Bad Luck When Joining the Shortest Queue

A frequent observation in service systems with queues in parallel is that customers in other queues tend to be served faster than those in one’s own queue. This paper quantifies the probability that one’s service would have started earlier if one had joined another queue than the queue that was actually chosen, for exponential multiserver systems with queues in parallel in which customers join one of the shortest queues upon arrival and in which jockeying is not possible.Queueing;Join-the-shortest-queue;Probability of bad luck;Power-series algorithm;Overtaking customers;Dedicated customers

Improved Distributed Algorithms for Exact Shortest Paths

Computing shortest paths is one of the central problems in the theory of distributed computing. For the last few years, substantial progress has been made on the approximate single source shortest paths problem, culminating in an algorithm of Becker et al. [DISC'17] which deterministically computes $(1+o(1))$-approximate shortest paths in $\tilde O(D+\sqrt n)$ time, where $D$ is the hop-diameter of the graph. Up to logarithmic factors, this time complexity is optimal, matching the lower bound of Elkin [STOC'04]. The question of exact shortest paths however saw no algorithmic progress for decades, until the recent breakthrough of Elkin [STOC'17], which established a sublinear-time algorithm for exact single source shortest paths on undirected graphs. Shortly after, Huang et al. [FOCS'17] provided improved algorithms for exact all pairs shortest paths problem on directed graphs. In this paper, we present a new single-source shortest path algorithm with complexity $\tilde O(n^{3/4}D^{1/4})$. For polylogarithmic $D$, this improves on Elkin's $\tilde{O}(n^{5/6})$ bound and gets closer to the $\tilde{\Omega}(n^{1/2})$ lower bound of Elkin [STOC'04]. For larger values of $D$, we present an improved variant of our algorithm which achieves complexity $\tilde{O}\left( n^{3/4+o(1)}+ \min\{ n^{3/4}D^{1/6},n^{6/7}\}+D\right)$, and thus compares favorably with Elkin's bound of $\tilde{O}(n^{5/6} + n^{2/3}D^{1/3} + D )$ in essentially the entire range of parameters. This algorithm provides also a qualitative improvement, because it works for the more challenging case of directed graphs (i.e., graphs where the two directions of an edge can have different weights), constituting the first sublinear-time algorithm for directed graphs. Our algorithm also extends to the case of exact $\kappa$-source shortest paths...Comment: 26 page

Steady-state analysis of shortest expected delay routing

We consider a queueing system consisting of two non-identical exponential servers, where each server has its own dedicated queue and serves the customers in that queue FCFS. Customers arrive according to a Poisson process and join the queue promising the shortest expected delay, which is a natural and near-optimal policy for systems with non-identical servers. This system can be modeled as an inhomogeneous random walk in the quadrant. By stretching the boundaries of the compensation approach we prove that the equilibrium distribution of this random walk can be expressed as a series of product-forms that can be determined recursively. The resulting series expression is directly amenable for numerical calculations and it also provides insight in the asymptotic behavior of the equilibrium probabilities as one of the state coordinates tends to infinity.Comment: 41 pages, 13 figure

Fast emergency paths schema to overcome transient link failures in ospf routing

A reliable network infrastructure must be able to sustain traffic flows, even when a failure occurs and changes the network topology. During the occurrence of a failure, routing protocols, like OSPF, take from hundreds of milliseconds to various seconds in order to converge. During this convergence period, packets might traverse a longer path or even a loop. An even worse transient behaviour is that packets are dropped even though destinations are reachable. In this context, this paper describes a proactive fast rerouting approach, named Fast Emergency Paths Schema (FEP-S), to overcome problems originating from transient link failures in OSPF routing. Extensive experiments were done using several network topologies with different dimensionality degrees. Results show that the recovery paths, obtained by FEPS, are shorter than those from other rerouting approaches and can improve the network reliability by reducing the packet loss rate during the routing protocols convergence caused by a failure.Comment: 18 page

Data Structures for Task-based Priority Scheduling

Many task-parallel applications can benefit from attempting to execute tasks in a specific order, as for instance indicated by priorities associated with the tasks. We present three lock-free data structures for priority scheduling with different trade-offs on scalability and ordering guarantees. First we propose a basic extension to work-stealing that provides good scalability, but cannot provide any guarantees for task-ordering in-between threads. Next, we present a centralized priority data structure based on $k$-fifo queues, which provides strong (but still relaxed with regard to a sequential specification) guarantees. The parameter $k$ allows to dynamically configure the trade-off between scalability and the required ordering guarantee. Third, and finally, we combine both data structures into a hybrid, $k$-priority data structure, which provides scalability similar to the work-stealing based approach for larger $k$, while giving strong ordering guarantees for smaller $k$. We argue for using the hybrid data structure as the best compromise for generic, priority-based task-scheduling. We analyze the behavior and trade-offs of our data structures in the context of a simple parallelization of Dijkstra's single-source shortest path algorithm. Our theoretical analysis and simulations show that both the centralized and the hybrid $k$-priority based data structures can give strong guarantees on the useful work performed by the parallel Dijkstra algorithm. We support our results with experimental evidence on an 80-core Intel Xeon system