Busy period, virtual waiting time and number of customers in G|M|1|B system

Victor Kadankov (1) , Tetyana Kadankova (2)

1 Institute of Mathematics of NAS of Ukraine
2 Center for Statistics

In this article, we determine the integral transforms of several two-boundary functionals for a difference of a compound Poisson process and a compound renewal process. Another part of the article is devoted to studying the above-mentioned process reflected at its infimum. We use the results obtained to study a G|M|1|B system with batch arrivals and finite buffer in the case when ∼ge(). We derive the distributions of the main characteristics of the queuing system, such as the busy period, the time of the first loss of a customer, the number of customers in the system, the virtual waiting time in transient and stationary regimes. The advantage is that these results are given in a closed form, namely, in terms of the resolvent sequences of the process.

Mots clés: Busy period; Time of the first loss of the customer; First exit time; Value of the overshoot; Linear component; Resolvent sequence; 60G40; 60K20

Domaines: Réseaux et télécommunications [cs.NI]

Victor Kadankov, Tetyana Kadankova. Busy period, virtual waiting time and number of customers in G|M|1|B system. Queueing Systems, 2010, 65 (2), pp.175-209. ⟨10.1007/s11134-010-9170-5⟩. ⟨hal-00686343⟩