Approximating the GI/GI/1+GI Queue with a Nonlinear Drift Diffusion: Hazard Rate Scaling in Heavy Traffic
Published Online:4 Aug 2008https://doi.org/10.1287/moor.1070.0303
References
- Drift rate control of a Brownian processing system. Ann. Appl. Probab. (2005) 15(2):1145–1160Crossref, Google Scholar
- Single-server queues with impatient customers. Adv. Appl. Probab. (1984) 16:887–905Crossref, Google Scholar
- Convergence of Probability Measures (1999) 2nd ed.(John Wiley and Sons, Inc., New York) Crossref, Google Scholar
- Statistical analysis of a telephone call center: A queueing-science perspective. J. Amer. Statist. Association (2005) 100:36–50Crossref, Google Scholar
- Fundamentals of Queueing Networks: Performance, Asymptotics, and Optimization (2001) (Springer-Verlag, New York) Crossref, Google Scholar
- A heavy traffic limit theorem for a class of open queueing networks with finite buffers. Queueing Systems (1999) 32:5–40Crossref, Google Scholar
- Real-time queues in heavy traffic with earliest-deadline-first queue discipline. Ann. Appl. Probab. (2001) 11:332–378Crossref, Google Scholar
- A criterion for invariant measures of Markov processes. Z. Wahrsch. Verw. Gebiete (1982) 61:1–16Crossref, Google Scholar
- Designing a call center with impatient customers. Manufacturing and Service Oper. Management (2002) 4:208–227Link, Google Scholar
- Martingale Limit Theory and Its Applications (1980) (Academic Press, New York) Google Scholar
- Brownian Motion and Stochastic Flow Systems (1985) (John Wiley and Sons, New York) Google Scholar
- Multiple channel queues in heavy traffic, Parts I and II. Adv. Appl. Probab. (1970) 2:150–177355364Crossref, Google Scholar
- Brownian Motion and Stochastic Calculus (1991) 2nd ed.(Springer-Verlag, New York) Google Scholar
- The single server queue in heavy traffic. Proc. Cambridge Philos. Soc. (1961) 57:902–904Crossref, Google Scholar
- On queues in heavy traffic. J. Roy. Statist. Soc. Ser. B (1962) 24:383–392Google Scholar
- Accuracy of state space collapse for earliest-deadline-first queues. Ann. Appl. Probab. (2006) 16(2):516–581Crossref, Google Scholar
- An explicit formula for doubly reflected processes in [0, a]. Ann. Probab. (2007) 35(5):1740–1768Crossref, Google Scholar
- Multiple-input heavy-traffic real-time queues. Ann. Appl. Probab. (2003) 13(1):54–99Crossref, Google Scholar
- Earliest-deadline-first service in heavy traffic acyclic networks. Ann. Appl. Probab. (2004) 14(3):1306–1352Crossref, Google Scholar
- Real-time queueing theory. Proc. IEEE Real-Time Systems Sympos. (1997) (IEEE, San Francisco) 186–195Crossref, Google Scholar
- Stability in queues with impatient customers. Stochastic Models (2001) 17:375–389Crossref, Google Scholar
- A model for rational abandonment from invisible queues. Queueing Systems (2000) 36:141–173Crossref, Google Scholar
- Etude des delais d'attente. Ericsson Technics (1937) 5:37–56Google Scholar
- A diffusion approximation for a generalized Jackson network with reneging. Proc. 42nd Allerton Conf. Comm., Control, and Comput. (2004) Monticello, ILGoogle Scholar
- , Disney R. L., Ott T. J. The heavy traffic diffusion approximation for sojourn times in Jackson networks. Applied Probability-Computer Science, The Interface (1982) (Birkhauser, Boston) Crossref, Google Scholar
- , Baccelli F., Fayolle G. Some diffusion approximations with state space collapse. Modelling and Performance Evaluation Methodology (1984) (Springer-Verlag, New York) 209–240Crossref, Google Scholar
- A Probability Path (1999) (Birkhauser, Boston) Google Scholar
- Stochastic equations for diffusions in a bounded region 1, Parts 1 and 2. Theoret. Probab. Its Appl. (1961) 6:264–274Crossref, Google Scholar
- Reneging phenomena in single channel queues. Math. Oper. Res. (1979) 4:162–178Link, Google Scholar
- On stability of queueing networks with job deadlines. J. Appl. Probab. (2003) 40:293–304Crossref, Google Scholar
- A diffusion approximation for a Markovian queue with reneging. Queueing Systems (2003a) 43:103–128Crossref, Google Scholar
- Properties of the reflected Ornstein-Uhlenbeck process. Queueing Systems (2003b) 44:109–123Crossref, Google Scholar
- A diffusion approximation for a GI/GI/1 queue with balking or reneging. Queueing Systems (2005) 50:371–400Crossref, Google Scholar
- Asymptotically optimal admission control of a queue with impatient customers. Math. Oper. Res. (2008) 33(1):167–202Link, Google Scholar
- Stochastic-Process Limits (2002) (Springer-Verlag, New York) Crossref, Google Scholar
- Heavy-traffic limits for loss proportions in single-server queues. Queueing Systems (2004) 46:507–536Crossref, Google Scholar
- Engineering solution of a basic call center model. Management Sci. (2005) 51(2):221–235Link, Google Scholar
- Call centers with impatient customers: Many-server asymptotics of the M/M/n+G queue. Queueing Systems (2005) 51(3/4):361–402Crossref, Google Scholar
- Adaptive behavior of impatient customers in tele-queues: Theory and empirical support. Management Sci. (2002) 48(4):566–583Link, Google Scholar

