This paper analyzes D/G/1 and M/G/1 queues where the service time for an arrival depends on the amount of work in the system upon arrival. The models are motivated by the bit dropping methods as a congestion control in broadband networks. The idea there is to reduce packet (cell) transmission time in case of congestion, while maintaining satisfactory quality of service. To study the load-dependent-service queues, the authors first derive a functional equation that characterizes the response time for an arbitrary arrival. Then, they employ and extend a technique based on Laguerre functions in to solve the equation. A new recursion is developed which significantly simplifies and enhances the applicability of the technique, and makes it easy to program on computers.
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