Large deviations of multiclass M/G/1 queues |
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Authors: | André Dabrowski Jiyeon Lee David R McDonald |
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Institution: | 1. Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario, Canada K1N 6N5;2. Department of Statistics, Yeungnam University, Kyeongbuk 712‐749, Republic of Korea |
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Abstract: | Consider a multiclass M/G/1 queue where queued customers are served in their order of arrival at a rate which depends on the customer class. We model this system using a chain with states represented by a tree. Since the service time distribution depends on the customer class, the stationary distribution is not of product form so there is no simple expression for the stationary distribution. Nevertheless, we can find a harmonic function on this chain which provides information about the asymptotics of this stationary distribution. The associated h‐transformation produces a change of measure that increases the arrival rate of customers and decreases the departure rate thus making large deviations common. The Canadian Journal of Statistics 37: 327–346; 2009 © 2009 Statistical Society of Canada |
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Keywords: | Change of measure h transform multiclass queues quasi‐stationarity rare events MSC 2000: Primary 60K25 secondary 60K20 |
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