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The areas under workload process and under queuing process in a single serverqueue over the busy period have many applications not only in queuing theorybut also in risk theory or percolation theory. We focus here on the tailbehaviour of distribution of these two integrals. We present various openproblems and conjectures, which are supported by partial results for somespecial cases.

Tail behaviour of the area under a random process, with applications to queueing systems, insurance and percolations