The pointwise stationary approximation for M1/M1/s
Management Science
Some effects of nonstationarity on multiserver Markovian queueing systems
Operations Research
Mt/G/∞ queues with sinusoidal arrival rates
Management Science
The physics of the Mt/G/ ∞ symbol Queue
Operations Research
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Queueing Systems: Theory and Applications
The impact of a heavy-tailed service-time distribution upon the M/GI/s waiting-time distribution
Queueing Systems: Theory and Applications
Optimal Pricing and Admission Control in a Queueing System with Periodically Varying Parameters
Queueing Systems: Theory and Applications
Evaluating the transient behavior of queueing systems via simulation and transfer function modeling
Proceedings of the 40th Conference on Winter Simulation
Using different response-time requirements to smooth time-varying demand for service
Operations Research Letters
Transient analysis of general queueing systems via simulation-based transfer function modeling
Proceedings of the Winter Simulation Conference
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In this paper we consider the M_t /G/\infty queueing model with infinitely many servers and a nonhomogeneous Poisson arrival process. Our goal is to obtain useful insights and formulas for nonstationary finite-server systems that commonly arise in practice. Here we are primarily concerned with the peak congestion. For the infinite-server model, we focus on the maximum value of the mean number of busy servers and the time lag between when this maximum occurs and the time that the maximum arrival rate occurs. We describe the asymptotic behavior of these quantities as the arrival changes more slowly, obtaining refinements of previous simple approximations. In addition to providing improved approximations, these refinements indicate when the simple approximations should perform well. We obtain an approximate time-dependent distribution for the number of customers in service in associated finite-server models by using the modified-offered-load (MOL) approximation, which is the finite-server steady-state distribution with the infinite-server mean serving as the offered load. We compare the value and lag in peak congestion predicted by the MOL approximation with exact values for M_t/M/s delay models with sinusoidal arrival-rate functions obtained by numerically solving the Chapman–Kolmogorov forward equations. The MOL approximation is remarkably accurate when the delay probability is suitably small. To treat systems with slowly varying arrival rates, we suggest focusing on the form of the arrival-rate function near its peak, in particular, on its second and third derivatives at the peak. We suggest estimating these derivatives from data by fitting a quadratic or cubic polynomial in a suitable interval about the peak.