Analyzing the Impact of Storage Shortage on Data Availability in Decentralized Online Social Networks

Table 1

The notations that are used in the derivation.

Notations

Descriptions

The user

The number of the user’s friends

Current time point

Target time point in near future, , where is a time duration after . We want to predict the state of the DOSN at the time point

The time point at which the user goes offline

The set of all online users in the friend circle of the user at current time

The number of online users in set

The set of all offline users in the friend circle of the user at current time

The number of offline users in set

The latest login time of the online user in before current time

The first logout time of the online user in after current time

The latest logout time of the offline user in before current time

The first login time of the offline user in after current time

The login and logout events, respectively. When any of these two events occurs, the state of a user changes from OFFLINE to ONLINE or from ONLINE to OFFLINE

The time duration of a user being online continuously (i.e., the time duration from an event to the following event), which is a random variable and whose probability density function and probability distribution function are denoted by and , respectively

The time duration of a user being offline, which is also a random variable and whose probability density function and probability distribution function are denoted by and , respectively

The number of times that the user publishes the data, which is a discrete random variable and whose probability density function in a duration t is denoted by

The statistical average size of the data published by the user each time. is a constant

The replication degree, that is, the number of replicas created for each data item

The publishing time of the oldest data stored in the storage pool

SS

The total storage capacity contributed by all online friends

S

The maximum storage capacity that each friend is able to contribute

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