Data storage times Consider a three-tier sensor network. The first tier generates the raw data and keeps it for a period T1. It passes to the second tier its decisions and associated likelihoods. The second tier keeps these for a period T2>T1. It may also request raw data from the first tier within T1, with a probability p1¼0.1. If it does so, the data are stored for a period T2. The second tier passes to the third tier its decisions and associated likelihoods. The third tier requests raw data with probability 0.8 if tier 2 had requested raw data, or 0.02 otherwise. Such a request, if it occurs, is generated with certainty within T2 with uniform probability on time.

(a) What value of T1 (with respect to T2) is required if raw data requests from the third tier must be met with probability 0.9?

(b) Suppose that, in fact, requests to higher tiers for raw data are related to the closeness of the decisions (i.e., first and second choices have similar likelihoods).

Devise an adaptive procedure to adjust storage times, assuming costs are known for failing to meet data requests or for taking memory away from other node operations.