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Year 2015, , 34 - 44, 30.10.2015
https://doi.org/10.36753/mathenot.421327

Abstract

References

  • [1] Choi, B. D. and Park, K. K., The M/G/1 queue with Bernoulli schedule. Queueing Systems. 7 (1990), 219-228.
  • [2] Cramer, M., Stationary distributions in queueing system with vacation times and limited service. Queueing Systems. 4 (1989), no. 1, 57-78.
  • [3] Doshi, B. T., A note on stochastic decomposition in a GI/G/1 queue with vacations or set-up times. J. Appl. Prob. 22 (1985), 419-428.
  • [4] Doshi, B. T., Queueing systems with vacations-a survey. Queueing Systems. 1 (1986), 29-66.
  • [5] Fuhrman, S. W., A note on the M/G/1 queue with server vacations. Operations Research. 32 (1984), 1368-1373.
  • [6] Keilson, J. and Servi, L. D., Oscillating random walk models for G1/G/1 vacation systems with Bernoulli schedules. J. App. Prob. 23 (1986), 790-802.
  • [7] Lee, T. T., M/G/1/N queue with vacation and exhaustive service discipline. Operations Research. 32 (1984), 774-784.
  • [8] Levy, Y. and Yechiali, U., An M/M/s queue with servers vacations. INFOR. 14 (1976), no. 2, 153-163.
  • [9] Medhi, J., Stochastic Processes. Wiley Eastern, 1982.
  • [10] Madan, Kailash C., An M/G/1 Queue with optional deterministic server vacations. Metron, LVII No. 3-4 (1999), 83-95.
  • [11] Madan, Kailash C., An M/G/1 queue with second optional service. Queueing Systems. 34 (2000), 37-46.
  • [12] Madan, Kailash C., On a single server queue with two-stage heteregeneous service and deterministic server vacations. International J. of Systems Science. 32 (2001), no. 7, 837-844.
  • [13] Scholl, M. and Kleinrock, L., On the M/G/1 queue with rest periods and certain service independent queueing disciplines. Oper. Res. 31 (1983), no. 4, 705-719.
  • [14] Servi, L. D., D/G/1 queue with vacation. Operations Research. 34 (1986), no. 4, 619-629.
  • [15] Servi, L. D., Average delay approximation of M/G/1 cyclic service queue with Bernoulli schedules, IEEE J. Sel. Areas Comm. 4 (1986), no. 6, 813 - 822.
  • [16] Shanthikumar, J. G., On stochastic decomposition in The M/G/1 type queues with generalized vacations. Operations Research. 36 (1988), 566-569.
  • [17] Shanthikumar, J. G. and Sumita, Ushio, Modified Lindley process with replacement: dynamic behavior, asymptotic decomposition and applications. J. Appl. Prob. 26 (1989), 552-565.
  • [18] Takagi, H., Queueing Analysis, Vol. 1: Vacation and Priority Systems. North-Holland, Amsterdam, 1991.

ON A M^[X]/G/1 QUEUEING SYSTEM WITH GENERALIZED COXIAN-2 SERVICE AND OPTIONAL GENERALIZED COXIAN-2 VACATION

Year 2015, , 34 - 44, 30.10.2015
https://doi.org/10.36753/mathenot.421327

Abstract

We study the steady state behaviour of a batch arrival single server
queue in which the first service with general service times G1 is compulsory
and the second service with general service times G2 is optional. We term such
a two phase service as generalized Coxian-2 service. Just after completion of a
service the server may take a vacation of random length of time with general
vacation times V1. After completion of the first phase of vacation the server
may or may not take the second optional vacation with general vacation times
V2. We term this two phase vacation as optional generalized Coxian-2 sever
vacation. We obtain steady state probability generating functions for the queue
size at a random epoch of time in explicit and closed forms. Some particular
cases of interest including some known results have been derived. 

References

  • [1] Choi, B. D. and Park, K. K., The M/G/1 queue with Bernoulli schedule. Queueing Systems. 7 (1990), 219-228.
  • [2] Cramer, M., Stationary distributions in queueing system with vacation times and limited service. Queueing Systems. 4 (1989), no. 1, 57-78.
  • [3] Doshi, B. T., A note on stochastic decomposition in a GI/G/1 queue with vacations or set-up times. J. Appl. Prob. 22 (1985), 419-428.
  • [4] Doshi, B. T., Queueing systems with vacations-a survey. Queueing Systems. 1 (1986), 29-66.
  • [5] Fuhrman, S. W., A note on the M/G/1 queue with server vacations. Operations Research. 32 (1984), 1368-1373.
  • [6] Keilson, J. and Servi, L. D., Oscillating random walk models for G1/G/1 vacation systems with Bernoulli schedules. J. App. Prob. 23 (1986), 790-802.
  • [7] Lee, T. T., M/G/1/N queue with vacation and exhaustive service discipline. Operations Research. 32 (1984), 774-784.
  • [8] Levy, Y. and Yechiali, U., An M/M/s queue with servers vacations. INFOR. 14 (1976), no. 2, 153-163.
  • [9] Medhi, J., Stochastic Processes. Wiley Eastern, 1982.
  • [10] Madan, Kailash C., An M/G/1 Queue with optional deterministic server vacations. Metron, LVII No. 3-4 (1999), 83-95.
  • [11] Madan, Kailash C., An M/G/1 queue with second optional service. Queueing Systems. 34 (2000), 37-46.
  • [12] Madan, Kailash C., On a single server queue with two-stage heteregeneous service and deterministic server vacations. International J. of Systems Science. 32 (2001), no. 7, 837-844.
  • [13] Scholl, M. and Kleinrock, L., On the M/G/1 queue with rest periods and certain service independent queueing disciplines. Oper. Res. 31 (1983), no. 4, 705-719.
  • [14] Servi, L. D., D/G/1 queue with vacation. Operations Research. 34 (1986), no. 4, 619-629.
  • [15] Servi, L. D., Average delay approximation of M/G/1 cyclic service queue with Bernoulli schedules, IEEE J. Sel. Areas Comm. 4 (1986), no. 6, 813 - 822.
  • [16] Shanthikumar, J. G., On stochastic decomposition in The M/G/1 type queues with generalized vacations. Operations Research. 36 (1988), 566-569.
  • [17] Shanthikumar, J. G. and Sumita, Ushio, Modified Lindley process with replacement: dynamic behavior, asymptotic decomposition and applications. J. Appl. Prob. 26 (1989), 552-565.
  • [18] Takagi, H., Queueing Analysis, Vol. 1: Vacation and Priority Systems. North-Holland, Amsterdam, 1991.
There are 18 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Kailash C. Madan This is me

Publication Date October 30, 2015
Submission Date October 8, 2014
Published in Issue Year 2015

Cite

APA Madan, K. C. (2015). ON A M^[X]/G/1 QUEUEING SYSTEM WITH GENERALIZED COXIAN-2 SERVICE AND OPTIONAL GENERALIZED COXIAN-2 VACATION. Mathematical Sciences and Applications E-Notes, 3(2), 34-44. https://doi.org/10.36753/mathenot.421327
AMA Madan KC. ON A M^[X]/G/1 QUEUEING SYSTEM WITH GENERALIZED COXIAN-2 SERVICE AND OPTIONAL GENERALIZED COXIAN-2 VACATION. Math. Sci. Appl. E-Notes. October 2015;3(2):34-44. doi:10.36753/mathenot.421327
Chicago Madan, Kailash C. “ON A M^[X]/G/1 QUEUEING SYSTEM WITH GENERALIZED COXIAN-2 SERVICE AND OPTIONAL GENERALIZED COXIAN-2 VACATION”. Mathematical Sciences and Applications E-Notes 3, no. 2 (October 2015): 34-44. https://doi.org/10.36753/mathenot.421327.
EndNote Madan KC (October 1, 2015) ON A M^[X]/G/1 QUEUEING SYSTEM WITH GENERALIZED COXIAN-2 SERVICE AND OPTIONAL GENERALIZED COXIAN-2 VACATION. Mathematical Sciences and Applications E-Notes 3 2 34–44.
IEEE K. C. Madan, “ON A M^[X]/G/1 QUEUEING SYSTEM WITH GENERALIZED COXIAN-2 SERVICE AND OPTIONAL GENERALIZED COXIAN-2 VACATION”, Math. Sci. Appl. E-Notes, vol. 3, no. 2, pp. 34–44, 2015, doi: 10.36753/mathenot.421327.
ISNAD Madan, Kailash C. “ON A M^[X]/G/1 QUEUEING SYSTEM WITH GENERALIZED COXIAN-2 SERVICE AND OPTIONAL GENERALIZED COXIAN-2 VACATION”. Mathematical Sciences and Applications E-Notes 3/2 (October 2015), 34-44. https://doi.org/10.36753/mathenot.421327.
JAMA Madan KC. ON A M^[X]/G/1 QUEUEING SYSTEM WITH GENERALIZED COXIAN-2 SERVICE AND OPTIONAL GENERALIZED COXIAN-2 VACATION. Math. Sci. Appl. E-Notes. 2015;3:34–44.
MLA Madan, Kailash C. “ON A M^[X]/G/1 QUEUEING SYSTEM WITH GENERALIZED COXIAN-2 SERVICE AND OPTIONAL GENERALIZED COXIAN-2 VACATION”. Mathematical Sciences and Applications E-Notes, vol. 3, no. 2, 2015, pp. 34-44, doi:10.36753/mathenot.421327.
Vancouver Madan KC. ON A M^[X]/G/1 QUEUEING SYSTEM WITH GENERALIZED COXIAN-2 SERVICE AND OPTIONAL GENERALIZED COXIAN-2 VACATION. Math. Sci. Appl. E-Notes. 2015;3(2):34-4.

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