  This paper studies an infinite-server queue in a random environment, meaning
that the arrival rate, the service requirements and the server work rate are
modulated by a general c\`{a}dl\`{a}g stochastic background process. To prove a
large deviations principle, the concept of attainable parameters is introduced.
Scaling both the arrival rates and the background process, a large deviations
principle for the number of jobs in the system is derived using attainable
parameters. Finally, some known results about Markov-modulated infinite-server
queues are generalized and new results for several background processes and
scalings are established in examples.
