Continuity of a queueing integral representation in the M1 topology

Annals of Applied Probability

Volumn 20, Issue 1, 2010, Pages 214-237

  Pang, Guodong ^a   Whitt, Ward ^a  

^a Columbia University ^*  (United States)

Author keywords

Bursty arrival processes; Continuous mapping theorem; Heavy traffic limits; Many server queues; Skorohod M1 topology

Indexed keywords

EID: 76449105590     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/09-AAP611     Document Type: Article

References (8)

1. BILLINGSLEY, P. (1999). Convergence of Probability Measures, 2nd ed. Wiley, New York. MR1700749
2. ETHIER, S. N. and KURTZ, T. G. (1986). Markov Processes: Characterization and Convergence. Wiley, New York. MR838085
3. KELLA, O. and WHITT, W. (1990). Diffusion approximations for queues with server vacations. Adv. in Appl. Probab. 22 706-729. MR1066971
4. 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
5. PANG, G. and WHITT, W. (2009). Heavy-traffic limits for many-server queues with service interruptions. Queueing Syst. 61 167-202. MR2485887
6. ROYDEN, H. L. (1968). Real Analysis, 2nd ed. Macmillan, New York. MR0151555
7. SKOROHOD, A. V. (1956). Limit theorems for stochastic processes. Theory Probab. Appl. 1 261-290. MR0084897
8. WHITT, W. (2002). Stochastic-Process Limits. Springer, New York. MR1876437