partial batch rejection in which the inter-arrival and service times are, respectively, arbitrary and geometrically distributed. The queue is analyzed by using the supplementary variable and the imbedded Markov-chain techniques. We obtain steady-state system length distributions at prearrival, arbitrary and outside observer-s observation epochs. We also present probability generation function (p.g.f.) of actual waiting-time distribution in the system and some performance measures.
[1] Baba, Y. Analysis of a GI/M/1 queue with multiple working vacations.
Operations Research Letters 33 (2005), 201-209.
[2] Banik, AD, Gupta, UC and Pathak, SS. On the GI/M/1/N queue with
multiple working vacations - analytic anaylsis and computation. Applied
Mathematical Modelling 31 (2007), 1701-1710.
[3] Chae, K. C., Lim, D.E., Yang, W.S. The GI/M/1 queue and the
GI/Geo/1 queue both with single working vacation. Performance Evaluation
66(7)(2009), 356-367 .
[4] Chang, SH, Choi, DW. Performance analysis of a finite-buffer discretetime
queue with bulk arrival, bulk service and vacations. Computers &
Operations Research 32 (2005), 2213-2234.
[5] Doshi, BT. Queueing systems with vacations - a survey. Queueing
Systems (1)(1986), 29-66.
[6] Goswami, V and Vijaya Laxmi, P. Analysis of renewal input bulk arrival
queue with single working vacation and partial batch rejection. Journal of
Industrial and Management Optimization 6(4)(2010), 911-927.
[7] Goswami, V and Mund, GB. Analysis of a discrete-time GI/GEO/1/N
queue with multiple working vacations. Journal of Systems Science and
Systems Engineering 19(3)(2010), 367-384.
[8] Kim, JD, Choi, DW and Chae, KC. Analysis of queue-length distribution
of the M/G/1 queue with working vacations. International Conference on
Statistics and Related Fields, Hawaii,2003.
[9] Li, J, Liu, W and Tian, N. Steady-state analysis of a discrete-time batch
arrival queue with working vacations. Performance Evaluation, 67 (2010),
897-912.
[10] Li, J and Tian, N. Performance analysis of a GI/M/1 queue with single
working vacation. Applied Mathematics and Computation 217(2011),
4960¨C4971 .
[11] Li, J, Tian, N and Liu, W.Discrete-time GI/Geo/1 queue with working
vacations. Queueing Systems 56 (2007), 53-63.
[12] Li, J, Tian, N, Zhang, ZG and Luh, H. Analysis of the M/G/1 queue with
exponentially working vacations-a matrix analytic approach. Queueing
Systems 61 (2009), 139-166.
[13] Liu, W, Xu, X and Tian, N. Stochastic decompositions in the M/M/1
queue with working vacations. Operations Research Letters 35 (2007),
595-600.
[14] Servi, LD and Finn, SG. M/M/1 queue with working vacations
(M/M/1/WV). Performance Evaluation 50 (2002), 41-52.
[15] Shanthikumar, JG. On stochastic decomposition in M/G/1 type queues
with generalized server vacations. Operations Research 36(1988), 566-569.
[16] Takagi, H. Queueing Analysis - A Foundation of Performance Evaluation
Vacation and Priority Systems. vol. 1, North-Holland, New York,
1991.
[17] Tian, N., Zhang, Z.G. Vacation Queueing Models: Theory and Applications,
Springer-Verlag, New York , 2006.
[18] Tian, N, Xu, X and Ma, Z. Discrete-time queueing theory. Science press,
Beijing, 2008.
[19] Wu, D and Takagi, H. M/G/1 queue with multiple working vacations.
Performance Evaluation 63 (2006), 654-681.
[20] Yi, XW et al. The Geo/G/1 queue with disasters and multiple working
vacations. Stochastic Models 23 (2007), 537-549.
[21] Yu, MM, Tang, YH and Fu, YH. Steady state analysis and computation
of the GI[x]/Mb/1/L queue with multiple working vacations and partial
batch rejection. Computers & Industrial Engineering 56 (2009), 1243-1253.
[22] Yu, MM, Tang, YH , Fu, YH and Pan, LM. GI/Geom/1/N/MWV
queue with changeover time and searching for the optimum service
rate in working vacation period. Journal of Computational and Applied
Mathematics 235 (2011), 2170-2184.
[23] Zhang Z.G., Tian N. Discrete time Geo/G/1 queue with multiple adaptive
vacations. Queueing Systems, 38(4)(2001), 419-430 .
[1] Baba, Y. Analysis of a GI/M/1 queue with multiple working vacations.
Operations Research Letters 33 (2005), 201-209.
[2] Banik, AD, Gupta, UC and Pathak, SS. On the GI/M/1/N queue with
multiple working vacations - analytic anaylsis and computation. Applied
Mathematical Modelling 31 (2007), 1701-1710.
[3] Chae, K. C., Lim, D.E., Yang, W.S. The GI/M/1 queue and the
GI/Geo/1 queue both with single working vacation. Performance Evaluation
66(7)(2009), 356-367 .
[4] Chang, SH, Choi, DW. Performance analysis of a finite-buffer discretetime
queue with bulk arrival, bulk service and vacations. Computers &
Operations Research 32 (2005), 2213-2234.
[5] Doshi, BT. Queueing systems with vacations - a survey. Queueing
Systems (1)(1986), 29-66.
[6] Goswami, V and Vijaya Laxmi, P. Analysis of renewal input bulk arrival
queue with single working vacation and partial batch rejection. Journal of
Industrial and Management Optimization 6(4)(2010), 911-927.
[7] Goswami, V and Mund, GB. Analysis of a discrete-time GI/GEO/1/N
queue with multiple working vacations. Journal of Systems Science and
Systems Engineering 19(3)(2010), 367-384.
[8] Kim, JD, Choi, DW and Chae, KC. Analysis of queue-length distribution
of the M/G/1 queue with working vacations. International Conference on
Statistics and Related Fields, Hawaii,2003.
[9] Li, J, Liu, W and Tian, N. Steady-state analysis of a discrete-time batch
arrival queue with working vacations. Performance Evaluation, 67 (2010),
897-912.
[10] Li, J and Tian, N. Performance analysis of a GI/M/1 queue with single
working vacation. Applied Mathematics and Computation 217(2011),
4960¨C4971 .
[11] Li, J, Tian, N and Liu, W.Discrete-time GI/Geo/1 queue with working
vacations. Queueing Systems 56 (2007), 53-63.
[12] Li, J, Tian, N, Zhang, ZG and Luh, H. Analysis of the M/G/1 queue with
exponentially working vacations-a matrix analytic approach. Queueing
Systems 61 (2009), 139-166.
[13] Liu, W, Xu, X and Tian, N. Stochastic decompositions in the M/M/1
queue with working vacations. Operations Research Letters 35 (2007),
595-600.
[14] Servi, LD and Finn, SG. M/M/1 queue with working vacations
(M/M/1/WV). Performance Evaluation 50 (2002), 41-52.
[15] Shanthikumar, JG. On stochastic decomposition in M/G/1 type queues
with generalized server vacations. Operations Research 36(1988), 566-569.
[16] Takagi, H. Queueing Analysis - A Foundation of Performance Evaluation
Vacation and Priority Systems. vol. 1, North-Holland, New York,
1991.
[17] Tian, N., Zhang, Z.G. Vacation Queueing Models: Theory and Applications,
Springer-Verlag, New York , 2006.
[18] Tian, N, Xu, X and Ma, Z. Discrete-time queueing theory. Science press,
Beijing, 2008.
[19] Wu, D and Takagi, H. M/G/1 queue with multiple working vacations.
Performance Evaluation 63 (2006), 654-681.
[20] Yi, XW et al. The Geo/G/1 queue with disasters and multiple working
vacations. Stochastic Models 23 (2007), 537-549.
[21] Yu, MM, Tang, YH and Fu, YH. Steady state analysis and computation
of the GI[x]/Mb/1/L queue with multiple working vacations and partial
batch rejection. Computers & Industrial Engineering 56 (2009), 1243-1253.
[22] Yu, MM, Tang, YH , Fu, YH and Pan, LM. GI/Geom/1/N/MWV
queue with changeover time and searching for the optimum service
rate in working vacation period. Journal of Computational and Applied
Mathematics 235 (2011), 2170-2184.
[23] Zhang Z.G., Tian N. Discrete time Geo/G/1 queue with multiple adaptive
vacations. Queueing Systems, 38(4)(2001), 419-430 .
@article{"International Journal of Engineering, Mathematical and Physical Sciences:63566", author = "Shan Gao", title = "On a Discrete-Time GIX/Geo/1/N Queue with Single Working Vacation and Partial Batch Rejection", abstract = "This paper treats a discrete-time finite buffer batch arrival queue with a single working vacation and partial batch rejection in which the inter-arrival and service times are, respectively, arbitrary and geometrically distributed. The queue is analyzed by using the supplementary variable and the imbedded Markov-chain techniques. We obtain steady-state system length distributions at prearrival, arbitrary and outside observer-s observation epochs. We also present probability generation function (p.g.f.) of actual waiting-time distribution in the system and some performance measures.
", keywords = "Discrete-time, finite buffer, single working vacation, batch arrival, partial rejection.", volume = "5", number = "12", pages = "2112-9", }
