Markus Fidler’s research while affiliated with Leibniz Universität Hannover and other places

Models of parallel processing systems typically assume that one has l workers and jobs are split into an equal number of k=l tasks. Splitting jobs into $k \gt l$ smaller tasks, i.e. using “tiny tasks”, can yield performance and stability improvements because it reduces the variance in the amount of work assigned to each worker, but as k increases, the overhead involved in scheduling and managing the tasks begins to overtake the performance benefit. We perform extensive experiments on the effects of task granularity on an Apache Spark cluster, and based on these, develop a four-parameter model for task and job overhead that, in simulation, produces sojourn time distributions that match those of the real system. We also present analytical results which illustrate how using tiny tasks improves the stability region of split-merge systems, and analytical bounds on the sojourn and waiting time distributions of both split-merge and single-queue fork-join systems with tiny tasks. Finally we combine the overhead model with the analytical models to produce an analytical approximation to the sojourn and waiting time distributions of systems with tiny tasks which include overhead. We also perform analogous tiny-tasks experiments on a hybrid multi-processor shared memory system based on MPI and OpenMP which has no load-balancing between nodes. Though no longer strict analytical bounds, our analytical approximations with overhead match both the Spark and MPI/OpenMP experimental results very well.

This paper contributes tail bounds of the age-of-information of a general class of parallel systems and explores their potential. Parallel systems arise in relevant cases, such as in multi-band mobile networks, multi-technology wireless access, or multi-path protocols, just to name a few. Typically, control over each communication channel is limited and random service outages and congestion cause buffering that impairs the age-of-information. The parallel use of independent channels promises a remedy, since outages on one channel may be compensated for by another. Surprisingly, for the well-known case of M$\mid$M$\mid$1 queues we find the opposite: pooling capacity in one channel performs better than a parallel system with the same total capacity. A generalization is not possible since there are no solutions for other types of parallel queues at hand. In this work, we prove a dual representation of age-of-information in min-plus algebra that connects to queueing models known from the theory of effective bandwidth/capacity and the stochastic network calculus. Exploiting these methods, we derive tail bounds of the age-of-information of parallel G$\mid$G$\mid$1 queues. In addition to parallel classical queues, we investigate Markov channels where, depending on the memory of the channel, we show the true advantage of parallel systems. We continue to investigate this new finding and provide insight into when capacity should be pooled in one channel or when independent parallel channels perform better. We complement our analysis with simulation results and evaluate different update policies, scheduling policies, and the use of heterogeneous channels that is most relevant for latest multi-band networks.

This paper contributes tail bounds of the age-of-information of a general class of parallel systems and explores their potential. Parallel systems arise in relevant cases, such as in multi-band mobile networks, multi-technology wireless access, or multi-path protocols, just to name a few. Typically, control over each communication channel is limited and random service outages and congestion cause buffering that impairs the age-of-information. The parallel use of independent channels promises a remedy, since outages on one channel may be compensated for by another. Surprisingly, for the well-known case of M|M|1 queues we find the opposite: pooling capacity in one channel performs better than a parallel system with the same total capacity. A generalization is not possible since there are no solutions for other types of parallel queues at hand. In this work, we prove a dual representation of age-of-information in min-plus algebra that connects to queueing models known from the theory of effective bandwidth/capacity and the stochastic network calculus. Exploiting these methods, we derive tail bounds of the age-of-information of G|G|1 queues. Tail bounds of the age-of-information of independent parallel queues follow readily. In addition to parallel classical queues, we investigate Markov channels where, depending on the memory of the channel, we show the true advantage of parallel systems. We continue to investigate this new finding and provide insight into when capacity should be pooled in one channel or when independent parallel channels perform better. We complement our analysis with simulation results and evaluate different update policies, scheduling policies, and the use of heterogeneous channels that is most relevant for latest multi-band networks.

Age-of-information is a metric that quantifies the freshness of information obtained by sampling a remote sensor. In signal-agnostic sampling, sensor updates are triggered at certain times without being conditioned on the actual sensor signal. Optimal update policies have been researched and it is accepted that periodic updates achieve smaller age-of-information than random updates. We contribute a study of a signal-aware policy, where updates are triggered by a random sensor event. By definition, this implies random updates and as a consequence inferior age-of-information. Considering a notion of deviation-of-information as a signal-aware metric, our results show, however, that event-triggered systems can perform equally well as time-triggered systems while causing smaller mean network utilization.

Models of parallel processing systems typically assume that one has l workers and jobs are split into an equal number of k=l tasks. Splitting jobs into $k > l$ smaller tasks, i.e. using ``tiny tasks'', can yield performance and stability improvements because it reduces the variance in the amount of work assigned to each worker, but as k increases, the overhead involved in scheduling and managing the tasks begins to overtake the performance benefit. We perform extensive experiments on the effects of task granularity on an Apache Spark cluster, and based on these, developed a four-parameter model for task and job overhead that, in simulation, produces sojourn time distributions that match those of the real system. We also present analytical results which illustrate how using tiny tasks improves the stability region of split-merge systems, and analytical bounds on the sojourn and waiting time distributions of both split-merge and single-queue fork-join systems with tiny tasks. Finally we combine the overhead model with the analytical models to produce an analytical approximation to the sojourn and waiting time distributions of systems with tiny tasks which include overhead. Though no longer strict analytical bounds, these approximations matched the Spark experimental results very well in both the split-merge and fork-join cases.

We consider networked sources that generate update messages with a defined rate and we investigate the age of that information at the receiver. Typical applications are in cyber-physical systems that depend on timely sensor updates. We phrase the age of information in the min-plus algebra of the network calculus. This facilitates a variety of models including wireless channels and schedulers with random cross-traffic, as well as sources with periodic and random updates, respectively. We show how the age of information depends on the network service where, e.g., outages of a wireless channel cause delays. Further, our analytical expressions show two regimes depending on the update rate, where the age of information is either dominated by congestive delays or by idle waiting. We find that the optimal update rate strikes a balance between these two effects.