Queues in DOCSIS cable modem networks

In this paper we determine the optimal fraction c* of the uplink channel capacity that should be dedicated to the contention channel in a DOCSIS cable network in order to minimize its mean response time. For this purpose, we have developed an open queueing network with a non-standard form of blocking consisting of tens to hundreds of nodes. The network contains several types of customers that enter the network at various points according to a Markovian arrival process with marked customers. One of the main building blocks of the model exists in capturing the behavior of the conflict resolution algorithm by means of a single processor sharing queue. To assess the performance characteristics of this open queueing network we rely on an advanced decomposition technique that is specifically designed to deal with the Markovian nature of the arrival pattern. Several simulations are run to confirm the accuracy of the decomposition technique. We also explore the impact of a variety of systems parameters, e.g., the number of cable modems, the initial backoff window size, the correlation structure of the arrival process, the mean packet sizes, etc., on the optimal fraction c*.