Abstract:
We consider an infinite-server queueing system where customers come by groups of random size at random i.d. intervals of time. The number of requests in a group and intervals between their arrivals can be dependent. We assume that service times have a regularly varying distribution with infinite mean. We obtain limit theorems for the number of customers in the system and prove limit theorems under approariate normalizations.
Key words:infinite-server queuing system, service times with heavy-tailed distribution, distribution of the number of customers in the system, regenerative flow.
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