Regenerative Analysis of a System with a Random Volume of Customers

We study a general multi-server system in which each customer has service time and a random volume. We consider two main cases: (i) the total volume of the present customers is unlimited and (ii) this volume is upper bounded by a finite constant. For this system, using the regenerative approach, we develop performance analysis. We establish a solidarity property of the basic processes: accumulated volume, waiting time (workload) and queue size. In case (i), we prove an analog of Little’s formula and, provided the system is single-server and the input is Poisson, the Pollaczeck-Khintchine formula. In case (ii), we suggest an approximation of the Pollaczeck-Khintchine formula, which is then verified by simulation.