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arXiv · 2609.21146

Exact analysis of a split--merge queue with latent Erlang-factor dependent subtask times

Dawit Zerom
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Abstract

This paper studies a two-server split--merge queue with positively dependent subtask service times modeled through a latent-factor bivariate Erlang construction. An exact characterization of the split--merge completion time is obtained, including explicit formulas for its first two moments and the resulting mean waiting time. Under fixed marginal service-time distributions, independence is shown to stochastically increase the completion time and hence overestimate mean waiting time. Numerical illustrations show that this benchmark gap can be substantial.

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Dawit Zerom. 2026-09-17. Exact analysis of a split--merge queue with latent Erlang-factor dependent subtask times. https://arxiv.org/abs/2609.21146

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