Age of Information in G/G/1/1 Systems

TL;DR

This paper derives exact and upper bound expressions for the age of information in G/G/1/1 queueing systems with arbitrary interarrival and service time distributions, considering different service disciplines.

Contribution

It provides the first exact formulas and bounds for age of information in G/G/1/1 systems with arbitrary distributions and different service policies.

Findings

Exact age of information expressions derived for both models.

Upper bounds that are easier to compute than exact formulas.

Additional bounds using stochastic ordering under specific distribution properties.

Abstract

We consider a single server communication setting where the interarrival times of data updates at the source node and the service times to the destination node are arbitrarily distributed. We consider two service discipline models. If a new update arrives when the service is busy, it is dropped in the first model; and it preempts the current update in the second model. For both models, we derive exact expressions for the age of information metric with no restriction on the distributions of interarrival and service times. In addition, we derive upper bounds that are easier to calculate than the exact expressions. In the case with dropping, we also derive a second upper bound by utilizing stochastic ordering if the interarrival times have decreasing mean residual life (DMRL) and service times have new better than use in expectation (NBUE) property.