In Vāyupurāṇa (Vayupurana), when the term Ahirvudhnya is used for the first time, it is referred to as one of the several yajñasthāna(s) (yajnasthana; place of fire-sacrifice). It is said that Ahirvudhnya is the name of gṛhapti (grihapati)agni or gārhapatya agnisthāna (garhapatya agnisthana, a ritual fireplace considered sacred for the life of a householder). Ahirvudhnya is also called Anuddeśya (Auddesya), perhaps because it burns all the time, and there is no need to rekindle it. again and again.
However, the root-concept behind this Anuddeśya Gārhapatya agni as Ahirvudhnya, lies in Vājasaneyī Saṃhitā (Vajasaneyi Samhita) of Śuklayajurveda (Suklayajurveda). Here, in the main mantra it is said, ahirasi vudhnya. In explaining the mantra, an ancient commentator like Mahīdhara (Mahidhara) has said that — the old gārhapatya agni that is established at the west of patnīśālā, is called Ahirvudhnya. The term ahi means something that has no decline — na hīyate ityahiḥ.
After the marriage of a new couple, this gārhapatya agni (garhapatya agni) has to be established towards the west of Patnīśāla (Patnisala; the place of wife). Situated at the gate of this yajña-place this newly established does not extinguish, nor is it allowed to put out. It is for this unextinguished nature of this holy fire, it is ahi. And Vudhnya means root, or base or origin. This agni emerges at the beginning of the new life of a householder, so this agni is also Ahirvudhnya. During the agnyādhāna (agnyadhana), this agni is kindled with agnimanthana (the churning of fire), and so it is conceptualised as the ‘origin’ or vudhnya –
vudhno mūlaṃ tatra bhavo vudhnyaḥ,
ādhānakāle prathamm āhitatvānmūlabhāvitvam,
sa hi prathamaṃ mathyate.

Later, in another chapter, Vāyupurāṇa (Vayupurana)gives another meaning of Ahirvudhnya — it is of the fifteen rātri-muhūrta(s) (ratri-muhurta; nocturnal moments) suitable for beneficial activities. But in another śloka (sloka; verse)of this very chapter, it is said that Ahirvudhnya is one of the eleven Rudra(s) born of the womb of Surabhī (Surabhi), daughter of Dakṣa, and sired by Kaśyapa Prajāpati (Kasyapa Prajapati; Kasyapa as a Ruler of the people), and by the boon of Mahādeva (Mahadeva).

In Mahābhārata (Mahabharata), too, Ahirvudhnya has been considered among the eleven Rudra(s). It also appears that a kind of fire-like manifestation always works in the name of Rudra, and according to mythological legends, agni contains Rudrateja (the energy of Rudra). In this regard, gārhapatya agni or ‘Ahirvudhnya’ has been one with Rudra —
ajaikapādahirvudhnyaḥ pinākī cha parantapaḥ.

Before the tradition of Mahābhārata and Purāṇa, Ahirvudhnya was not considered in identification with Rudra or Agni, but a vague form and idea of agni was associated with the term Ahirvudhnya. In two instances from Ṛgveda, Arhirvudhnya has been mentioned in the following way —
*śaṃ no’hirvudhnya śaṃ samudraḥ.
That means –let the Deity called Ahirvudhnya determine peace for us.
*mā no’hirvudhnyoriṣeṣdhāt —
that is, ‘let not Ahirvudhnya offer us to those who hate us. Yāska (Yaska), author of Nirukta, has determined the meaning of this Ahirvudhnya as some deity who moves in Antarīkṣa (Antariksha), or Antarīkṣa itself. Yāska says — whatever is Ahi, is also Vudhnya. Vudhnya means Antarīkṣa (Antariksha), and the god who resides in Antarīkṣa, is Ahirvudhnya.
yo’hi sa vudhnyaḥ, vudhnyamantarīkṣaṃ tannivāsāt.
Yāska has not given any general name similar to that deity, but in another mantra of Ṛgveda (Rigveda), we see – avjāmukthairahiṃ gṛṇīṣe vudhnye nadīnāṃ rajaḥsuṣīdan.
(Praise that agni, which emerges from water, in stead of the river that invites cloud).
Here it is to be noted that, in several mantra(s) of Ṛgveda, the term rajaḥ is used in the sense of Antarīkṣa. Thus, agni that emerges from water or cloud and sits in Antarīkṣa, is most probably the electric fire. So here too, Ahirvudhnya is one kind of manifestation of fire, which can also be the manifestation of Rudra. There should be no problem to call Ahirbudhnya by the name of Rudrāgni (fire or energy of Rudra).