Overbooking Microservices in the Cloud

We consider the problem of scheduling serverless-computing instances such as Amazon Lambda functions, or scheduling microservices within (privately held) virtual machines (VMs). Instead of a quota per tenant/customer, we assume demand for Lambda functions is modulated by token-bucket mechanisms per tenant. Such quotas are due to, e.g., limited resources (as in a fog/edge-cloud context) or to prevent excessive unauthorized invocation of numerous instances by malware. Based on an upper bound on the stationary number of active "Lambda servers" considering the execution-time distribution of Lambda functions, we describe an approach that the cloud could use to overbook Lambda functions for improved utilization of IT resources. An earlier bound for a single service tier is extended to multiple service tiers. For the context of scheduling microservices in a private setting, the framework could be used to determine the required VM resources for a token-bucket constrained workload stream. Finally, we note that the looser Markov inequality may be useful in settings where the job service times are dependent