MX/G/1/∞ single-server queueing system with random volume customers and multiple vacations

In the present paper, we investigate the model of a single-server queueing system with unlimited queue (of MX /G/1/∞-type), random volume customers, unlimited memory buffer and multiple vacations. In analyzed system, arriving customers (that form Poisson entrance flow of groups of customers) transport some information measured in bytes so they are assumed to be additionally characterized by some non-negative random volume. Customer’s service time generally depends on his volume. Information delivered by a customer is written out into dedicated unlimited memory buffer until customer ends his service. In addition, in considered system the mechanism of multiple vacations is implemented which means that server can have some breaks (rests) for a random period of time but breaks begin only in the moments when there is no customer present in the system. The above-mentioned mechanism has obvious influence on customer’s waiting time and, in consequence, on customers’ total volume. For the introduced model, we obtain general formula for the steady-state customers’ total volume distribution in the terms of Laplace–Stieltjes transforms as well as formulae defining its first two moments. Analysis of some interesting, practical special cases of the model and numerical computations are attached as well together with examples of possible applications of the model regarding real telecommunication or computer systems.