Fast Discrete-Event Simulation of Markovian Queueing Networks through Euler Approximation
CoRR(2024)
摘要
The efficient management of large-scale queueing networks is critical for a
variety of sectors, including healthcare, logistics, and customer service,
where system performance has profound implications for operational
effectiveness and cost management. To address this key challenge, our paper
introduces simulation techniques tailored for complex, large-scale Markovian
queueing networks. We develop two simulation schemes based on Euler
approximation, namely the backward and forward schemes. These schemes can
accommodate time-varying dynamics and are optimized for efficient
implementation using vectorization. Assuming a feedforward queueing network
structure, we establish that the two schemes provide stochastic upper and lower
bounds for the system state, while the approximation error remains bounded over
the simulation horizon. With the recommended choice of time step, we show that
our approximation schemes exhibit diminishing asymptotic relative error as the
system scales up, while maintaining much lower computational complexity
compared to traditional discrete-event simulation and achieving speedups up to
tens of thousands times. This study highlights the substantial potential of
Euler approximation in simulating large-scale discrete systems.
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