Stochastic modelling and analysis: a computational approach
Stochastic modelling and analysis: a computational approach
Introduction to queueing theory (2nd ed)
Introduction to queueing theory (2nd ed)
Subexponential loss rates in a GI/GI/1 queue with applications
Queueing Systems: Theory and Applications
Heavy-traffic analysis for the GI/G/1 queue with heavy-tailed distributions
Queueing Systems: Theory and Applications
An overview of Brownian and non-Brownian FCLTs for the single-server queue
Queueing Systems: Theory and Applications
Performance evaluation of a single node with general arrivals and service
ASMTA'11 Proceedings of the 18th international conference on Analytical and stochastic modeling techniques and applications
Input uncertainty in outout analysis
Proceedings of the Winter Simulation Conference
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We establish heavy-traffic stochastic-process limits for the queue-length and overflow stochastic processes in the standard single-server queue with finite waiting room (G/G/1/K). We show that, under regularity conditions, the content and overflow processes in related single-server models with finite waiting room, such as the finite dam, satisfy the same heavy-traffic stochastic-process limits. As a consequence, we obtain heavy-traffic limits for the proportion of customers or input lost over an initial interval. Except for an interchange of the order of two limits, we thus obtain heavy-traffic limits for the steady-state loss proportions. We justify the interchange of limits in M/GI/1/K and GI/M/1/K special cases of the standard GI/GI/1/K model by directly establishing local heavy-traffic limits for the steady-state blocking probabilities.