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A LIFO queue in heavy traffic. (English) Zbl 1015.60079
The author analyzes the heavy-traffic behaviour of an M/G/1 last-in-first-out preemptive resume queue using measure-valued processes developed by J.-F. Le Gall and Y. Le Jan [Ann. Probab. 26, No. 4, 1407-1432 (1998; Zbl 0945.60090)]. This approach captures all the relevant information about evolution of the queue. The heavy-traffic diffusion approximation for the residual services measure and queue-length process are derived.
MSC:
60K25Queueing theory
90B22Queues and service (optimization)
60J80Branching processes