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Volumn 20, Issue 5, 2010, Pages 1854-1890

Many-server diffusion limits for G/Ph/n+GI queues

Author keywords

Customer abandonment; Efficiency driven regime; Halfin whitt regime; Many server heavy traffic; Multi server queues; Phase type distribution; Quality and efficiency driven regime

Indexed keywords


EID: 77957706923     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/09-AAP674     Document Type: Article
Times cited : (54)

References (35)
  • 2
    • 0007262360 scopus 로고
    • On limit laws for service processes in multi-channel systems
    • MR0222973
    • BOROVKOV, A. A. (1967). On limit laws for service processes in multi-channel systems. Sibirsk. Mat. J. 8 746-763. MR0222973
    • (1967) Sibirsk. Mat. J. , vol.8 , pp. 746-763
    • Borovkov, A.A.1
  • 3
    • 77953086430 scopus 로고    scopus 로고
    • Customer abandonment in many-server queues
    • DAI, J. G. and HE, S. (2010). Customer abandonment in many-server queues. Math. Oper. Res. 35 347-362.
    • (2010) Math. Oper. Res. , vol.35 , pp. 347-362
    • Dai, J.G.1    He, S.2
  • 4
    • 77957714887 scopus 로고    scopus 로고
    • State space collapse in many-server diffusion limits of parallel server systems in many-server limits
    • Available at
    • DAI, J. G. and TEZCAN, T. (2005). State space collapse in many-server diffusion limits of parallel server systems in many-server limits. Preprint. Available at http://www2.isye.gatech.edu/~dai/publications/ssc-mor100324.pdf.
    • (2005) Preprint
    • Dai, J.G.1    Tezcan, T.2
  • 5
    • 50249152331 scopus 로고    scopus 로고
    • Optimal control of parallel server systems with many servers in heavy traffic
    • MR2430811
    • DAI, J. G. and TEZCAN, T. (2008). Optimal control of parallel server systems with many servers in heavy traffic. Queueing Syst. 59 95-134. MR2430811
    • (2008) Queueing Syst. , vol.59 , pp. 95-134
    • Dai, J.G.1    Tezcan, T.2
  • 7
    • 49449088914 scopus 로고    scopus 로고
    • Steady-state analysis of a multiserver queue in the Halfin-Whitt regime
    • MR2433709
    • GAMARNIK, D. and MOMČILOVIĆ, P. (2008). Steady-state analysis of a multiserver queue in the Halfin-Whitt regime. Adv. in Appl. Probab. 40 548-577. MR2433709
    • (2008) Adv. in Appl. Probab. , vol.40 , pp. 548-577
    • Gamarnik, D.1    Momčilović, P.2
  • 9
    • 0019560371 scopus 로고
    • Heavy-traffic limits for queues with many exponential servers
    • MR629195
    • HALFIN, S. and WHITT, W. (1981). Heavy-traffic limits for queues with many exponential servers. Oper. Res. 29 567-588. MR629195
    • (1981) Oper. Res. , vol.29 , pp. 567-588
    • Halfin, S.1    Whitt, W.2
  • 10
    • 0014756893 scopus 로고
    • Multiple channel queues in heavy traffic. I
    • MR0266331
    • IGLEHART, D. L. and WHITT, W. (1970). Multiple channel queues in heavy traffic. I. Adv. in Appl. Probab. 2 150-177. MR0266331
    • (1970) Adv. in Appl. Probab. , vol.2 , pp. 150-177
    • Iglehart, D.L.1    Whitt, W.2
  • 11
    • 3142745264 scopus 로고    scopus 로고
    • Heavy traffic limits for queues with many deterministic servers
    • MR2074672
    • JELENKOVIĆ, P., MANDELBAUM, A. and MOMČILOVIĆ, P. (2004). Heavy traffic limits for queues with many deterministic servers. Queueing Syst. 47 53-69. MR2074672
    • (2004) Queueing Syst. , vol.47 , pp. 53-69
    • Jelenković, P.1    Mandelbaum, A.2    Momčilović, P.3
  • 13
    • 77957695286 scopus 로고    scopus 로고
    • Fluid limits of many-server queues with reneging
    • To appear
    • KANG, W. N. and RAMANAN, K. (2010). Fluid limits of many-server queues with reneging. Ann. Appl. Probab. To appear.
    • (2010) Ann. Appl. Probab.
    • Kang, W.N.1    Ramanan, K.2
  • 15
    • 78651233746 scopus 로고    scopus 로고
    • Law of large numbers limits for many server queues
    • To appear
    • KASPI, H. and RAMANAN, K. (2010). Law of large numbers limits for many server queues. Ann. Appl. Probab. To appear.
    • (2010) Ann. Appl. Probab.
    • Kaspi, H.1    Ramanan, K.2
  • 16
    • 0002299055 scopus 로고
    • On the theory of queues with many servers
    • MR0066587
    • KIEFER, J. and WOLFOWITZ, J. (1955). On the theory of queues with many servers. Trans. Amer. Math. Soc. 78 1-18. MR0066587
    • (1955) Trans. Amer. Math. Soc. , vol.78 , pp. 1-18
    • Kiefer, J.1    Wolfowitz, J.2
  • 18
    • 0032264872 scopus 로고    scopus 로고
    • Strong approximations for Markovian service networks
    • MR1663767
    • MANDELBAUM, A., MASSEY, W. A. and REIMAN, M. I. (1998). Strong approximations for Markovian service networks. Queueing Syst. 30 149-201. MR1663767
    • (1998) Queueing Syst. , vol.30 , pp. 149-201
    • Mandelbaum, A.1    Massey, W.A.2    Reiman, M.I.3
  • 19
    • 77953106969 scopus 로고    scopus 로고
    • Queues with many servers and impatient customers
    • Available at
    • MANDELBAUM, A. and MOMČILOVIĆ, P. (2009). Queues with many servers and impatient customers. Preprint. Available at http://iew3.technion. ac.il/serveng/References/MM0309.pdf.
    • (2009) Preprint
    • Mandelbaum, A.1    Momčilović, P.2
  • 20
    • 0032221189 scopus 로고    scopus 로고
    • State-dependent stochastic networks. I. Approximations and applications with continuous diffusion limits
    • MR1624965
    • MANDELBAUM, A. and PATS, G. (1998). State-dependent stochastic networks. I. Approximations and applications with continuous diffusion limits. Ann. Appl. Probab. 8 569-646. MR1624965
    • (1998) Ann. Appl. Probab. , vol.8 , pp. 569-646
    • Mandelbaum, A.1    Pats, G.2
  • 21
    • 52949126577 scopus 로고    scopus 로고
    • Martingale proofs of many-server heavy-traffic limits for Markovian queues
    • MR2368951
    • PANG, G., TALREJA, R. and WHITT, W. (2007). Martingale proofs of many-server heavy-traffic limits for Markovian queues. Probab. Surv. 4 193-267. MR2368951
    • (2007) Probab. Surv. , vol.4 , pp. 193-267
    • Pang, G.1    Talreja, R.2    Whitt, W.3
  • 22
    • 76449113197 scopus 로고    scopus 로고
    • On many-server queues in heavy traffic
    • MR2582645
    • PUHALSKII, A. A. and REED, J. E. (2010). On many-server queues in heavy traffic. Ann. Appl. Probab. 20 129-195. MR2582645
    • (2010) Ann. Appl. Probab. , vol.20 , pp. 129-195
    • Puhalskii, A.A.1    Reed, J.E.2
  • 23
    • 0034207369 scopus 로고    scopus 로고
    • The multiclass GI/PH/N queue in the Halfin-Whitt regime
    • MR1778580
    • PUHALSKII, A. A. and REIMAN, M. I. (2000). The multiclass GI/PH/N queue in the Halfin-Whitt regime. Adv. in Appl. Probab. 32 564-595. MR1778580
    • (2000) Adv. in Appl. Probab. , vol.32 , pp. 564-595
    • Puhalskii, A.A.1    Reiman, M.I.2
  • 24
    • 73949131467 scopus 로고    scopus 로고
    • The G/GI/N queue in the Halfin-Whitt regime
    • MR2588244
    • REED, J. (2009). The G/GI/N queue in the Halfin-Whitt regime. Ann. Appl. Probab. 19 2211-2269. MR2588244
    • (2009) Ann. Appl. Probab. , vol.19 , pp. 2211-2269
    • Reed, J.1
  • 25
    • 0021481522 scopus 로고
    • Open queueing networks in heavy traffic
    • MR757317
    • REIMAN, M. I. (1984). Open queueing networks in heavy traffic. Math. Oper. Res. 9 441-458. MR757317
    • (1984) Math. Oper. Res. , vol.9 , pp. 441-458
    • Reiman, M.I.1
  • 26
    • 19744369999 scopus 로고    scopus 로고
    • Diffusions, Markov Processes, and Martingales
    • Cambridge Univ. Press, Cambridge. MR1780932
    • ROGERS, L. C. G. and WILLIAMS, D. (2000). Diffusions, Markov Processes, and Martingales. Cambridge Mathematical Library 2. Cambridge Univ. Press, Cambridge. MR1780932
    • (2000) Cambridge Mathematical Library , pp. 2
    • Rogers, L.C.G.1    Williams, D.2
  • 27
    • 0001353916 scopus 로고
    • Limit theorems for random walks, birth and death processes, and diffusion processes
    • MR0158440
    • STONE, C. (1963). Limit theorems for random walks, birth and death processes, and diffusion processes. Illinois J. Math. 7 638-660. MR0158440
    • (1963) Illinois J. Math. , vol.7 , pp. 638-660
    • Stone, C.1
  • 29
    • 77249151776 scopus 로고    scopus 로고
    • Dynamic control of N-systems with many servers: Asymptotic optimality of a static priority policy in heavy traffic
    • TEZCAN, T. and DAI, J. G. (2010). Dynamic control of N-systems with many servers: Asymptotic optimality of a static priority policy in heavy traffic. Oper. Res. 58 94-110.
    • (2010) Oper. Res. , vol.58 , pp. 94-110
    • Tezcan, T.1    Dai, J.G.2
  • 31
    • 8344231672 scopus 로고    scopus 로고
    • Efficiency-driven heavy-traffic approximations for many-server queues with abandonments
    • WHITT, W. (2004). Efficiency-driven heavy-traffic approximations for many-server queues with abandonments. Manag. Sci. 50 1449-1461.
    • (2004) Manag. Sci. , vol.50 , pp. 1449-1461
    • Whitt, W.1
  • 32
    • 84858522672 scopus 로고    scopus 로고
    • */n/m queue
    • MR2125135
    • */n/m queue. Math. Oper. Res. 30 1-27. MR2125135
    • (2005) Math. Oper. Res. , vol.30 , pp. 1-27
    • Whitt, W.1
  • 33
    • 33644523065 scopus 로고    scopus 로고
    • Fluid models for multiserver queues with abandonments
    • MR2201245
    • WHITT, W. (2006). Fluid models for multiserver queues with abandonments. Oper. Res. 54 37-54. MR2201245
    • (2006) Oper. Res. , vol.54 , pp. 37-54
    • Whitt, W.1
  • 34
    • 58149237635 scopus 로고    scopus 로고
    • Proofs of the martingale FCLT
    • MR2368952
    • WHITT, W. (2007). Proofs of the martingale FCLT. Probab. Surv. 4 268-302. MR2368952
    • (2007) Probab. Surv. , vol.4 , pp. 268-302
    • Whitt, W.1
  • 35
    • 77957704215 scopus 로고    scopus 로고
    • Ph. D. thesis, School of Industrial and Systems Engineering, Georgia Institute of Technology
    • ZHANG, J. (2009). Limited processor sharing queues and multi-server queues. Ph. D. thesis, School of Industrial and Systems Engineering, Georgia Institute of Technology.
    • (2009) Limited Processor Sharing Queues and Multi-server Queues
    • Zhang, J.1


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