Abbreviation:
MCM: Mid-Call Mobility Problem; R_MCM: prediction result of MCM;
HRFR: Home Registrar Failure Restoration Problem; R_HRFR: prediction result of HRFR;
PCM: Pre-Call Mobility Problem; R_PCM: prediction result of PCM;
Predictor1 (CR): Predictor 1 at Phase III with input of a set of Calling Rules;
Predictor1 (MR): Predictor 1 at Phase III with input of a set of Moving Rules;
Predictor2 (MR): Predictor 2 at Phase III with input of a set of Moving Rules;
Output: Output of prediction result set;
Input:
The set of mobile host ∈ FM set with their corresponding MR;
The set of mobile host ∈ FCM set with their corresponding CR Output:
Adapted prediction results for MCM, HRFR and PCM Problems Pseudo Code:
STAMP_Online (FM_R, FCM_R) Begin
While every time a mobile host moves into a different domain, Do Set Output＝φ ;
While every time backup after Home Registrar crash, Do Set Output＝φ ;
IF MH ∈ FM set, Do
R_HRFR ← Predictor2 (MR);
Output ← R_HRFR;
Return Output;
End
Chapter 4.
Sequential Terminal Mobility Pattern Mining and Predicting (STAMP)
The literal meaning of “STAMP” indicates that once this algorithm is in use, no matter the transient packets or call requests will be definitely forwarded to where the user is most likely being located at present. The core of “STAMP” is to find the moving portfolios of those people who are at high-risk in advance so as to solve any of the three problems by adaptively online-predicting. Overall, the algorithm ultimately contributes to both fast handoff and smooth handoff for seamless mobility in SIP over WLAN.
4.1 Preprocessing — Adaptive High-Risk Sifting
Before getting into the principle part of “STAMP”, there is a prior phase for preprocessing. Why we need preprocessing? The reason lies in the reality that we should solve problems in an efficient way. Hence, the number of users for further phases depends on how many resources (power, load, and so forth) are currently available at the server. According to the performance status of the server, we can dynamically adjust the amount of users without any overhead at server’s side.
(However, the parameter adjustment remains a future work.)
Since Adaptive High-Risk Sifting (AHRS) phase aims at rescuing high-risk people. We define two mobile host sets. One is Frequent Moving (FM) set, which stands for Frequent Moving mobile hosts. The other is Frequent Calling while Moving (FCM) set, which represents Frequent Calling while Moving mobile hosts.
For each user belonging to FM set, it implies the users with higher moving frequency than others. That is, users in FM set are high-risk of HRFR Problem and PCM Problem, resulting in call failures. As a result, for FM set, we focus on finding users’ Moving Behavior. On the other hand, for each user belonging to FCM set, it suggests the users with higher calling while moving frequency than others. In other words, users in FCM set are high-risk of MCM Problem, resulting in packet loss.
Consequently, for FCM set, our concern is to find uses’ Calling Behavior. The main concept is illustrated in Figure 4.1
Figure 4.1 : Two sets of mobile users: FM set vs. FCM set
z Moving Frequency
Parameter: The Moving Frequency is defined as “Average Moving Occurrence Volume within per time period unit”.
ex: Within last year, Jenny moved 5000 times but Anny moved 1500 times in total; in other word, Jenny moves more frequently
than Anny.
z Moving while Calling Frequency
Parameter: The Moving while Calling Frequency is defined as
“Average Moving while Calling Occurrence Volume per call”. i.e., Velocity = Moving Occurrence Volume in CDR / Call Volume in CDR.
ex: Within last year, Jenny moved 2000 times in 1000 calls (Velocity = 2) while Anny moved 1000 times in 125 calls (Velocity = 8); in other words, Anny moves while calling at a much higher frequency.
z Moving Distribution
We suppose the moving distribution curve is depicted in Figure 4.2.
Figure 4.2
4.2
: Moving Frequency of FM or FCM set
Phase I — Partitioning & Filtering
We assume that the input of “STAMP” is the Moving History, on behalf of the individual registration lists, kept by Home Registrar. Each Moving History is composed of a sequence of tuples, (location, time), recording “at which moment”
the certain user moves into some different “domain”. As the input is a long record, it goes without saying that the reason why we need Phase I is obviously because the long record doesn’t convey any explicit information about “one meaningful moving behavior”, which is valuable information for further mining. Therefore, the objective of Partitioning & Filtering (P&F) phase is to transform these raw data into
available information.
Firstly, the “Partitioner” module partitions a long, meaningless personal Moving History of whomever in FM or FCM set into many valid Moving Sequences. Each Moving Sequence represents a moving behavior at one time. The
“Partitioner” segments out a meaningful Moving Sequence from the Moving History, based on two criteria: (1) If any two consecutive moving paths (Di-1 & Di) are not adjacent domains, then partition for the first time; (2) If the residence time of each domain Di-1 (i.e., ΔT＝Ti－Ti-1) is longer than a predefined or statistical maximal window size, then partition for the second time. The former criterion implies strict consistency with the Adjacent Property of Moving Pattern & Calling Pattern Definition at Section 3.3. The latter criterion suggests that the meaningful Moving Sequence should be limited within a time space, such as the interval from registration to deregistration or per day.
Lemma 1: Every two consecutive items in a Moving Sequence β＝<b1, b2, …, bn>, i.e., bi & bi+1, are adjacent domains.
Proof: Based on the definition of Adjacent Property of Moving Patterns and Calling Patterns in Section 3.3 as well as the fact that a mobile user could never cross a non-neighboring domain, it is easy to know the lemma is true.
□ Moreover, for people belonging to FCM set, the “Filter” module will further filter Calling Sequences via Call Detail Record. Each Calling Sequence stands for a moving behavior while calling.
Lemma 2: For every Calling Sequence α＝<a1, a2, …, am>, there exists a Moving Sequence β＝<b1, b2, …, bn> such that the Calling Sequence α is the Consecutive
Subsequence of the Moving Sequence β, denoted by α ⊆ β.
Proof: Each Calling Sequence records the moving behavior of a mobile user within the same call session, and is filtered from some Moving Sequence by the Call Detail Record, so the above lemma is true.
□ Theorem 1: Given a mobile user p, there exists a Moving History γp of the mobile user, a set of Moving Sequences M p＝{β1, β2, …, βm}, and a set of Calling Sequences C p＝{α1, α2, …, αn}, such that αi ⊆ βj ⊆ γp, where 1≦i≦n, 1≦j≦m, and i, j belong to integer.
Proof: It follows from the Adjacent Property, Lemma 1, and Lemma 2, thoroughly constituting the Phase I — Partitioning and Filtering, thus it is definitely true.
□ The whole process of both Partitioner and Filter modules is illustrated in the following example, Figure 4.3. Regarding the phase operation, refer to Algorithm 3.
Figure 4.3 : Example of Phase I - Partitioning & Filtering