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About this paper
Philip Doldo, Jamol Pender
Doldo and Pender derive a fixed-point equation and closed-form approximations to quantify the amplitude of queue length oscillations in service systems where customers receive periodically updated information. Their analysis, applied to N-parallel queues, reveals how system parameters influence oscillation magnitude and uncovers distinct bifurcation behaviors for even versus odd numbers of queues.
Key insights
- The non-stationary and piecewise continuous nature of the delay function in periodically updated queueing systems necessitates new analytical methods for amplitude characterization.
- For N=2, the relationship between minimum and maximum queue lengths simplifies to a fixed-point equation, $L+U=\rho$.
- Multi-queue systems (N>2) exhibit structured oscillatory behavior, with queues dividing into two out-of-phase groups, the characteristics of which depend on whether N is even or odd.
Summary by alphaXiv.
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