Limit Theorems for Queueing Systems with Infinite Number of Servers and Group Arrival of Requests / E. A. Chernavskaya. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2016. № 6. P. 55-59 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 257-260].

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 appropriate normalizations.

Key words: infinite-server queuing system, service times with heavy-tailed distribution, distribution of the number of customers in the system, regenerative flow.