In this work, we consider the problem of jointly minimizing the average cost of sampling and transmitting status updates by users over a wireless channel subject to average Age of Information (AoI) constraints. Errors in the transmission may occur and a scheduling policy has to decide if the users sample a new packet or attempt for retransmission of the packet sampled previously. The cost consists of both sampling and transmission costs. The sampling of a new packet after a failure imposes an additional cost on the system. We formulate a stochastic optimization problem with the average cost in the objective under average AoI constraints. To solve this problem, we propose three scheduling policies; a) a dynamic policy, that is centralized and requires full knowledge of the state of the system, b) two stationary randomized policies that require no knowledge of the state of the system. We utilize tools from Lyapunov optimization theory in order to provide the dynamic policy, and we prove that its solution is arbitrary close to the optimal one. In order to provide the randomized policies, we model the system by utilizing Discrete Time Markov Chain (DTMC). We provide closed-form and approximated expressions for the average AoI and its distribution, for each randomized policy. Simulation results show the importance of providing the option to transmit an old packet in order to minimize the total average cost.
翻译:在这项工作中,我们考虑的问题是,在信息的平均年龄限制下,共同尽量减少用户在无线频道上对无线频道进行取样和传送情况更新的平均平均费用;传输可能发生错误,时间安排政策必须决定用户是抽样新包还是试图对以前抽样的包进行再传送;费用包括抽样和传输费用;在失败后对新包进行取样使系统产生额外费用;我们根据AoI平均限制下的目标平均费用,以随机化优化问题为标准优化问题。为了解决这个问题,我们提出了三项时间安排政策;a) 动态政策,该政策是集中的,需要充分了解系统的状况;b) 两项固定的随机化政策,不需要对系统的状况有所了解;我们利用Lyapunov优化理论的工具来提供动态政策,我们证明其解决办法与最佳政策相近。为了提供随机化的政策,我们利用Discrete Tim Markov 链(DMC)来模拟系统。我们提供了一种封闭式和大概的表达方式,要求完全了解系统的状况;b) 两项固定式的随机政策,不需要了解系统状况;我们提供平均分配价格,以显示其全部格式,以显示AMIAsalalalsalsalsaldalsalsalsalsalsionaldaldal。