移动边缘计算中资源供给不确定下的最优投资和定价问题

林德铭, 林姿琼, 郑艺峰, 杨敬民, 张文杰

Optimal investment and pricing under uncertain resource supply in mobile edge computing

Deming Lin, Ziqiong Lin, Yifeng Zheng, Jingmin Yang, Wenjie Zhang

表3 第一阶段最优能量收集时间策略

Table 3 Optimal energy harvesting time strategy in Phase I

时间 $T$ 取值	条件判断	最优时间 $T^{*}$	第一阶段最优利润 $R_{І}^{*} (T)$
$T \leq C V_{1}$	$P_{h} \leq α P_{c}$	$T^{*} = C V_{1}$	$R_{І} (T) = G + (α P_{c} - P_{h}) \times C V_{1}$
$T \leq C V_{1}$	$P_{h} > α P_{c}$	$T^{*} = 0$	$R_{І} (T) = G$
$C V_{1} \leq T \leq C V_{2}$	$E P < C V_{1}$	$T^{*} = C V_{1}$	$R_{І} (T) = \frac{α^{2}}{A} C V_{1}^{2} + (\frac{B α}{A} - P_{h}) \times C V_{1}$
	$C V_{1} < E P < C V_{2}$	$T^{*} = E P$	$R_{І} (T) = \frac{α^{2}}{A} E P^{2} + (\frac{B α}{A} - P_{h}) \times E P$
	$E P > C V_{2}$	$T^{*} = C V_{2}$	$R_{І} (T) = \frac{α^{2}}{A} C V_{2}^{2} + (\frac{B α}{A} - P_{h}) \times C V_{2}$
$T > C V_{2}$		$T^{*} = C V_{2}$	$R_{І} (T) = - \frac{B^{2}}{4 A} - C V_{2} \times P_{h}$