$.$ Suppose a switch is built using a computer workstation and that it can forward packets at a rate of $500,000$ packets per second, regardless $($within limits$)$ of size. Assume the workstation uses direct memory access $($DMA$)$ to move data in and out of its main memory, which has a bandwidth of $2$ Gbps$,$ and that the I$/$O bus has a bandwidth of $1$ Gbps$.$ At what packet size would the bus bandwidth become the limiting factor?