how to pass multi value query params in swagger

From the docs:

parameters:
- name: id
  in: path
  description: ID of pet to use
  required: true
  schema:
    type: array
    style: simple
    items:
      type: string

You have to define the parameter as array.

You are almost there. Name the parameter page_id[], make it type: array and use collectionFormat: multi:

      parameters:
        - name: page_id[]
          in: query
          description: some description
          required: false
          type: array
          items:
            type: string   # or type: integer or whatever the type is 
          collectionFormat: multi

Note that the requests will be sent with the [ and ] characters percent-encoded as %5B and %5D, because they are reserved characters according to RFC 3986.

http://example.com/pages?page_id%5B%5D=123&page_id%5B%5D=456