In this paper,we investigate the trade-offs between delay and capacity in mobile wireless networks with infrastructure support.We consider three different mobility models,independent and identically distributed (i.i.d) mobility model,random walk mobility model with constant speed and L’evy flight mobility model.For i.i.d mobility model and random walk mobility model with the speed θ(1/n～(1/2)),,we get the theoretical results of the average packet delay when capacityis θ(1),θ(1/n～(1/2)) individually,where n is the number of nodes.We find that the optimal average packet delay is achieved whencapacity λ(n) <(1/(2.n.log_2(1/((1-e)-(k/n))+1)),where K is the number of gateways.It is proved that average packet delay D(n) dividedby capacity λ(n) is bounded below by (n/(k·w)).When ω(n～(1/2))≤KO(n((1-η)·(α+1))/2)ln n) when K=o(n～η)(0≤η<1).We also provethat when ω(1/2)≤K O (n ((1-η) · (α + 1)) / 2) ln n) when K = o (n ~ η) (0≤η <1) .We also prolethat when ω (1/2) ≤K