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Partially shared buffers with full or mixed priority
Stability of a retrial queueing network with different classes of customers and restricted resource pooling
1.  Department of Mathematics, Korea University, 145 Anamro, Seongbukgu, Seoul, 136713, South Korea 
References:
[1] 
M. Bramson, Stability of two families of queueing networks and a discussion of fluid limits, Queueing Systems Theory Appl., 28 (1998), 731. doi: 10.1023/A:1019182619288. 
[2] 
B. D. Choi and B. Kim, Nonergodicity criteria for denumerable continuous time Markov processes, Operations Research Letters, 32 (2004), 574580. doi: 10.1016/j.orl.2004.03.001. 
[3] 
J. G. Dai, On positive Harris recurrence of multiclass queueing network: A unified approach via fluid limit models, Annals of Applied Probability, 5 (1995), 4977. doi: 10.1214/aoap/1177004828. 
[4] 
J. G. Dai, A fluidlimit model criterion for instability of multiclass queueing networks, Annals of Applied Probability, 6 (1996), 751757. doi: 10.1214/aoap/1034968225. 
[5] 
J. G. Dai, J. J. Hasenbein and B. Kim, Stability of jointheshortestqueue networks, Queueing Systems, 57 (2007), 129145. doi: 10.1007/s1113400790465. 
[6] 
G. I. Falin, A survey of retrial queues, Queueing Systems Theory Appl., 7 (1990), 127167. doi: 10.1007/BF01158472. 
[7] 
G. I. Falin and J. G. C. Templeton, "Retrial Queues," Chapman & Hall, London, 1997. 
[8] 
R. Foley and D. McDonald, Join the shortest queue: Stability and exact asymptotics, Ann. Appl. Probab., 11 (2001), 569607. doi: 10.1214/aoap/1015345342. 
[9] 
S. Foss and N. Chernova, On the stability of a partially accessible multistation queue with statedependent routing, Queueing Systems Theory Appl., 29 (1998), 5573. doi: 10.1023/A:1019175812444. 
[10] 
Q.M. He, H. Li and Y. Q. Zhao, Ergodicity of the $BMAP$/$PH$/$s$/$s+K$ retrial queue PHretrial times, Queueing Systems Theory Appl., 35 (2000), 323247. doi: 10.1023/A:1019110631467. 
[11] 
B. Kim and I. Lee, Tests for nonergodicity of denumerable continuous time Markov processes, Computers and Mathematics with Applications, 55 (2008), 13101321. doi: 10.1016/j.camwa.2007.07.003. 
[12] 
I. A. Kurkova, A loadbalanced network with two servers, Queueing Systems, 37 (2001), 379389. doi: 10.1023/A:1010841517511. 
[13] 
T. PhungDuc, H. Masuyama, S. Kasahara and Y. Takahashi, Performance analysis of optical burst switched networks with limitedrange wavelength conversion, retransmission and burst segmentation, Journal of the Operations Research Society of Japan, 52 (2009), 5874. 
[14] 
Yu. M. Sukhov and N. D. Vvedenskaya, Fast Jackson networks with dynamic routing, Problems of Information Transmission, 38 (2002), 136153. doi: 10.1023/A:1020010710507. 
[15] 
T. Yang and J. G. C. Templeton, A survey of retrial queues, Queueing Systems Theory Appl., 2 (1987), 201233. doi: 10.1007/BF01158899. 
show all references
References:
[1] 
M. Bramson, Stability of two families of queueing networks and a discussion of fluid limits, Queueing Systems Theory Appl., 28 (1998), 731. doi: 10.1023/A:1019182619288. 
[2] 
B. D. Choi and B. Kim, Nonergodicity criteria for denumerable continuous time Markov processes, Operations Research Letters, 32 (2004), 574580. doi: 10.1016/j.orl.2004.03.001. 
[3] 
J. G. Dai, On positive Harris recurrence of multiclass queueing network: A unified approach via fluid limit models, Annals of Applied Probability, 5 (1995), 4977. doi: 10.1214/aoap/1177004828. 
[4] 
J. G. Dai, A fluidlimit model criterion for instability of multiclass queueing networks, Annals of Applied Probability, 6 (1996), 751757. doi: 10.1214/aoap/1034968225. 
[5] 
J. G. Dai, J. J. Hasenbein and B. Kim, Stability of jointheshortestqueue networks, Queueing Systems, 57 (2007), 129145. doi: 10.1007/s1113400790465. 
[6] 
G. I. Falin, A survey of retrial queues, Queueing Systems Theory Appl., 7 (1990), 127167. doi: 10.1007/BF01158472. 
[7] 
G. I. Falin and J. G. C. Templeton, "Retrial Queues," Chapman & Hall, London, 1997. 
[8] 
R. Foley and D. McDonald, Join the shortest queue: Stability and exact asymptotics, Ann. Appl. Probab., 11 (2001), 569607. doi: 10.1214/aoap/1015345342. 
[9] 
S. Foss and N. Chernova, On the stability of a partially accessible multistation queue with statedependent routing, Queueing Systems Theory Appl., 29 (1998), 5573. doi: 10.1023/A:1019175812444. 
[10] 
Q.M. He, H. Li and Y. Q. Zhao, Ergodicity of the $BMAP$/$PH$/$s$/$s+K$ retrial queue PHretrial times, Queueing Systems Theory Appl., 35 (2000), 323247. doi: 10.1023/A:1019110631467. 
[11] 
B. Kim and I. Lee, Tests for nonergodicity of denumerable continuous time Markov processes, Computers and Mathematics with Applications, 55 (2008), 13101321. doi: 10.1016/j.camwa.2007.07.003. 
[12] 
I. A. Kurkova, A loadbalanced network with two servers, Queueing Systems, 37 (2001), 379389. doi: 10.1023/A:1010841517511. 
[13] 
T. PhungDuc, H. Masuyama, S. Kasahara and Y. Takahashi, Performance analysis of optical burst switched networks with limitedrange wavelength conversion, retransmission and burst segmentation, Journal of the Operations Research Society of Japan, 52 (2009), 5874. 
[14] 
Yu. M. Sukhov and N. D. Vvedenskaya, Fast Jackson networks with dynamic routing, Problems of Information Transmission, 38 (2002), 136153. doi: 10.1023/A:1020010710507. 
[15] 
T. Yang and J. G. C. Templeton, A survey of retrial queues, Queueing Systems Theory Appl., 2 (1987), 201233. doi: 10.1007/BF01158899. 
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