Gerund or Participle?

It is a present participle.

A rule of thumb is that it's a present participle if it's used like a verb, or a gerund like a noun.

Longman Dictionary of Contemporary English says:

gerund

a noun in the form of the present participle of a verb

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Edit:
This edit has little to do with the OP's question.
Due to constraints on space and markdown tags in comments, here are some sources for Jason Bassford.

Oxford Collocations Dictionary for Students of English says:

waiting
I. noun
Waiting is used before these nouns: area, list, lounge, period, room, staff, time

swimming
noun
Swimming is used before these nouns: cap, championship, costume, gala, gear, goggles, instructor, lesson, pool, shorts, stroke, suit, thing, trunk

running
I. noun
activity/sport
• RUNNING + NOUN event, race | gear | clothes (AmE), pants (AmE), shoe, shorts, tights (AmE), vest (BrE) | track

sewing
noun
• SEWING + NOUN basket, kit | needle, thread | machine | room (esp. AmE)

OALD says (in addition to the online version linked to in the comment far below):

waiting
wait·ing 7 [waiting] BrE [ˈweɪtɪŋ] NAmE [ˈweɪtɪŋ] noun uncountable
1. the fact of staying where you are or delaying doing sth until sb/sth comes or sth happens
• No waiting (= on a sign at the side of the road, telling vehicles that they must not stop there).
2. the fact of working as a waiter or waitress

From Roget's II The New Thesaurus 3th Ed.:

waiting
noun
An act or the time of waiting: wait. See CONTINUE.

From AHD:

wait·ing wātĭng)
n.
1. The act of remaining inactive or stationary.
2. A period of time spent waiting.

From Webster's New World:

waiting wait·ing
noun
Waiting is defined as the process of remaining or staying.

There are tons more, but I suppose these should be more than enough.

Also, please have a look at noun adjunct.

I agree with johnlee that "waiting" in this sentence should be classified as a participle, not a gerund, if you are working in a framework that makes that distinction.

(Comments by members like BillJ correctly point out that not all frameworks do make this distinction; however, as far as I know, there is not yet a unanimous consensus in favor of the position that it is theoretically impossible to distinguish "gerunds" from "present participles" in English. You can see some relevant comments beneath the following Language Log post : Gerunds vs. participles. The linguist Greg Lee made the following comments on this site about the post:

• Liberman's post makes no sense to me. Because Liberman as a child couldn't tell the difference between gerund and participle, I'm supposed to assume they're the same? What kind of reasoning is that? – Greg Lee Dec 22 '16 at 5:11

• I looked below in the comments at Stephen C. Carlson's summarizing the CGEL "argument". He says "OK, I've had a look at CGEL about abolishing the distinction between gerund and participle, and I have to admit that I didn't find the discussion particularly clear or persuasive." Based on his account, I agree with him. – Greg Lee Dec 22 '16 at 5:21

Also, see Araucaria's answer here: Difference between gerund and present participle. There is more complicated discussion beneath Greg Lee's answers to "Do these two sentences use the possessive case of gerunds properly?" and "How can you tell when a participle is being used as an adjective?")

I disagree with johnlee's statement that "A rule of thumb is that it's a present participle if it's used like a verb, or a gerund like a noun."

The salient characteristic of a participle is not that it is "used like a verb" but that it is a verb used like an adjective. (We wouldn't need any special word for a verb used as a verb.)

For example, in the progressive construction ("They are waiting"), the participle "waiting" is used after the copular verb be, similarly to how an adjective like "awake" occurs with the copular verb be when used predicatively: "They are awake".

To distinguish a participle from a gerund, therefore, you should try to figure out if the verb (or the phrase headed by the verb) is acting more like an adjective--in which case it is a participle--or more like a noun (more properly, according to some linguists, this would say "like a noun phrase")--in which case it is a gerund. (One point that may cause confusion: according to most systems of grammatical terminology for English, neither the term "gerund" nor the term "participle" is applicable if the word actually is a noun or an adjective—only if the word is a verb "acting as"/"used as" as noun or adjective. A noun ending in "-ing" may be categorized as a "gerundial noun" and an adjective ending in "-ing" may be categorized as a "(de)participial adjective", but these are not considered to be the same as gerunds and present participles.)

We can use adjectives after "while":

• While awake, we generally have a clear sense of a personal “I”-being, which awakens at a specific point early in life.

  (According to Matthew: Lecture 8 of 12, by Rudolf Steiner)

As far as I know, we can't use nouns after "while" in a similar fashion:

• *While sleep, people dream.

So it seems to me that "waiting" is not a gerund here, and therefore must be a participle.

(Specifically, the answer by Araucaria that I linked to earlier said that "In traditional grammar, a gerund is an -ing form of a verb that heads a phrase functioning as a: Subject of a clause - Object of a verb - Complement of a preposition". So it would only make sense to analyze "waiting" in "While waiting for service" as a gerund if you analyze "while" here as a preposition. I don't think it is.)

Another reason I feel like "waiting" is a participle here is because the sentence seems similar in meaning, and I think in structure, to sentences like "While patrons are waiting for service, they can enjoy coffee and snacks and mingle with their neighbors in need." In the preceding sentence, "waiting" is obviously a participle and not a gerund.