A Poisson Fishing Model

Thomas S. Ferguson


A fishing model of Starr, Wardrop, and Woodroofe is related to the sequential search model of Cozzolino. The latter is generalized to allow an arbitrary joint distribution of capture times and fish sizes. There are a random number, M, of fish in a pond. Each fish has a random size, X (with finite variance), and a random time of being caught, Y>0 (with finite mean). It is assumed that given M=m, (X(1),Y(1)), . . ., (X(m),Y(m)) are i.i.d.. The problem is to choose a stopping time, T, to maximize the sum of the sizes of the fish caught by time T minus c(T), a cost of time. Implications to the foraging models of Oaten and Green and to debugging software are indicated.