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In Part I of this paper, the optimal throughput-delay tradeoff for static wireless networks was shown to be 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 tradeoff captures the essential network dynamics, packets need to scale down with the network size. In this "fluid model, " no buffers are required. Due to this packet scaling, D(n) does not correspond to the average delay per bit. This leads to the question whether the tradeoff remains the same when the packet size is kept constant, which necessitates packet scheduling in the network. In this correspondence, this question is answered in the affirmative by showing that the optimal throughput-delay tradeoff 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 queuing network and analyzing the corresponding delay. Our method consists of deriving packet schedules in the discrete-time network by devising a corresponding continuous-time network and then analyzing the delay induced in the actual discrete network using results from queuing theory for continuous-time networks.