Thesis (Ph. D.)--University of Washington, 2000The role of timing information is considered as the key to an information theoretic understanding of communication networks. In this dissertation, we focus on the analysis of problems related to timing information in data networks from an information theoretic perspective.One problem is that of identifying the timing capacity of network components, i.e. the maximum information rate achievable by encoding information in the timing of packets. We first consider the timing capacity of discrete-time queues in which at most one packet may arrive or finish service in a slot, and demonstrate the extremal nature of the geometric service time distribution among such queues. We then analyze a discrete-time queueing model with batch arrivals and a batch service mechanism that is related to the leaky bucket flow control system. Within this model, we obtain a closed form expression for the timing capacity of the queue that can serve a geometrically distributed number of packets in a slot. We also establish a connection between the extremal nature of the geometric server and a queueing theoretic property of such queues. Finally, we obtain an upper bound to the timing capacity of a queueing system with multiple servers having i.i.d. geometrically distributed packet service times.Another problem is that of quantifying the amount of information about the times at which messages arrive at the source that must be transmitted to the destination to enable it to decode the messages within a finite amount of time. Suppose that messages are transmitted one at a time, and are decoded in the same order they arrived at the source. By viewing the message arrival and decoding processes as the arrival and departure processes from a hypothetical single-server queue, we can associate a service time with each message. The rate-distortion function of the message arrival process with message service time as the distortion measure is a lower bound for the amount of information about message arrival times that the receiver must receive. We explicitly obtain this rate-distortion function for the Poisson message arrival process
