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., [12]) 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 [8] 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. Numerical examples for packetized voice in a broadband network are included. The enhanced technique is also applicable to other communication and computer systems that can be characterized by similar functional equations.