Throughput-delay scaling in wireless networks with constant-size packets

In previous work (2004), we characterized the optimal throughput-delay trade-off in static wireless networks as D(n) = Theta(nT(n)), where D(n) and T(n) are the average packet delay and throughput in a network of n nodes, respectively. While this trade-off captured the essential network dynamics, packets needed to scale down with the network size. In this "fluid model", no buffers were required. Due to this packet scaling, D(n) did not correspond to the average delay per bit. That led to the question whether the trade-off remains the same when the packet size is kept constant, which necessitates buffers and packet scheduling in the network. In this paper, we answer this question in the affirmative by showing that the optimal throughput-delay trade-off is still D(n) = Theta(nT(n)), where now D(n) is the average delay per bit. Packets of constant size necessitate the use of buffers in the network, which in turn requires scheduling packet transmissions in a discrete-time queueing network and analyzing the corresponding delay. Our method consists of deriving packet schedules in the discrete-time network by looking at a corresponding continuous-time network and then analyzing the delay induced in the actual discrete network using results from queueing theory for continuous-time networks