Minimizing the Maximum Expected Waiting Time in a Periodic Single-Server Queue with a Service-Rate Control

References

• Adusumilli KM, Hasenbein JJ (2010) Dynamic admission and service rate control of a queue. Queueing Systems 66(2):131–154.Google Scholar
• Asmussen S (2003) Applied Probability and Queues, 2nd ed. (Springer, New York).Google Scholar
• Asmussen S, Glynn PW (2007) Stochastic Simulation, 2nd ed. (Springer, New York).Google Scholar
• Bertsimas D, Mourtzinou G (1997) Transient laws of nonstationary queueing systems and their applications. Queueing Systems 25(1–4):115–155.Google Scholar
• Billingsley P (1999) Convergence of Probability Measures (John Wiley & Sons, New York).Google Scholar
• Chen H, Mandelbaum A (1991) Discrete flow networks: Bottleneck analysis and fluid approximations. Math. Oper. Res. 16(2):408–446.Link, Google Scholar
• Choudhury GL, Mandelbaum A, Reiman MI, Whitt W (1997) Fluid and diffusion limits for queues in slowly changing random environments. Stochastic Models 13(1):121–146.Google Scholar
• Defraeye M, van Nieuwenhuyse I (2013) Controlling excessive waiting times in small service systems with time-varying demand: An extension of the ISA algorithm. Decision Support Systems 54(4):1558–1567.Google Scholar
• Falin GI (1989) Periodic queues in heavy traffic. Adv. Appl. Probab. 21(2):485–487.Google Scholar
• Feldman Z, Mandelbaum A, Massey WA, Whitt W (2008) Staffing of time-varying queues to achieve time-stable performance. Management Sci. 54(2):324–338.Link, Google Scholar
• Fralix BH, Riano G (2010) A new look at transient versions of Little’s law. J. Appl. Prob. 47(02):459–473.Google Scholar
• Fu MC, ed. (2015) Handbook of Simulation Optimization, International Series in Operations Research and Management Science, vol. 216 (Springer, New York).Google Scholar
• George JM, Harrison JM (2001) Dynamic control of a queue with adjustable service rate. Oper. Res. 49(5):720–731.Link, Google Scholar
• He B, Liu Y, Whitt W (2016) Staffing a service system with non-Poisson nonstationary arrivals. Probab. Engrg. Inform. Sci. 30(1):593–621.Google Scholar
• Heyman DP (1968) Optimal operating policies for M/G/1 queueing systems. Oper. Res. 16(2):362–382.Link, Google Scholar
• Jennings OB, Mandelbaum A, Massey WA, Whitt W (1996) Server staffing to meet time-varying demand. Management Sci. 42(10):1383–1394.Link, Google Scholar
• Jian N, Henderson SG (2015) An introduction to simulation optimization. Yilmaz L, Chan WKV, Moon I, Roeder TMK, Macal C, Rossetti MD, eds. Proc. 2015 Winter Simulation Conf. (ACM, New York), 1780–1794.Google Scholar
• Kleinrock L (1964) Communication Nets: Stochastic Message Flow and Delay (Dover, New York).Google Scholar
• Kwon S, Gautam N (2016) Guaranteeing performance based on time stability for energy-efficient data centers. IIE Trans. 48(9):812–825.Google Scholar
• Liu Y (2018) Staffing to stabilize the tail probability of delay in service systems with time-varying demand. Oper. Res. 66(2):514–534.Link, Google Scholar
• Liu Y, Whitt W (2011) A network of time-varying many-server fluid queues with customer abandonment. Oper. Res. 59(4):835–846.Link, Google Scholar
• Liu Y, Whitt W (2012a) The Gt/GI/st+GI many-server fluid queue. Queueing Systems 71(4):405–444.Google Scholar
• Liu Y, Whitt W (2012b) Stabilizing customer abandonment in many-server queues with time-varying arrivals. Oper. Res. 60(6):1551–1564.Link, Google Scholar
• Loynes RM (1962) The stability of a queue with non-independent inter-arrival and service times. Math. Proc. Cambridge Philos. Soc. 58(3):497–520.Google Scholar
• Ma N, Whitt W (2015) Using simulation to study service-rate controls to stabilize performance in a single-server queue with time-varying arrival rate. Yilmaz L, Chan WKV, Moon I, Roeder TMK, Macal C, Rossetti MD, eds. Proc. 2015 Winter Simulation Conf. (ACM, New York), 1–12.Google Scholar
• Ma N, Whitt W (2016) Efficient simulation of non-Poisson non-stationary point processes to study queueing approximations. Statist. Probab. Lett. 102:202–207.Google Scholar
• Ma N, Whitt W (2018) A rare-event simulation algorithm for periodic single-server queues. INFORMS J. Comput. 30(1):71–89.Link, Google Scholar
• Massey WA, Whitt W (1994) Unstable asymptotics for nonstationary queues. Math. Oper. Res. 19(2):267–291.Link, Google Scholar
• Nieuwenhuis G (1989) Equivalence of functional limit theorems for stationary point processes and their Palm distributions. Probab. Theoret. Related Fields 81(4):593–608.Google Scholar
• Pender J, Massey WA (2017) Approximating and stabilizing dynamic rate Jackson networks with abandonment. Probab. Engrg. Inform. Sci. 31(01):1–42.Google Scholar
• Puhalskii A (1994) On the invariance principle for the first passage time. Math. Oper. Res. 19(4):946–954.Link, Google Scholar
• Rolski T (1981) Queues with nonstationary input stream: Ross’s conjecture. Adv. Appl. Probab. 13(03):603–618.Google Scholar
• Rolski T (1989) Queues with nonstationary inputs. Queueing Systems 5(1–3):113–129.Google Scholar
• Sigman K (1995) Stationary Marked Point Processes: An Intuitive Approach (Chapman and Hall/CRC, New York).Google Scholar
• Sigman K, Whitt W (2019) Marked point processes in discrete time. Queuing Systems 92(1–2):47–81.Google Scholar
• Stolletz R (2008) Approximation of the nonstationary M(t)/M(t)/c(t)-queue using stationary models: The stationary backlog-carryover approach. Eur. J. Oper. Res. 190(2):478–493.Google Scholar
• Sun X, Whitt W (2018) Delay-based service differentiation with many servers and time-varying arrival rates. Stochastic Systems 8(3):230–263.Link, Google Scholar
• Suriadi S, Wynn MT, Xu J, van der Aalst WMP, ter Hofstede AHM (2017) Discovering work prioritization patterns from event logs. Decision Support Systems 100:77–92.Google Scholar
• Whitt W (1971) Weak convergence theorems for priority queues: Preemptive-resume discipline. J. Appl. Probab. 8(1):74–94.Google Scholar
• Whitt W (2002) Stochastic-Process Limits (Springer, New York).Google Scholar
• Whitt W (2014) Heavy-traffic limits for queues with periodic arrival processes. Oper. Res. Lett. 42(6–7):458–461.Google Scholar
• Whitt W (2015) Stabilizing performance in a single-server queue with time-varying arrival rate. Queueing Systems 81(4):341–378.Google Scholar
• Whitt W (2018) Time-varying queues. Queueing Models Service Management 1(2):79–164.Google Scholar
• Whitt W, Zhang X (2019) Periodic Little’s law. Oper. Res. 67(1):267–280.Link, Google Scholar
• Yadin M, Naor P (1963) Queueing systems with a removable service station. Oper. Res. Quart. 14(4):393–405.Google Scholar