Case Study: Heroku Inc.

Heroku Inc. is a fictional company based in Montreal that provides platform-as-a-service to its numerous customers. Some of its customers include Netflix - a web streaming service that provides streaming content to its millions of subscribers, ZeroCater - a catering service that wants to expand its business with an Online Marketplace on Heroku and Forever Living - a health and wellness products company that provides real-time data to millions of distributors.
Heroku needs to meet its customers demands while minimizing costs of providing service to them. Service provision entails renting virtual machines (VMs, loosely referred to as resources) from Cloud Service Providers such as Amazon, Google etc.
Generally, cloud providers offer two types

To make an optimal decision, the demand uncertainty from our customers and the price uncertainty from cloud providers should be taken into account to adjust the trade-off between on-demand and over-subscribed costs of under-provisioning and over-provisioning.
Assumptions
• Different types of VMs are classified by VM Classes. It is assumed that one VM class represents a distinct type of job. In Heroku’s case, one class for database applications and another class for web applications. Certain amount of resources are required for running
VMs as they are different for VM in different classes.
• Each cloud provider supplies a pool of resources. Resources are grouped into resource types are they include computing power (in unit of CPU-hours), storage (in unit of GBs/month) and network bandwidth for data transfer (in units of GBs/month).
• Each VM class specifies the amount of resources in each resource type.
• Cloud providers offer reservation contracts that is to be considered when making reservations.
E.g Amazon offers 1 and 3 years contract. Certain amount of resources are reserved for 1 year in the one-year contract starting from the time they are provisioned.

• Reservation in the first stage can be performed without any uncertainty.
• Customer’s demand should be met.
• Allocation of resources for VM must not exceed the maximum resource offered by the cloud provider. • The number of VMs provisioned must be non-negative integer numbers.
Data
Heroku has 2 different types of applications representing 2 distinct VM classes namely, Database server (DB) and Web server (Web). Each VM class requires different amount of resources given in Table 1.
Price of resources for the different phases for different providers is given in Table 2. The price in the on-demand phase can be doubly increased with probability 0.1 and remains the same with probability 0.9 from the data given in Table 2. For the demand uncertainty, the actual required number of VMs in the second provisioning stage of VM class (i.e., Web and DB) varies from
1 to 50. The demand of one VM class is assumed to be the same as the other. Two demand distributions are considered namely normal distribution and uniform distribution. Means of both distributions are 25.50. The variance of the normal distribution is 6 while the variance of the uniform distribution is