where N
s is the number of contamination events, X is the decision vector and defined
as X = [x1 2 , x ,L, xn], xi is an integer parameter which takes on values of “one” or
“zero” depending on the presence of a sensor at the junction i, n is the number of
candidate junctions, td s is the detection time of the contamination event s using
decision vector X which is defined as td s (X ) = Min{td i (x )}, td(xi) is the detection
x
i =1
time at candidate junction