SYSTEM ANALYSIS AND SIMULATION
In the following
discussion, the node duty cycle and message latency of a network employing the
distributed MD protocol are evaluated. For simplicity, it is also assumed that
all the devices are within communication range of each other.
4.4.1 Duty Cycle
Exhibit 5 illustrates a typical timing schedule for a
node employing the distributed MD algorithm.
Exhibit 5: A Typical Timing Schedule for a Node
Employing the Distributed Mediation Device Protocol
In Exhibit 5, Tc is the
communication (Tx or Rx) time duration for each communication slot, Tm is the MD listening time duration, T1 is the repeating period of the communication
(Tx or Rx) slots and T2 is the average
repeating period of the MD mode.
It is assumed that
In the period of T2, the total
number of communication slots can be written as
The total operation time to
The duty cycle α can be written as
Putting Equations 6 and 7 into Equation 8,
By considering Equation 5, the third term of the preceding equation can
be ignored. Finally, the duty cycle α can be written
as
For example, if Tc = 1
millisecond, T1 = 1 second, Tm = 2 seconds, and T2 = 1000 seconds, then the overall duty cycle can
be as low as 0.3 percent.
4.4.2 Latency
One concern for this protocol is message latency;
specifically, the time a node must wait between first transmitting an RTS beacon
and having it heard by an MD. (The average time between MD reception of an RTS
beacon and transmission of data is, from inspection of Exhibit 3, 4T1.) An analysis of latency is as follows.
As illustrated in Exhibit 6, at time t1,
Node A transmits an RTS message. No MD is available at this time, so node A
needs to repeat the RTS message until time t3
when an MD becomes available. To guarantee that the RTS will not miss the MD
period at time t3, the duration of the MD
listening time has a lower bound. Clearly, if
Exhibit 6: A Typical Timing Schedule for Two
Devices
the RTS will not miss the MD
listening period. The longest latency, therefore, is about T2.
The smallest network has only two nodes, one source node and one
destination node. In this case, the probability density function of the latency
can be written as
The average latency is T2/2.
For a larger network, at any given time there exists more than one
node that may enter the MD mode; thus, the latency can be reduced. Exhibit 7 illustrates
the simulated latency probability density function, normalized to T2, for networks of order 2, 4, 6, 11, and 21. It
is clear from Exhibit
7 that normalized message latency decreases significantly for relatively
dense networks. Exhibit 8 illustrates the normalized average latency as a
function of the number of nodes in range of a node generating a message. By
increasing the number of nodes within the communication range, the latency can
be dramatically reduced. This feature makes the distributed MD protocol especially suitable for wireless sensor networks,
which are expected to be relatively dense in many applications.
Exhibit 7: Normalized Latency Probability
Density Function for Networks of Several Orders
Exhibit 8: Normalized Average Latency versus
Network Order
Sections
