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Exact analysis of a split--merge queue with latent Erlang-factor dependent subtask times
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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BibTeX
@misc{zerom2026exact,
title = {{Exact analysis of a split--merge queue with latent Erlang-factor dependent subtask times}},
author = {Dawit Zerom},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21146},
eprint = {2609.21146},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21146},
}
RIS
TY - UNPB
TI - Exact analysis of a split--merge queue with latent Erlang-factor dependent subtask times
AU - Dawit Zerom
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.21146
UR - https://arxiv.org/abs/2609.21146
AB - 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.
ER -