We consider the setting of a distributed storage system where a single file is subdivided into smaller fragments of same size which are then replicated with a common replication factor across servers of identical cache size. An incoming file download request is sent to all the servers, and the download is completed whenever the request gathers all the fragments. At each server, we are interested in determining the set of fragments to be stored, and the sequence in which fragments should be accessed, such that the mean file download time for a request is minimized. We model the fragment download time as an exponential random variable independent and identically distributed for all fragments across all servers, and show that the mean file download time can be lower bounded in terms of the expected number of useful servers summed over all distinct fragment downloads. We present deterministic storage schemes that attempt to maximize the number of useful servers. We show that finding the optimal sequence of accessing the fragments is a Markov decision problem, whose complexity grows exponentially with the number of fragments. We propose heuristic algorithms that determine the sequence of access to the fragments which are empirically shown to perform well.

We consider a distributed storage system storing a single file, where the file is divided into equal sized fragments. The fragments are replicated with a common replication factor, and stored across servers with identical storage capacity. An incoming download request for this file is sent to all the servers, and it is considered serviced when all the unique fragments are downloaded. The download time for all fragments across all servers, is modeled as an independent and identically distributed (i.i.d.) random variable. The mean download time can be bounded in terms of the expected number of useful servers available after gathering each fragment. We find the mean number of useful servers after collecting each fragment, for a random storage scheme for replication codes. We show that the performance of the random storage for replication code achieves the upper bound for expected number of useful servers at every download asymptotically in number of servers for any storage capacity. Further, we show that the performance of this storage scheme is comparable to that of Maximum Distance Separable (MDS) coded storage.

Given the unpredictable nature of the nodes in distributed computing systems, some of the tasks can be significantly delayed. Such delayed tasks are called stragglers. Straggler mitigation can be achieved by redundant computation. In maximum distance separable (MDS) redundancy method, a task is divided into$k$subtasks which are encoded to$n$coded subtasks, such that a task is completed if any$k$out of$n$coded subtasks are completed. Two important metrics of interest are task completion time, and server utilization which is the aggregate completed work by all servers in this duration. We consider a proactive straggler mitigation strategy where$n_{0}$out of$n$coded subtasks are started at time 0 while the remaining$n-n_{0}$coded subtasks are launched when$\ell _{0}\le \min \left \{{n_{0},k}\right \}$of the initial ones finish. The coded subtasks are halted when$k$of them finish. For this flexible forking strategy with multiple parameters, we analyze the mean of two performance metrics when the random service completion time at each server is independent and distributed identically (i.i.d.) to a shifted exponential. From this study, we find a tradeoff between the metrics which provides insights into the parameter choices. Experiments on Intel DevCloud illustrate that the shifted exponential distribution adequately captures the random coded subtask completion times, and our derived insights continue to hold.

Straggler mitigation can be achieved by redundant computation. In MDS redundancy method, a task is divided into k sub-tasks which are encoded to n coded sub-tasks, such that a task is completed if any k coded sub-tasks are completed. Two important metrics of interest are task completion time, and server utilization cost which is the aggregate completed work by all servers in this duration. We consider a proactive straggler mitigation strategy where n0out of n coded sub-tasks are started at time 0 while the remaining n - n0coded sub-tasks are launched when ℓ0≤ min(n0, k) of the initial ones finish. The coded sub-tasks are halted when k of them finish. For this flexible forking strategy with multiple parameters, we analyze the mean of two performance metrics for the proposed forking strategy when the random service completion time at each server is independent and distributed identically to a shifted exponential. Our analysis demonstrates that the regime of n00= n), and is thus not a regime of interest. For n0≥ k, we find that there is a tradeoff between the two performance metrics and leads to decrease in mean server utilization cost at the expense of mean service completion time and an efficient choice of the parameters is helpful.

The performance of large-scale distributed compute systems is adversely impacted by stragglers when the execution time of a job is uncertain. To manage stragglers, we consider a multi-fork approach for job scheduling, where additional parallel servers are added at forking instants. In terms of the forking instants and the number of additional servers, we compute the job completion time and the cost of server utilization when the task processing times are assumed to have a shifted exponential distribution. We use this study to provide insights into the scheduling design of the forking instants and the associated number of additional servers to be started. Numerical results demonstrate orders of magnitude improvement in cost in the regime of low completion times as compared to the prior works.

Modern communication and computation systems often consist of large networks of unreliable nodes. Still, it is well known that such systems can provide aggregate reliability via redundancy. While duplication may increase the load on a system, it can lead to significant performance improvement when combined with the judicious management of extra system resources. Prime examples of this abstract paradigm include multi-path routing across communication networks, content access from multiple caches in delivery networks, and master/slave computations on compute clusters. Several recent contributions in the area establish bounds on the performance of redundant systems, characterizing the latency-redundancy tradeoff under specific load profiles. Following a similar line of research, this paper introduces new analytical bounds and approximation techniques for the latency-redundancy tradeoff for a range of system loads and a class of symmetric redundancy schemes, under the assumption of Poisson arrivals, exponential service-rates, and fork-join scheduling policy. The proposed approach can be employed to efficiently approximate the latency distribution of a queueing system at equilibrium. Various metrics can subsequently be derived for this system, including the mean and variance of the sojourn time, and the tail decay rate of the stationary distribution. This paper also establishes the stability region in terms of arrival rates for redundant systems with certain symmetries. Finally, it offers selection guidelines for design parameters to provide latency guarantees based on the proposed approximations. Findings are substantiated by numerical results.