The Israeli queue with a general group-joining policy (Q2095197)

The study of the paper under review is devoted to a variant of a so-called `Israeli queue' that has been originally introduced in [\textit{O. Boxma} et al., Stoch. Models 24, No. 4, 604--625 (2008; Zbl 1158.60040)]. The Israeli queue is a multi-queueing system, in which the server first visits the queue with the ``oldest'' customer. The authors consider a single-server multi-queue system with unlimited-size batch service, where the next queue to be served is the one with the most senior customer (the aforementioned `Israeli queue'). The described system is a Markovian system with state-dependent group-joining policy, for which the authors derive results for various performance measures, such as steady-state distribution of the number of groups in the system, sojourn times, group sizes, and lengths of busy periods. Closed-form expressions are obtained for both the uniform and geometric joining policies. Numerical results are presented.