One Analytics Infrastructure-as-a-Service model is to not only have a consulting partner perform your analytics on a recurring basis but also have them manage the data required for your analytics with infrastructure and software they've acquired.  The costs of such infrastructure becomes bundled as part of their subscription offering to you in a fixed price.   If you use a firm that partners with a major cloud platform then they will likely stand-up or re-deploy the technology and capacity needed to answer your questions for the given task at hand, instantly.  Once the question is answered, some or all of the capacity may be relinquished, saving them money.  This savings is passed on to their customer. The cost of all of the analytics software, infrastructure and technology would be included fixed price in your subscription: ~ $1000/Month added to your consulting fees for small monthly data processing <1TB.  Expect about $5000/month for around 10-50TBs of data processing with a few Data Visualization licenses.

In the multi-tenancy scenario, your consulting partner will share infrastructure and software that they subscribe to (in the cloud) across multiple customers of theirs.  The savings of scale are then shared with you in the subscription rates.  A good example of this is with a data warehouse technology like Redshift or Vertica.  A single monthly subscription for several terabytes of such a tool is more affordable and less effort to manage then each customer buying their own install of Redshift/Vertica and having that platform each administered individually.  Multi-tenancy doesn’t mean your data has to be comingled with other customer’s data.  Safeguards to ensure each customer have their own databases and tables are standard best practice within the industry.

Perhaps most importantly with a multi-tenancy Analytics Infrastructure-as-a-Service offering is that the customer becomes free from the technology decision and acquisition process.  Your consulting partner will decide whether to use technology A, B, C ... Z or some combination of the above to answer your analytics question.  For them to maximize ROI on their technology spend they will keep-up with the latest options in the cloud and adapt more quickly by taking advantage of the real-time, short commitments and free software options the cloud has to offer.