Load-Dependent Service Queues with Application to Congestion Control in Broadband Networks

We analyze 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 (e.g., [SMS91]) 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, we first derive a functional equation that characterizes the response time for an arbitrary arrival. Then, we employ and extend a technique based on Laguerre functions in [LE90] to solve the equation. A new recursion is developed in this paper, which significantly simplifies and enhances the applicability of the technique, and makes it easy to program on computers.