2020
DOI: 10.48550/arxiv.2008.00625
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Non-Stationary Queues with Batch Arrivals

Abstract: Motivated by applications that involve setting proper staffing levels for multi-server queueing systems with batch arrivals, we present a thorough study of the queue-length process {Q(t); t ≥ 0}, departure process {D(t); t ≥ 0}, and the workload process {W (t); t ≥ 0} associated with the M Bt t /G t /∞ queueing system, where arrivals occur in batches, with the batch size distribution varying with time. Notably, we first show that both Q(t) and D(t) are equal in distribution to an infinite sum of independent, s… Show more

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