A Standard Measure of Mobility for Evaluating Mobile Ad Hoc Network Performance By Joseph Charboneau Karthik Raman

MANET Unpredictable topology changes. Performance related to efficiency of routing protocol.  Performance studies are done with simulations.

Performance Measure Problem  There are many mobility models but not a unified quantitative “measure” of mobility.  Ex. A is the performance of protocol R1 using model M1. B is the performance of protocol R2 using model M2. There are two different models used so results can’t be compared between A and B.

Performance Measure (Cont.) Other studies are based on  Average speed  Maximum speed  Pause time  Rate of link changes  Mobility factor Problem  Still no unified quantitative measure of mobility.

Performance Measure (Cont.) The study approached in this paper is a solution for unified quantitative measure of mobility. Solution  Use a standard that is flexible and consistent. Flexible because the mobility measure can be customized by using a remoteness function. Consistent because mobility measure has a linear relationship to link change rate.

Remoteness Remoteness is based on the distance between two nodes.  n i (t), i = 0,1,…,N-1, represent the location vector of node i at time t.  d ij (t)=|n j (t)-n i (t)| is the distance between node i to j at time t.  Remoteness is defined by R ij (t)=F(d ij (t)) Where F(.) is a function of the distance.

Remoteness (Cont.) Requirements that function F(.) must meet. a. F(0)=0, lim x→∞ F(x)=1 b. dF(x)/dx ≥ 0 for all x ≥ 0 c. dF(x)/dx| x=0 =0 d. lim x→∞ dF(x)/dx=0 e. dF(x)/dx| x=R ≥ dF(x)/dx for all x ≥ 0

Remoteness (Cont.) Requirements of function F(.) defined. a. Normalizes F(.) to have a unity maximum value. b. Guarantees that the remoteness is monotonically increasing function of distance. c. and d. give the boundary condition of F(.), which guarantee that the remoteness of a node at extreme locations does not change with movement. e. Makes the remoteness most sensitive to the movement of a node at communication range.

Remoteness (Cont.) One function of F(.) that meets all of the requirements is.  F(x) = 1/Γ(r)  With λ=(r-1)/R where r can be a non-integer.  r is the sensitivity to the remoteness at communication range.

Mobility Measure Mobility measure is defined in terms of the time derivatives of the remoteness.    N is the number of nodes and M i (t) is a measure of the relative movement of other nodes seen by i.

Mobility Measure (Cont.) The mobility measure M(t) represents the average amount of the relative movement of the nodes in the network at time t. For a network in steady state, the time average of mobility measure can be used. 

Mobility Measure (Cont.) If the function chosen for F(.) is the function discussed earlier then the mobility measure function will be. 

Mobility Measure (Cont.) If the function chosen for F(.) is the identity function then the mobility measure function will be. 

Mobility Measure (Cont.) Both M G (t) and M I (t) are both mobility measures but only M G (t) meets the given requirements.

Mobility Models Random Waypoint Model (RWP)  Node selects random destination & speed  Speed uniformly distributed between min and max speeds  Pauses at destination for random time and selects a new destination

Mobility Models (Cont.) Random Gauss-Markov Model (RGM)  Each node is assigned a speed, direction and updated every Δt  Speed and direction are uniformly distributed between their min and max values  At boundary node reflects and chooses a new random direction

Mobility Models (Cont.) Reference Point Group Mobility Model (RPGM)  Each group has a logical center which defines location, speed, direction, etc  Defines a reference point and random motion vector for each node in a group  Random motion vector is updated periodically and is given by the length and direction, distributed uniformly over the intervals [0, RM max ] and [0, 2π)

Network Scenarios

Network Scenarios (Cont.)

Simulation Results All scenarios are done with 500 seconds warm up time and measured for the next 500 seconds. The first equation is based on L(t) which defines the number of link changes. 

The formula to calculate the time average of the normalized link change is.  If N(t) is a constant N the equation is.  If N(t) is a function of time the equation is.  Simulation Results (Cont.)