Year: 2026
Type: preprint
Abstract: We study multiserver queues with Marshall--Olkin dependent service mechanisms, heterogeneous servers, and fixed idle-set assignment. An explicit matrix-analytic solution links the stationary queue distribution to departure and customer-delay laws. Waiting time conditional on delay is exactly exponential, and the stationary \chg{sojourn law has a phase-type representation with at most one more phase than the number of servers.} A consistency condition characterizes when Markovian completions admit a Poisson shock representation. For two three-server families with identical bivariate residual-service laws, we prove a conditional waiting-time ordering and identify when their unconditional waiting tails cross. The results show how higher-order dependence affects performance beyond marginal rates and pairwise service dependence.
Source: arXiv (Cornell University)
Authors: Bu, Qihui, Thapa, Suman, Zhao, Yiqiang Q.
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7165801972