Kunal, yes, of course. If service times are fixed, or even if they are normally distributed (as one typically assumes), then everything depends on arrival times.

Take this real-world example:

Waiting times to get in public transportation, let's say, toward the end of a busy working day, and into the evening. Assume trains are running on a consistent schedule. (Oh, and assume pre- or post-COVID restrictions!)

As the rush hour(s) period ends, waiting times may decrease, as trains become less packed. As soon as the train arrives, people can easily get on board, and the train departs quickly. No problem having to wait for another train, as you might have had to do one hour ago.

Then there's a game in town, and it lets out late. Suddenly, the stations adjacent to the game venue are overcrowded again, and people may have to wait for a couple of trains, before getting their ride home.

Waiting times decreased, then increase, then decrease again, after the game crowd has been serviced.