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Patterns of buffer overflow in a class of queues with long memory in the input stream. (English) Zbl 0905.60070
The authors consider a G/G/1/$$L$$ queue with finite buffer capacity $$L$$ and determine time to buffer overflow. The arrival process is produced by an on/off source with heavy tailed on-distribution. The mean time to overflow increases polynomially fast with increasing capacity $$L$$, contrary to the classical case with light tales for the on-distribution. Pooling of resources in case of superposition of several such arrival processes is investigated.