Kumbh Mela celebration depends on the position of the planets and stars

Where and when is Kumbh Mela Celebrated?

The Maha Kumbh festival is celebrated at different places depending on the position of the planets Bṛhaspati (Jupiter) and the Sun.
Following are the city wise positions of Brhaspati (Jupiter) and Sun.

Kumbh at Prayag or Allahabad
When Jupiter is in Aries circle and Sun and Moon are in Capricorn Kumbh mela is held at Prayag on the lunar conjunction day (अमावस्या)
Sanskrit verse:
मेष राशि गते जीवे मकरे चन्द्र भास्करौ ।
अमावस्या तदा योगः कुम्भख्यस्तीर्थ नायके ।।

When Jupiter is in Taurus (Vrishabha Rashi) and Sun is in Capricorn (Makar Rashi) during the month of Magha (January-February) then Kumbha Mela is celebrated at Prayag.
मकरे च दिवा नाथे ह्‍म‍जगें च बृहस्पतौ कुम्भ योगोभवेत्तत्र प्रयागे ह्‌यति दूलर्भ:

Kumbh at Haridwar

When Jupiter is in Aquarius and Sun is in Aries (Mesha Rashi) during the month of Chaitra (March-April) then Kumbha Mela is celebrated at Haridwar.
Sanskrit verse
पद्‍मिनी नायके मेषे कुम्भ राशि गते गुरोः ।
गंगा द्वारे भवेद योगः कुम्भ नामा तथोत्तमाः।।

Kumbh at Ujjain

When Jupiter (Guru) is in Leo and Sun is in Scorpio (Vrishchik Rashi) or when all three are in Libra during the month of Vaisakha (April-May) then Kumbha Mela is celebrated at Ujjain.

मेष राशि गते सूर्ये सिंह राशौ बृहस्पतौ ।
उज्जियन्यां भवेत कुम्भः सदामुक्‍ति प्रदायकः ।।

घरेसूरिः शशि सूर्य कुह्‍मं दामोदरे यदा।
धरायां च तदा कुम्भों जायते खलु मुक्‍तिद: ।।
अहं राष्‍ट्री संगमनी वसूनाम्‌श्‍

Kumbh at Nashik

When Jupiter (Guru) and Sun are in the zodiac sign Leo (Simha Rashi) during the month of Bhadrapada (August-September) then Kumbha Mela is celebrated at Trimbakeshwar, Nashik

सिंह राशि गते सूर्ये सिंह राशौ बृहस्पतौ ।
गोदावर्या भवेत कुम्भों जायते खलु मुक्‍तिदः ।।

कर्के गुरू स्तथा भानुचन्द्रश्‍चन्द्रर्क्षगतस्था ।
गोदावर्या तदा कुम्भो जयाते Sवनि मण्डले ।।

For more Information Please refer following Vedic scriptures.
Naradiya (Narada नारद पुराण ) Purana 2-66-44
Shiva Purana 1-12-22-23
Astrological analysis is available in Barah Purana 1-71-47-48
Brahma Purana about events of (Kumbh mela occurring every 12 years)