We study a discrete-time model where each packet has a cost of not being sent -- this cost might depend on the packet content. We study the tradeoff between the age and the cost where the sender is confined to packet-based strategies. The optimal tradeoff is found by an appropriate formulation of the problem as a Markov Decision Process (MDP). We show that the optimal tradeoff can be attained with finite-memory policies and we devise an efficient policy iteration algorithm to find these optimal policies. We further study a related problem where the transmitted packets are subject to erasures. We show that the optimal policies for our problem are also optimal for this new setup. Allowing coding across packets significantly extends the packet-based strategies. We show that when the packet payloads are small, the performance can be improved by coding.

翻译：我们研究一个离散时间模型,每个包包都有不发送的成本 -- -- 这个成本可能取决于包包内容。 我们研究发件人限于基于包包的战略的年龄和成本之间的权衡。 最佳权衡是通过以Markov决定程序(MDP)对问题的适当表述找到的。 我们显示,通过有限模范政策可以实现最佳权衡。 我们设计了一个有效的政策循环算法,以找到这些最佳政策。 我们进一步研究了一个相关问题,即传送的包包要被删除。 我们显示,我们的问题的最佳政策也是这个新设置的最佳选择。 允许包包的编码大大扩展基于包件的战略。 我们显示,当包装有效载荷很小时,可以通过编码改进性能。