
A Stochastic System and Its Corresponding Deterministic System 319
statement in S9 is e quivalent to generating a random number z
e
from an ex-
ponential distribution with rate parameter ¯a
ι
and then setting
˜
t
ι
= z
e
+ t. We
remark that to increase the efficiency of the next reaction method the a lgo-
rithm proposed in [28] uses the notion of a dependency graph and a propriety
queue, where the dependency graph is us ed to update only those transition
rates that actually change during an iteration, and the propriety queue is used
to quickly determine the minimum in S5. We refer the interested reader to
[28] for more information on this.
8.2.2.2 The Modified