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We consider a status update communication system consisting of asource-destination link. A stochastic process is observed at the source, wheresamples are extracted at random time instances, and delivered to thedestination, thus, providing status updates for the source. In this paper, weexpand the concept of information ageing by introducing the cost of updatedelay (CoUD) metric to characterize the cost of having stale information at thedestination. The CoUD captures the freshness of the information at thedestination and can be used to reflect the information structure of the source.Moreover, we introduce the value of information of update (VoIU) metric thatcaptures the reduction of CoUD upon reception of an update. Using the CoUD, itsby-product metric called peak cost of update delay (PCoUD), and the VoIU, weevaluate the performance of an M/M/1 system in various settings that considerexact expressions and bounds. Our results indicate that the performance of CoUDdiffers depending on the cost assigned per time unit, however the optimalpolicy remains the same for linear ageing and varies for non-linear ageing.When it comes to the VoIU the performance difference appears only when the costincreases non-linearly with time. The study illustrates the importance of thenewly introduced variants of age, furthermore supported in the case of VoIU byits tractability.

The Cost of Delay in Status Updates and their Value: Non-linear Ageing