Analysis of polling systems
Polling and greedy servers on a line
Queueing Systems: Theory and Applications
Light-traffic analysis for queues with spatially distributed arrivals
Mathematics of Operations Research
Queueing analysis of polling models: progress in 1990-1994
Frontiers in queueing
Polling on a space with general arrival and service time distribution
Operations Research Letters
Queueing Systems: Theory and Applications
The M/G/∞ system revisited: finiteness, summability, long range dependence, and reverse engineering
Queueing Systems: Theory and Applications
Computational Geometry: Theory and Applications
Stability and performance of greedy server systems
Queueing Systems: Theory and Applications
Continuous polling with rerouting and applications to ferry assisted wireless LANs
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
Proceedings of the Winter Simulation Conference
Mixed polling with rerouting and applications
Performance Evaluation
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A snowblower is circling a closed-loop racetrack, driving clockwise and clearing off snow in a constant snowblowing rate. Both the snowfall and the snowblower's driving speed vary randomly (in both space and time coordinates). The snowblower's motion and the snowload profile on the racetrack are co-dependent and co-evolve, resulting in a coupled stochastic dynamical system of ‘random motion (snowblower) in a random environment (snowload profile)’. Snowblowing systems are closely related to continuous polling systems – or, so-called, polling systems on the circle – which are the continuum limits of ‘standard’ polling systems. Our aim in this manuscript is to introduce a stochastic model that would apply to a wide class of stochastic snowblower-type systems and, simultaneously, generalize the existing models of continuous polling systems. We present a general snowblowing-system model, with arbitrary Lévy snowfall and arbitrary snowblower delays, and study it by analyzing an underlying stochastic Poincaré map governing the system's evolution. The log-Laplace transform and mean of the Poincaré map are computed, convergence to steady state (equilibrium) is proved, and the system's equilibrium behavior is explored.