The reason why you see paging by IMSI in real-world GSM networks

During my work on airprobe and OsmocomBB I've been wondering why you see paging by IMSI in real-world GSM networks.

A quick recap: The IMSI is the world-wide unique serial number of your SIM. Since it is easy to identify and track people, the TMSI was introduced as a temporary identifier that is frequently re-allocated over encrypted channels. The only reason for the TMSI to exist is to prevent tracking of a subscriber by watching where his IMSI appears on the paging channel.

According to the theory, the IMSI is only used when first registering to any GSM network. At that time, a TMSI is allocated to the SIM card in the phone, and this TMSI is used for the next transaction(s). Later, this TMSI is re-allocated and re-allocated, but the IMSI shouldn't show up again in any paging requests.

Even if you switch mobile networks (i.e. in the roaming case), you would once send the IMSI as part of a LOCATION UPDATE REQUEST or IDENTITY RESPONSE, but the network has no need to page the SIM by IMSI.

So far the theory. If you look at the Paging Channel (PCH) of cells in real-world networks, you see a significant (10-20%) amount of paging requests that contain paging by IMSI. This seems strange on first sight, given the theory described above.

I have the following plausible explanation for this:

• The VLR keeping the IMSI-TMSI mappings doesn't have non-volatile storage. This means at a VLR restart, all the TMSI allocations will be lost, and the network has to resort to paging by IMSI.
• The VLR has a limited amount of RAM, which can store a limited number of IMSI-TMSI mappings. Especially if the operator is interested in saving money, the amount of memory is insufficient for all subscribers in the network. This means, the VLR will expire some old entries in the mapping table to store new entries. Thus, mobile phones whose last transaction with the GSM network was relatively long ago are likely candidates for such VLR expiration. Once a phone for an expired entry needs to be paged again, paging will happen by IMSI.
• Last, but not least: GSM networks do not page a phone by the last known cell, but by the last known location area of the phone. A location area might be relatively big. This means that at any cell you will see a lot of paging messages, even for phones that are not even anywhere near this cell. If there is no response within the location area, the MSC might decide to do paging on a larger radius, possibly the entire MSC area. Since such MSC-wide paging is likely to occur for phones that haven't shown activity for a long time (and thus might have moved or disappeared without properly unregistering from the network), those are the exact same phones for which the IMSI-TMSI mappings have expired from the VLR. Thus, the rate of paging-by-IMSI looks disproportionately high.

So the relatively high percentage of paging by IMSI vs. TMSI should not be taken as a measurement with regard to the total number of transactions or even the total number of subscribers. It is simply the mechanics of the network resulting in a distortion of those figures caused by phones that have never properly unregistered from the network.