hard_worker.rb

class HardWorker
  include Sidekiq::Worker

  def perform
    random = Random.new
    init_val = random.rand(1..99999)
    apeend_val = random.rand(1..99999)
    Hoge.piyo({init_val: init_val, apeend_val: apeend_val})
    p "HardWorker perform args: #{init_val} / #{apeend_val} => Hoge.data is #{Hoge.data}"
  end
end

hoge.rb

class Hoge
  class << self

    attr_accessor :data

    def piyo(data)
      # ここで初期化する
      @data = {
        init_val: data[:init_val]
      }

      # 適当に重い処理
      5.times{ |i| BCrypt::Password.create(i.to_s) }

      # ここでハッシュにデータを追加する
      # すると、1番最後に初期化されたものが Sidekiq worker で利用され、
      # 重い処理をし終えた順に、それぞれの追加キーがセットされて処理が継続する
      @data.merge!(append_val: data[:apeend_val])
    end
  end
end

result.md

10.times { HardWorker.perform_async }

"HardWorker perform args: 68785 / 78839 now: {:init_val=>90834, :append_val=>78839}"
"HardWorker perform args: 14057 / 99365 now: {:init_val=>90834, :append_val=>99365}"
"HardWorker perform args: 14573 / 16901 now: {:init_val=>90834, :append_val=>16901}"
"HardWorker perform args: 87319 / 70622 now: {:init_val=>90834, :append_val=>70622}"
"HardWorker perform args: 15643 / 70140 now: {:init_val=>90834, :append_val=>70140}"
"HardWorker perform args: 90834 / 7108 now: {:init_val=>90834, :append_val=>7108}"