Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2016, Number 6, Pages 55–59 (Mi vmumm196)  
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Limit theorems for queueing systems with infinite number of servers and group arrival of requests

E. Chernsvakaya

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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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.
Received: 13.04.2016
English version:
Moscow University Mathematics Bulletin, 2016, Volume 71, Issue 6, Pages 257–260
DOI: https://doi.org/10.3103/S0027132216060073
Bibliographic databases:
Document Type: Article
UDC: 511
Language: Russian
Citation: E. Chernsvakaya, “Limit theorems for queueing systems with infinite number of servers and group arrival of requests”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2016, no. 6, 55–59; Moscow University Mathematics Bulletin, 71:6 (2016), 257–260
Citation in format AMSBIB
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