This is a somewhat complicated question. Increasing the number of active trigger campaigns will always slow down trigger evaluation to some extent, which can introduce latency between, action, evaluation and flow execution. This does not necessary mean that this will slow down flow execution significantly, as that is dependent on how many flow steps are being added by your trigger campaigns. If there's a significant number of flows being triggered, then yes they will cause a slow down in performance of batch campaigns as trigger campaigns run at a higher priority than batch campaign by default if they:
A) do not start with a wait step of five minutes or more
or
B) have flow steps other than change score in them
This means that triggered flows will run before any batched flows.
Your trigger evaluation can also get slowed down by having a higher number of triggers evaluating conditions which use "contains" or "not contains" as these are by far the slowest evaluations you can perform in triggers. A large number(hundreds) can drag your trigger evluation and web activity data to a total slog.
What does your campaign queue look like? Are you seeing large numbers of trigger and high priority flow steps there on a regular basis? Do you have a lot of web activity-triggered campaigns? This could give you a high volume of flows which are executing ahead of your batch campaign flow steps.
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