1. Fairness in Dead Reckoning Based Distributed Multi-Player Games Sudhir Aggarwal, Hemant Banavar, Sarit Mukherjee, and Sampath Rangarajan presented by Christopher Jones ● Main Points:  Different delays between different players causes different errors that give some players an unfair advantage. Players with less network delay have a more accurate simulation than players with a slower connection.  The authors propose three algorithms to moderate this unfairness: ● Scheduling Algorithm ● Probabilistic Budget Algorithm ● Deterministic Budget Algorithm

2. General Model of Dead Reckoning Vector Error Genereal Figure

3. Scheduling Model

4. Scheduling Equation

5. Scheduling Algorithm Steps ● Compute the Dead Reckoning (DR) vector along with estimated delay for each receiver ● DR are sent out according to schedule. Recievers send back the actual delay. ● Sender recomputes delay for the recievers making appropriate adjustments. ● Repeat the above steps.

6. Scheduling Special Cases ● New DR is ready before all the old DR's are ready to send out.  Flush the queue  Recalculate with new DR for all that have not received it yet ● If new DR ready before all receivers have sent back actual delay  Assume zero delay for reciever, with adjustment made to future DR

7. Scheduling Algorithm Results ● Game was fairer, but at the cost of more error for everyone. ● A late DR increases error for the receiver that causes every receiver's error to increase. ● So they tried the other two algorithms.

8. The Budget Base Algorithms ● Lower the threshold in the application so that it generates more DRs ● However, do not send all DRs to everyone, but instead, to the one that “needs” it the most ● They used two methods, Probabilistic and Deterministic, as ways to calculate this need.

9. Probabilistic Algorithm ● At every DR trigger compare the accumulated error for each receiver. (receiver's error / total of all receiver's error) ● Send DR to receiver with highest probability ● Results:  Greater fairness, but still overall increase in mean accumulated error.

10. Deterministic Algorithm ● Follow first to steps of probabilistic algorithm. ● If one of the receivers is scheduled to receive a DR send it, and continue, else wait. ● Receiver's probability is multiplied by budget available at each trigger ● If any receiver frequencies exceed 1, set to 1 and distribute the difference equally to all other receivers. Do this until all frequencies are <=1 ● 1/frequency is the schedule, but frequency is put through ceiling function. Any rounding is subtracted off future frequency. ● Tag receivers that just received with next schedule to receive

11. Deterministic Results ● Fairer play without increase in mean error than tested base case. ● Always lower mean error than probabilistic case but not inconclusive on “fairer” in some case of higher variance.

12. ● Questions? Comments