Araştırma Makalesi
BibTex RIS Kaynak Göster

Approximate anlysis of an unreliable M/M/c retrial queue with phase merging algorithm

Yıl 2016, Cilt: 4 Sayı: 3, 9 - 21, 30.09.2016

Öz



In this paper, we investigate an approximate analysis
of unreliable
 retrial queue with  in which all servers are subject to
breakdowns and repairs. Arriving customers that are unable to access a server
due to congestion or failure can choose to enter a retrial orbit for an
exponentially distributed amount of time and persistently attempt to gain
access to a server, or abandon their request and depart the system. Once a
customer is admitted to a service station, he remains there for a random
duration until service is complete and then depart the system. However, if the
server fails during service, i.e., an active breakdown, the customer may choose
to abandon the system or proceed directly to the retrial orbit while the server
begins repair immediately. In the unreliable model, there are no exact
solutions when the number of servers exceeds one. Therefore, we seek to
approximate the steady-state joint distribution of the number of customers in
orbit and the status of the
 servers for the case of Markovian
arrival and service times. Our approach to deriving the approximate
steady-state probabilities employs a phase-merging algorithm.




Kaynakça

  • Aissani, A and J.R. Artalejo, , On the single server retrial queue subject to breakdown, Queueing Sys., 30 (1998), 309-321.
  • Artalejo, J.R. and A. Gomez-Corral, Retrial Queueing Systems: A Computational Approach, Springer, Spain, pp: 318. (2008)
  • Artalejo, J.R., A classified bibliography of research on retrial queues: Progress in 1990-1999., Busin. Econ., 7 (1999), 187-211.
  • Artalejo, J.R., Accessible bibliography on retrial queues, Math. Comp. Mod., 30 (1999), 1-6.
  • Artalejo, J.R., Accessible bibliography on retrial queues: Progress in 2000-2009., Math. Comp. Mod., 51 (2010), 1071-1081.
  • Brian, P. Crawford, Approximate analysis of an unreliable M/M/2 retrial queue, thesis, (2012)
  • Courtoi, P.J., Decomposability, instabilities, and saturation in multiprogramming systems, Communications of the ACM, 18 (7) (1975), 371-377.
  • Falin, G., , A survey of retrial queues, Queueing Sys., 7, (1990), 127-167.
  • Falin, G.I. and J.G.C. Templeton, Retrial queues, Champman and Hall, London, pp: 328. (1997)
  • Korolyuk, V.S. and V.V. Korolyuk, Stochastic models of systems. Kluwer Academic Publishers, Boston (1999).
  • Kulkarni, V.G. and B.D. Choi, Retrial queues with server subject to breakdown and repairs, Queueing Sys., 7 (1990), 191-208.
  • Subramanian, M.G., G. Ayyappan and G. Sekar, M/M/c Retrial queueing system with breakdown and repair of services, Asian Journal of Mthematics and Statistics 4 (4) (2011), 214-223.
Yıl 2016, Cilt: 4 Sayı: 3, 9 - 21, 30.09.2016

Öz

Kaynakça

  • Aissani, A and J.R. Artalejo, , On the single server retrial queue subject to breakdown, Queueing Sys., 30 (1998), 309-321.
  • Artalejo, J.R. and A. Gomez-Corral, Retrial Queueing Systems: A Computational Approach, Springer, Spain, pp: 318. (2008)
  • Artalejo, J.R., A classified bibliography of research on retrial queues: Progress in 1990-1999., Busin. Econ., 7 (1999), 187-211.
  • Artalejo, J.R., Accessible bibliography on retrial queues, Math. Comp. Mod., 30 (1999), 1-6.
  • Artalejo, J.R., Accessible bibliography on retrial queues: Progress in 2000-2009., Math. Comp. Mod., 51 (2010), 1071-1081.
  • Brian, P. Crawford, Approximate analysis of an unreliable M/M/2 retrial queue, thesis, (2012)
  • Courtoi, P.J., Decomposability, instabilities, and saturation in multiprogramming systems, Communications of the ACM, 18 (7) (1975), 371-377.
  • Falin, G., , A survey of retrial queues, Queueing Sys., 7, (1990), 127-167.
  • Falin, G.I. and J.G.C. Templeton, Retrial queues, Champman and Hall, London, pp: 328. (1997)
  • Korolyuk, V.S. and V.V. Korolyuk, Stochastic models of systems. Kluwer Academic Publishers, Boston (1999).
  • Kulkarni, V.G. and B.D. Choi, Retrial queues with server subject to breakdown and repairs, Queueing Sys., 7 (1990), 191-208.
  • Subramanian, M.G., G. Ayyappan and G. Sekar, M/M/c Retrial queueing system with breakdown and repair of services, Asian Journal of Mthematics and Statistics 4 (4) (2011), 214-223.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Meriem El Haddad Bu kişi benim

Faiza Belarbi Bu kişi benim

Yayımlanma Tarihi 30 Eylül 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 4 Sayı: 3

Kaynak Göster

APA El Haddad, M., & Belarbi, F. (2016). Approximate anlysis of an unreliable M/M/c retrial queue with phase merging algorithm. New Trends in Mathematical Sciences, 4(3), 9-21.
AMA El Haddad M, Belarbi F. Approximate anlysis of an unreliable M/M/c retrial queue with phase merging algorithm. New Trends in Mathematical Sciences. Eylül 2016;4(3):9-21.
Chicago El Haddad, Meriem, ve Faiza Belarbi. “Approximate Anlysis of an Unreliable M/M/C Retrial Queue With Phase Merging Algorithm”. New Trends in Mathematical Sciences 4, sy. 3 (Eylül 2016): 9-21.
EndNote El Haddad M, Belarbi F (01 Eylül 2016) Approximate anlysis of an unreliable M/M/c retrial queue with phase merging algorithm. New Trends in Mathematical Sciences 4 3 9–21.
IEEE M. El Haddad ve F. Belarbi, “Approximate anlysis of an unreliable M/M/c retrial queue with phase merging algorithm”, New Trends in Mathematical Sciences, c. 4, sy. 3, ss. 9–21, 2016.
ISNAD El Haddad, Meriem - Belarbi, Faiza. “Approximate Anlysis of an Unreliable M/M/C Retrial Queue With Phase Merging Algorithm”. New Trends in Mathematical Sciences 4/3 (Eylül 2016), 9-21.
JAMA El Haddad M, Belarbi F. Approximate anlysis of an unreliable M/M/c retrial queue with phase merging algorithm. New Trends in Mathematical Sciences. 2016;4:9–21.
MLA El Haddad, Meriem ve Faiza Belarbi. “Approximate Anlysis of an Unreliable M/M/C Retrial Queue With Phase Merging Algorithm”. New Trends in Mathematical Sciences, c. 4, sy. 3, 2016, ss. 9-21.
Vancouver El Haddad M, Belarbi F. Approximate anlysis of an unreliable M/M/c retrial queue with phase merging algorithm. New Trends in Mathematical Sciences. 2016;4(3):9-21.