On the GI/M/∞ queue with batch arrivals of constant size
暂无分享,去创建一个
In this note, the GI/M/∞ queue with batch arrivals of constant sizek is investigated. It is shown that the stationary probabilities that an arriving batch findsi customers in the system can be computed in terms of the corresponding binomial moments (Jordan's formula), which are determined by a recursive relation. This generalizes well-known results by Takács [12] for GI/M/∞. Furthermore, relations between batch arrival- and time-stationary probabilities are given.
[1] H. P. Galliher,et al. Dynamics of Two Classes of Continuous-Review Inventory Systems , 1959 .
[2] P. Franken,et al. Queues and Point Processes , 1983 .
[3] L. Takács. On the generalization of Erlang's formula , 1956 .
[4] V. Schmidt,et al. Queues and Point Processes , 1983 .
[5] John F. Reynolds. Letter to the Editor - Some Results for the Bulk-Arrival Infinite-Server Poisson Queue , 1968, Oper. Res..