🤖 AI Summary
研究了具有潜在Erlang因子依赖子任务时间的两服务器拆分-合并队列问题，通过精确分析得到完成时间和平均等待时间，并证明独立性会高估平均等待时间。
📝 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.