Status Updating with Time Stamp Errors

A status updating system is considered in which multiple processes are sampled and transmitted through a shared channel. Each process has its dedicated server that processes its samples before time stamping them for transmission. Time stamps, however, are prone to errors, and hence the status updates received may not be credible. Our setting models the time stamp error rate as a function of the servers' busy times. Hence, to reduce errors and enhance credibility, servers need to process samples on a relatively prolonged schedule. This, however, deteriorates timeliness, which is captured through the age of information (AoI) metric. An optimization problem is formulated whose goal to characterize the optimal processes' schedule and sampling instances to achieve the optimal trade-off between timeliness and credibility. The problem is first solved for a single process setting, where it is shown that a threshold-based sleep-wake schedule is optimal, in which the server wakes up and is allowed to process newly incoming samples only if the AoI surpasses a certain threshold that depends on the required timeliness-credibility trade-off. Such insights are then extended to the multi-process setting, where two main scheduling and sleep-wake policies, namely round-robin scheduling with threshold-waiting and asymmetric scheduling with zero-waiting, are introduced and analyzed.