Abstract
We consider a multiple server queueing loss system where the service times of server i are exponential with rate μ i , where μ i decreases in i. Arrivals have associated vectors (X 1, …, X n ) of binary variables, with X i = 1 indicating that server i is eligible to serve that arrival. Arrivals finding no idle eligible servers are lost. Letting I j be the indicator variable for the event that the jth arrival enters service, we show that, for any arrival process, the policy that assigns arrivals to the smallest numbered idle eligible server stochastically maximizes the vector (I 1, …, I r ) for every r if the eligibility vector of arrivals is either (a) exchangeable, or (b) a vector of independent variables for which P(X i = 1) increases in i.
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