For slopes where the gradient is the same at every position, this resembles a gambler’s ruin process. To apply classical gambler ruin theory (see e.g. [7]) two technicalities need to be taken into account. Firstly, two different gambler ruin games need to be considered, one for ...
These processes are likely to apply to any system in which worker agents are allocated to tasks with fluctuating demand, and should therefore be instructive to understanding optimal task allocation and inactive workers in any distributed system. Some of these processes imply that a certain proportion...