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 as a congestion control in broadband networks. The idea there is to reduce the packet (cell) transmission time in case of congestion, while maintaining a 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 proposed by Leung and Eisenberg (1990) 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. 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