Age of Information of Parallel Server Systems with Energy Harvesting

Motivated by current communication networks in which users can choose different transmission channels to operate and also by the recent growth of renewable energy sources, we study the average Age of Information of a status update system that is formed by two parallel homogeneous servers and such that there is an energy source that feeds the system following a random process. An update, after getting service, is delivered to the monitor if there is energy in a battery. However, if the battery is empty, the status update is lost. We allow preemption of updates in service and we assume Poisson generation times of status updates and exponential service times. We show that the average Age of Information can be characterized by solving a system with eight linear equations. Then, we show that, when the arrival rate to both servers is large, the average Age of Information is one divided by the sum of the service rates of the servers. We also perform a numerical analysis to compare the performance of our model with that of a single server with energy harvesting and to study in detail the aforementioned convergence result.

Stability of Parallel Server Systems

A parallel server system is a queueing system in which jobs are routed upon their arrivals to one of several buffers, each handled by a different server. The main operational and theoretical problem in such systems is to find an efficient routing policy that maximizes their throughput (or minimizes waiting times). The paper “Stability of Parallel Server Systems” considers a large class of routing policies, which includes the most prevalent policies studies in the literature, under the assumption that routing errors may occur because ofincomplete information about the state of the system at decision epochs. The stability region for this class of policies is studied as a function of the error probability, and it is shown that the standard stability condition, namely, that the traffic intensity is smaller than one, does not guarantee that the system is stable.

Learning Unknown Service Rates in Queues: A Multiarmed Bandit Approach

Traditional scheduling problems in stochastic queueing systems assume that the statistical parameters are known a priori. In ''Learning unknown service rates in queues: A multiarmed bandit approach'', Krishnasamy, Sen, Johari, and Shakkottai consider the problem of online scheduling in a parallel-server system when the statistical parameters are unknown. They study this question in the stochastic multiarmed bandits framework with the queue length as the performance objective. In contrast to the classic stochastic multiarmed bandits problem, where the regret scales logarithmically with time, the authors show that the queue regret (difference in expected queue length between a bandit algorithm and a genie policy) exhibits a more complex behavior. It grows logarithmically in the initial stage and eventually decays almost inversely with time. This remarkable behavior is explained through the analysis of regenerative cycle lengths, which shorten with time as the bandit algorithm learns to stabilize the queues.

Persistent-Idle Load-Distribution

A parallel server system is considered in which a dispatcher routes incoming jobs to a fixed number of heterogeneous servers, each with its own queue. Much effort has been previously made to design policies that use limited state information (e.g., the queue lengths in a small subset of the set of servers, or the identity of the idle servers). However, existing policies either do not achieve the stability region or perform poorly in terms of job completion time. We introduce Persistent-Idle (PI), a new, perhaps counterintuitive, load-distribution policy that is designed to work with limited state information. Roughly speaking, PI always routes to the server that has last been idle. Our main result is that this policy achieves the stability region. Because it operates quite differently from existing policies, our proof method differs from standard arguments in the literature. Specifically, large time properties of reflected random walk, along with a careful choice of a Lyapunov function, are combined to obtain a Lyapunov condition over sufficiently long-time intervals. We also provide simulation results that indicate that job completion times under PI are low for different choices of system parameters, compared with several state-of-the-art load-distribution schemes.