Asymptotically Optimal Admission Control of a Queue with Impatient Customers

References

• Afanas'eva L. G. On the existence of a limit distribution in queueing systems with bounded sojourn time. Teor. Verojatnostej Primenen. (1965) 10:570–578Google Scholar
• Ata B., Kumar S. Heavy traffic analysis of open processing networks with complete resource pooling: Asymptotic optimality of discrete review policies. Ann. Appl. Probab. (2005) 15:331–391Crossref, Google Scholar
• Baccelli F., Boyer P., Hebuterne G. Single-server queues with impatient customers. Adv. Appl. Probab. (1984) 16:887–905Crossref, Google Scholar
• Baykal-Gursoy M., Xiao W. Stochastic decomposition in M/M/∞ queues with Markov modulated service rates. Queueing Systems (2004) 48:75–88Crossref, Google Scholar
• Bell S. L., Williams R. J. Dynamic scheduling of a system with two parallel servers in heavy traffic with resource pooling: Asymptotic optimality of a threshold policy. Ann. Appl. Probab. (2001) 11:608–649Crossref, Google Scholar
• Bell S. L., Williams R. J. Dynamic scheduling of a parallel server system with complete resource pooling: Asymptotic optimality of a threshold policy. Electronic J. Probab. (2004) 10:1044–1115Google Scholar
• Billingsley P.Convergence of Probability Measures (1999) 2nd ed.(John Wiley & Sons, New York) Crossref, Google Scholar
• Budhiraja A., Ghosh A. P. A large deviations approach to asymptotically optimal control of crisscross network in heavy traffic. Ann. Appl. Probab. (2005) 15(3):1887–1935Crossref, Google Scholar
• Chen M., Pandit C., Meyn S. P. In search of sensitivity in network optimization. Queueing Systems (2003) 44(4):313–363Crossref, Google Scholar
• Dai J. G., Dai W. A heavy traffic limit theorem for a class of open queueing networks with finite buffers. Queueing Systems (1999) 32:5–40Crossref, Google Scholar
• Daley D. J. General customer impatience in the queue GI/G/1. J. Appl. Probab. (1965) 2:186–205Crossref, Google Scholar
• Garnett O., Mandelbaum A., Reiman M. I. Designing a call center with impatient customers. Manufacturing Service Oper. Management (2002) 4:208–227Link, Google Scholar
• Gut A.Stopped Random Walks: Limit Theorems and Applications. Applied Probability (1988) 5(Springer-Verlag, New York) Crossref, Google Scholar
• Harrison J. M.Brownian Motion and Stochastic Flow Systems (1985) (Krieger, Malabar, FL) Google Scholar
• Harrison J. M., Fleming W., Lions P. L. Brownian models of queueing networks with heterogeneous customer populations. Stochastic Differential Systems, Stochastic Control Theory and Applications. IMA Volumes in Mathematics and Its Applications (1988) 10(Springer-Verlag, New York) 147–186Crossref, Google Scholar
• Harrison J. M., Lopez M. J. Heavy traffic resource pooling in parallel-server systems. Queueing Systems (1999) 33:339–368Crossref, Google Scholar
• Harrison J. M., Taksar M. I. Instantaneous control of Brownian motion. Math. Oper. (1982) 8:439–453Link, Google Scholar
• Harrison J. M., Wein L. M. Scheduling networks of queues: Heavy traffic analysis of a simple open network. Queueing Systems (1989) 5:265–280Crossref, Google Scholar
• Harrison J. M., Wein L. M. Scheduling networks of queues: Heavy traffic analysis of a two-station closed network. Oper. Res. (1990) 38:1052–1064Link, Google Scholar
• Karatzas I., Shreve S. E.Brownian Motion and Stochastic Calculus (1991) 2nd ed.(Springer, New York) Google Scholar
• Kovalenko I. N. Some queueing problems with restrictions. J. Appl. Probab. (1965) 2:204–208Google Scholar
• Kruk L., Lehoczky J., Ramanan K., Shreve S. An explicit formula for the Skorodhod map on [0, a]. Annals Probab. (2007) 35(5):1740–1768Crossref, Google Scholar
• Kumar S. Two-server closed networks in heavy traffic: Diffusion limits and asymptotic optimality. Ann. Appl. Probab. (2000) 10:930–961Crossref, Google Scholar
• Kumar S., Muthuraman M. A numerical method for solving singular stochastic control problems. Oper. Res. (2004) 52(4):563–582Link, Google Scholar
• Lillo R. E., Martin M. Stability in queues with impatient customers. Stochastic Models (2001) 17:357–389Crossref, Google Scholar
• Lorden G. On excess over the boundary. Ann. Math. Statist. (1970) 41:520–527Crossref, Google Scholar
• Mandelbaum A., Stolyar A. L. Scheduling flexible servers with convex delay costs: Heavy-traffic optimality of the generalized cμ rule. Oper. Res. (2004) . ForthcomingGoogle Scholar
• Martins L. F., Shreve S. E., Soner H. M. Heavy traffic convergene of a controlled, multiclass queueing system. SIAM J. Control Optim. (1996) 34(6):2133–2171Crossref, Google Scholar
• Palm C. Etude des delais d'attente. Ericsson Technics (1937) 5:37–56Google Scholar
• Polyanin A. D., Zaitsev V. F.Handbook of Exact Solutions for Ordinary Differential Equations (1995) (CRC Press, Boca Raton, FL) Google Scholar
• Reed J., Ward A. R., Srikat R., Voulgaris G. A diffusion approximation for a generalized Jackson network with reneging. Proc. 42nd Annual Allerton Conf. Commun., Control, Comput. (2004) Monticello, ILGoogle Scholar
• Reed J., Ward A. R. Approximating the GI/GI/1+GI queue with a nonlinear drift diffusion: Hazard rate scaling in heavy traffic. Math. Oper. Res. (2006) . ForthcomingGoogle Scholar
• Skorokhod A. V. Stochastic equations for diffusions in a bounded region. Theor. Probab. Its Appl. (1961) 6:264–274Crossref, Google Scholar
• Slater L. J., Abramowitz M., Stegun I. A. Confluent hypergeometric functions. Handbook of Mathematical Functions (1972) (Dover, New York) 503–536Google Scholar
• Stanford R. E. Reneging phenomena in single channel queues. Math. Oper. Res. (1979) 4:162–178Link, Google Scholar
• Stolyar A. L. Maxweight scheduling in a generalized switch: State space collapse and workload minimization in heavy traffic. Ann. Appl. Probab. (2004) 14(1):1–53Crossref, Google Scholar
• Ward A. R., Glynn P. W. A diffusion approximation for a Markovian queue with reneging. Queueing Systems (2003) 43:103–128Crossref, Google Scholar
• Ward A. R., Glynn P. W. A diffusion approximation for a GI/GI/1 queue with balking or reneging. Queueing Systems (2005) 50:371–400Crossref, Google Scholar
• Weerasinghe A. A bounded variation control problem for diffusion processes. SIAM J. Control Optim. (2005) 44(2):389–417Crossref, Google Scholar
• Whitt W.Stochastic-Process Limits (2002) (Springer, New York) Crossref, Google Scholar
• Zeltyn S., Mandelbaum A. Call centers with impatient customers: Many-server asymptotics of the M/M/N+G queue. Queueing Systems (2006) . ForthcomingGoogle Scholar