Staffing of Time-varying Queues to Achieve Time-stable Performance Unabridged Version: Internet Supplement
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چکیده
This is a longer version of a paper with the same title, which has been submitted to Management Science. Abstract from the Journal Versionfrom the Journal Version This paper develops methods to determine appropriate staffing levels in call centers and other many-server queueing systems with time-varying arrival rates. The goal is to achieve targeted time-stable performance, even in the presence of significant time-variation in the arrival rates. The main contribution is a flexible simulation-based iterative-staffing algorithm (ISA) for the Mt/G/st + G model with nonhomogeneous Poisson arrival process (the Mt) and customer abandonment (the +G). For Markovian Mt/M/st + M special cases, the ISA is shown to converge. For that Mt/M/st+M model, simulation experiments show that the ISA yields timestable delay probabilities across a wide range of target delay probabilities. With ISA, other performance measures such as agent utilizations, abandonment probabilities and average waiting times are stable as well. The ISA staffing and performance agree closely with the modified-offered-load (MOL) approximation, which was previously shown to be an effective staffing algorithm without customer abandonment. While the ISA algorithm so far has only been extensively tested for Mt/M/st + M models, it can be applied much more generally, to Mt/G/st + G models and beyond. What is Contained Here? This longer version presents more examples; e.g., it treats the Mt/M/st model (without customer abandonment) and the Mt/M/st + M model with θ > μ and θ < μ, where θ is the abandonment rate and μ is the service rate. It treats the challenging example from Jennings et al. (1996). There is extra detail for the previous examples; there are 47 figures here, but only 10 in the journal version. This longer version also provides additional theoretical support.
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Electronic Companion — “ Staffing of Time - Varying Queues to Achieve Time - Stable Performance
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