A Probabilistic Protocol for Multihop Routing in VANETs

Algorithm 1

Algorithm SteadyTraffic

Inputs:

 𝑇: time limit,

𝐻: maximum number of hops,

𝑀: map with 𝑚 positions,

𝑅: transmission range,

  𝑃(𝑢₁,𝑢₂): carry probability for every (𝑢₁,𝑢₂), that is, probability

that a car appears at space time 𝑢₁ and moves to 𝑢₂,

𝑠,𝑑∈𝑀: source and destination on the map 𝑀.

Output:

 Communication probability 𝜌(𝑠,𝑑,𝑇) from 𝑠 to 𝑑 with time limit 𝑇.

begin

  (1). /^∗ The final value of Answer(𝑥,𝑡,𝑘) will be the probability that there

  exists a communication path from (𝑠,0) to (𝑥,𝑡) with at most 𝑘 carries. ∗/

  (2). For every space time 𝑢=(𝑥,𝑡) do Answer(𝑥,𝑡,0)=0;

  (3). Answer(𝑠,0,0)=1;

  (4). for 𝑘=1 to 𝐻 do

  4-1. for every space time 𝑢=(𝑥,𝑡) do

   4-1-1. Answer(𝑥,𝑡,𝑘)=𝑃((𝑠,0),𝑢);

   4-1-2. for every other space time 𝑢₁=(𝑥₁,𝑡₁) such that 𝑡₁≤𝑡 do

     4-1-2-1. /^∗ Let 𝐷(𝑥) for 𝑥∈𝑀 be the set of 𝑅-neighbors of 𝑥   ∗/

     4-1-2-2. 𝑝₁=1−∏_{𝑥2∈𝐷(𝑥1)}(1−Answer(𝑥₂,𝑡₁,𝑘−1));

     4-1-2-3. 𝑝₂=𝑃(𝑢₁,𝑢)⋅𝑝₁;

     4-1-2-4. Answer(𝑥,𝑡,𝑘)=Answer(𝑥,𝑡,𝑘)(1−𝑝₂)+𝑝₂;

   4-1-3. end for

  4-2. end for

  (5). end for

  (6). return 1−∏_{𝑥∈𝐷(𝑑)𝑡≤𝑇}(1−Answer(𝑥,𝑡,𝐻));

end