한국데이터정보과학회:학술대회논문집
- 한국데이터정보과학회 2006년도 PROCEEDINGS OF JOINT CONFERENCEOF KDISS AND KDAS
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- Pages.43-47
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- 2006
Exact Asymptotics in a Multi-class M/G/1 Queue
- 이지연 (영남대학교) ;
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- Lee, Ji-Yeon (Department of Statistics, Yeungnam University) ;
- Dabrowski, Andre (Department of Mathematics and Statistics, University of Ottawa) ;
- McDonald, David R. (Department of Mathematics and Statistics, University of Ottawa)
- 발행 : 2006.04.28
초록
Consider a multitype queue where queued customers arc served in their order of arrival at a rate which depends on the customer type. Here we calculate the sharp asymptotics of the probability the total number of customers in the queue reaches a high level before emptying. The natural state space to describe this queue is a tree whose branches increase in length as the number of customers in the queue grows. Consequently it is difficult to prove a large deviation principle. Moreover, since service rates depend on the customer type the stationary distribution is not of product form so there is no simple expression for the stationary distribution. Instead, we use a change of measure technique which increases the arrival rate of customers and decreases the departure rate thus making large deviations common.