Before revision:  We also establish an impossibility result: we show that zero queueing delay cannot be achieved if d = e^{o\left(\frac{\log N{\log k}\right)}} \left({\left({\log k}}\right)}\right) .
After revision:  We also establish an impossibility result: we show that zero queueing delay cannot be achieved if d = e^{o\left(\frac{\log N{\log k}\right)}} \exp\left({\left({\log k}}\right)}\right) .