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Staffing of time-varying queues to achieve time-stable performance (2005)

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by Z. Feldman , A. Mandelbaum , W. A. Massey , W. Whitt
Citations:20 - 13 self
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@TECHREPORT{Feldman05staffingof,
    author = {Z. Feldman and A. Mandelbaum and W. A. Massey and W. Whitt},
    title = {Staffing of time-varying queues to achieve time-stable performance },
    institution = {},
    year = {2005}
}

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Abstract

Continuing research by Jennings, Mandelbaum, Massey and Whitt (1996), we investigate methods to perform time-dependent staffing for many-server queues. Our aim is to achieve time-stable performance in face of general time-varying arrival rates. It turns out that it suffices to target a stable probability of delay. That procedure tends to produce time-stable performance for several other operational measures. Motivated by telephone call centers, we focus on many-server models with customer abandonment, especially the Markovian Mt/M/st + M model, having an exponential time-to-abandon distribution (the +M), an exponential servicetime distribution and a nonhomogeneous Poisson arrival process. We develop three different methods for staffing, with decreasing generality and decreasing complexity: First, we develop a simulation-based iterativestaffing algorithm (ISA), and conduct experiments showing that it is effective. The ISA is appealing because it applies to very general models and is automatically validating: we directly see how well it works. Second, we extend the square-root-staffing rule, proposed by Jennings et al., which is based on the associated infinite-server model. The rule dictates that the staff level at time t be st = mt + β √ mt, where mt is the offered load (mean number of busy servers in the infinite-server model) and the constant β reflects the service grade. We show that the service grade β in the staffing formula can be represented as a function of the target delay probability α by

Citations

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22 Heavy traffic limits for queues with many deterministic servers. Queueing Syst. Theory Appl - Jelenković, Mandelbaum, et al. - 2004
21 A staffing algorithm for call centers with skill-based routing. Manufacturing Service Oper.Management 7(4 - Wallace, Whitt - 2005
20 Estimating the parameters of a nonhomogeneous poisson process with linear rate - Massey, Parker, et al. - 1996
19 The pointwise stationary approximation for Mt/Mt/s queues is asymptotically correct as the rates increase - Whitt - 1991
17 Peak congestion in multi-server service systems with slowly varying arrival rates. Queueing Systems 25 - Massey, Whitt - 1997
15 Improving the SIPP Approach for Staffing Service Systems that have Cyclic Demand - Green, Kolesar, et al. - 2001
15 The impact of a heavy-tailed service-time distribution upon the M/GI/s waiting-time distribution, Queueing Systems 36 - Whitt - 2000
14 Stochastic Processes, second edition - Ross - 1997
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2 Modeling the M(t)/M/s(t) Queue with an Exhaustive Discipline. Available at: http : //www.bus.ualberta.ca/aingolfsson/workingpapers.htm - Ingolfsson - 2002
1 The pointwise stationary approximation for M t/M t/s queues is asymptotically correct as the rates increase. Management Sci - Whitt - 1991
1 Momcilovic P. 2004. Heavy Traffic Limits for Queues with Many Deterministic Servers - Jelenkovic, Mandelbaum
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