Due to the high installation cost associated with each node, the target lifetime for the device is 10 years. The device is also limited in size and thus uses a 20 Ah (Ampere-hour) battery at 3.6V.

The node can house three sensors - two Magnetic and one Acoustic sensor. The node also contains a microprocessor to digitize samples and perform computation and a radio transceiver to communicate event information to a central server. The following table lists performance parameters for each component.

Acoustic Sensor
Sleep State Power 3 µW
Startup Latency 1 ms
Active State Power 1.73 mW

Magnetic Sensor
Sleep State Power 3 µW
Startup Latency 41 ms
Active State Power 19.4 mW

Processor
Sleep State Power 30 µW
Startup Latency 0.2 ms
Active State Power 24 mW

Radio
Sleep State Power 3 µW
Startup Latency 2.5 ms
Active State Power 48 mW

As a simplification, assume that all vehicles are 20 feet in length and can travel at a maximum speed of 100 mph. The inter-vehicle distance is at least 2 sec. If an event was detected, the radio requires 2.5 ms to report the message to a base station. The two magnetic sensors are placed 2 feet apart to estimate speed using event correlation. Components consume active power during startup.

Q1) Assume for now that all components are powered up simultaneously and that event detection is instantaneous. This means that one does not need to consider sampling or processing time. Also, all three sensors are required for unambiguous event detection. Compute the worst case duty cycle that can be allowed. (Hint: Find the longest time that the node can be put to sleep without missing an event. Note that there are two distinct cases: (i) when a node wakes up and detects the presence of a vehicle, and (ii) when the node wakes up in the inter-vehicle gap).

Q2) What is the worst case average power consumption with this strategy ? What is the expected lifetime of the node ?