Abstract
We consider M/M/l-PS queues where the arrival rate is a function of the instantaneous number of customers using the system. We obtain asymptotic approximations to the first two moments of the response time, conditioned on both the total service time and the number of customers in the system at time of arrival. In addition, we remove the conditioning on the number at time of arrival to obtain approximations to the response time conditioned on the service time only. Our approximations are valid for systems with small mean service requests and a rapid arrival rate that depends weakly on the number of customers present. Both open and closed systems are considered.
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