Age of information distributions analyzed for server update policies
Distribution of Age of Information in the Erlang Loss System
Information TheoryPerformance
Summary
This paper looks at how fresh information is in systems where updates arrive randomly and are processed by a fixed number of servers. The authors study different ways to handle new updates when all servers are busy, either by blocking, randomly replacing, or replacing the oldest update from the same source. They use a mathematical method called absorbing Markov chains to find the exact behavior of the information's freshness over time. Their results help understand how different policies affect the timeliness of updates in shared server environments.
What this means in practice
- •For network schedulers: Design server update handling policies to optimize information freshness under limited processing capacity.
- •For data center operators: Provision server resources based on exact age distribution constraints to meet freshness requirements of multiple data sources.
Authors
Nail Akar, Sennur Ulukus
Abstract
In this paper, we study the exact distributions of the age of information (AoI) and peak AoI (PAoI) in a bufferless setting in which time-stamped updates, or processed tasks, generated by one or several information sources according to a Poisson process for each source, are submitted to a shared pool of $c$ homogeneous servers with exponentially distributed service times, i.e., the so-called M/M/c/c or the Erlang loss system. We consider three update management policies which come into play when a new update arrives to find all the servers busy: the arriving update is blocked (non-preemptive, NP) as in the Erlang loss system, or it preempts a randomly chosen update of its own source in service (preempt at random, PR), or the stalest such update (preempt the stalest, PS). All three policies preserve the same birth-death structure of the server occupancy process associated with the underlying Erlang loss system. However, their AoI and PAoI distributions can be very different. The approach we take is the absorbing Markov chain (AMC) method, in which a single AoI cycle, rather than the entire sample path of the system, is modeled by an absorbing Markov chain. Via the AMC method, we derive the exact distributions of AoI and PAoI in matrix-exponential form. The method extends to multiple sources sharing the same pool of servers, with the AoI of a given source being affected by the remaining sources only through their aggregate update rate. Numerical examples illustrate the implications of our findings, including distribution-based server provisioning under age violation constraints.