Alert: An Adaptive Low-Latency Event-Driven MAC Protocol for Wireless Sensor Networks

Algorithm 3

Procedure get𝑀(𝑁_guess).

(1) Use timing constants 𝜏₁ and 𝜏₂ of specific radio used

(2) for each 𝑀≤𝑀_max  do

(3) 𝜏_slot(𝑀)=𝑀𝜏₁+𝜏₂

(4) Get the expected number of frames needed, 𝐹(𝑀),

   based on value of 𝑁_guess:

   ⟨𝐏,𝐹(𝑀)⟩=get𝐏(𝑁_guess,𝑀)

(5) end for

(6) Get optimal 𝑀 for reading all messages:

   𝑀_temp=argmin_𝑀𝐹(𝑀)×𝜏_slot(𝑀)

(7) Get associated time to read all messages:

   𝑡^𝑀temp_val=𝐹(𝑀_temp)×𝜏_slot(𝑀_temp)

(8) Find largest 𝑀 within some factor 𝛽 of 𝑡^𝑀temp_val:

   𝑀_opt=max{𝑀|𝑡^𝑀_val≤(1+𝛽)𝑡^𝑀temp_val}

(9) Return 𝑀_opt